Cooperative Game Theory-Based CAC Strategy for Mobile Communication

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博弈论介绍 Game Theory

2. 生活中的“囚徒困境”例子
例子1 商家价格战例子1
出售同类产品的商家之间本来可以通过共同将价格维持在高位而获利，但实际上却是相互杀价，结果都赚不到钱。当一些商家共谋将价格抬高，消费者实际上不用着急，因为商家联合维持高价的垄断行为一般不会持久，可以等待垄断的自身崩溃，价格就会掉下来。
表2 智猪博弈小猪按按大猪等待 5,1 9, -1 等待 4,4 0,0
这个博弈大猪没有劣战略。但是，小猪有一个劣战略“按”，因为无论大猪作何选择，小猪选择“等待”是比选择“按”更好一些的战略。所以，小猪会剔除“按”，而选择“等待”；大猪知道小猪会选择“等待”，从而自己选择“按”，所以，可以预料博弈的结果是(按,等待）。这称为“ 重复剔除劣战略的占优战略均衡 ”，其中小猪的战略“等待” 占优于战略“按”，而给定小猪剔除了劣战略“按”后，大猪的战略“按”又占优于战略“等待”
表4 有补贴时的博弈空中客车开发开发波音不开发 -10,10 0, 120 不开发 100,0 0,0
这时只有一个纳什均衡，即波音公司不开发和空中客车公司开发的均衡（不开发,开发），这有利于空中客车。在这里，欧共体对空中客车的补贴就是使空中客车一定要开发（无论波音是否开发）的威胁变得可置信的一种“承诺行动”。
类似的例子还有：渤海中的鱼愈来愈少了，工业化中的大气及河流污染，森林植被的破坏等。解决公共资源过度利用的出路是政府制订相应的规制政策加强管理，如我国政府规定海洋捕鱼中，每年有一段时间的“休渔期”，此时禁止捕鱼，让小鱼苗安安静静地生长，大鱼好好地产卵，并对鱼网的网眼大小作出规定，禁用过小网眼的捕网打鱼，保护幼鱼的生存。又如在三峡库区，为了保护库区水体环境，关闭了前些年泛滥成灾的许多小造纸厂等。问题：1、为什么在城市中心道路上禁止汽车鸣喇叭？

博弈论 Game theory (全)

博弈论 Game Theory博弈论亦名“对策论”、“赛局理论”，属应用数学的一个分支, 目前在生物学，经济学，国际关系，计算机科学, 政治学，军事战略和其他很多学科都有广泛的应用。

在《博弈圣经》中写到：博弈论是二人在平等的对局中各自利用对方的策略变换自己的对抗策略，达到取胜的意义。

主要研究公式化了的激励结构间的相互作用。

是研究具有斗争或竞争性质现象的数学理论和方法。

也是运筹学的一个重要学科。

博弈论考虑游戏中的个体的预测行为和实际行为，并研究它们的优化策略。

表面上不同的相互作用可能表现出相似的激励结构（incentive structure），所以他们是同一个游戏的特例。

其中一个有名有趣的应用例子是囚徒困境（Prisoner's dilemma）。

具有竞争或对抗性质的行为称为博弈行为。

在这类行为中，参加斗争或竞争的各方各自具有不同的目标或利益。

为了达到各自的目标和利益，各方必须考虑对手的各种可能的行动方案，并力图选取对自己最为有利或最为合理的方案。

比如日常生活中的下棋，打牌等。

博弈论就是研究博弈行为中斗争各方是否存在着最合理的行为方案，以及如何找到这个合理的行为方案的数学理论和方法。

生物学家使用博弈理论来理解和预测演化（论）的某些结果。

例如，约翰·史密斯（John Maynard Smith）和乔治·普莱斯（George R. Price）在1973年发表于《自然》杂志上的论文中提出的“evolutionarily stable strategy”的这个概念就是使用了博弈理论。

其余可参见演化博弈理论（evolutionary game theory）和行为生态学（behavioral ecology）。

博弈论也应用于数学的其他分支，如概率，统计和线性规划等。

历史博弈论思想古已有之，我国古代的《孙子兵法》就不仅是一部军事著作，而且算是最早的一部博弈论专著。

博弈论最初主要研究象棋、桥牌、赌博中的胜负问题，人们对博弈局势的把握只停留在经验上，没有向理论化发展。

Cooperative Game Theory

Cooperative Game Theory:Characteristic Functions,Allocations,Marginal ContributionAdam BrandenburgerVersion01/04/071IntroductionGame theory is divided into two branches,called the non-cooperative and co-operative branches.The payo¤matrices we have been looking at so far belong to the non-cooperative branch.Now,we are going to look at the cooperative branch.The two branches of game theory di¤er in how they formalize interdepen-dence among the players.In the non-cooperative theory,a game is a detailed model of all the moves available to the players.By contrast,the cooperative theory abstracts away from this level of detail,and describes only the outcomes that result when the players come together in di¤erent combinations.Though standard,the terms non-cooperative and cooperative game theory are perhaps unfortunate.They might suggest that there is no place for cooper-ation in the former and no place for con‡ict,competition etc.in the latter.In fact,neither is the case.One part of the non-cooperative theory(the theory of repeated games)studies the possibility of cooperation in ongoing relationships. And the cooperative theory embodies not just cooperation among players,but also competition in a particularly strong,unfettered form.The non-cooperative theory might be better termed procedural game the-ory,the cooperative theory combinatorial game theory.This would indicate the real distinction between the two branches of the subject,namely that the …rst speci…es various actions that are available to the players while the second describes the outcomes that result when the players come together in di¤erent combinations.This is an important analytical distinction which should become clear as we proceed.The idea behind cooperative game theory has been expressed this way: With the assistance of Amanda Friedenberg.c o o p-01-04-07“Cooperative theory starts with a formalization of games that abstracts away altogether from procedures and...concentrates,instead,on the possibilities for agreement....There are sev-eral reasons that explain why cooperative games came to be treatedseparately.One is that when one does build negotiation and en-forcement procedures explicitly into the model,then the results of anon-cooperative analysis depend very strongly on the precise form ofthe procedures,on the order of making o¤ers and counter-o¤ers andso on.This may be appropriate in voting situations in which preciserules of parliamentary order prevail,where a good strategist can in-deed carry the day.But problems of negotiation are usually moreamorphous;it is di¢cult to pin down just what the procedures are.More fundamentally,there is a feeling that procedures are not re-ally all that relevant;that it is the possibilities for coalition forming,promising and threatening that are decisive,rather than whose turnit is to speak....Detail distracts attention from essentials.Somethings are seen better from a distance;the Roman camps aroundMetzada are indiscernible when one is in them,but easily visiblefrom the top of the mountain.”(Aumann,R.,“Game Theory,”in Eatwell,J.,Milgate,M.,and P.Newman,The New Palgrave,New York,Norton,1989,pp.8-9.)2De…nition of a Cooperative GameA cooperative game consists of two elements:(i)a set of players,and(ii)a characteristic function specifying the value created by di¤erent subsets of the players in the game.Formally,let N=f1;2;:::;n g be the(…nite)set of players, and let i,where i runs from1through n,index the di¤erent members of N. The characteristic function is a function,denoted v,that associates with every subset S of N,a number,denoted v(S).The number v(S)is interpreted as the value created when the members of S come together and interact.In sum,a cooperative game is a pair(N;v),where N is a…nite set and v is a function mapping subsets of N to numbers.Example1As a simple example of a cooperative game,consider the following set-up.There are three players,so N=f1;2;3g.Think of player1as a seller, and players2and3as two potential buyers.Player1has a single unit to sell, at a cost of$4.Each buyer is interested in buying at most one unit.Player 2has a willingness-to-pay of$9for player1’s product,while player3has a willingness-to-pay of$11for player1’s product.The game is depicted in Figure 1below.2$4$11$4$9WtP Cost Cost WtP Figure 1We de…ne the characteristic function v for this game as follows:v (f 1;2g )=$9 $4=$5;v (f 1;3g )=$11 $4=$7;v (f 2;3g )=$0;v (f 1g )=v (f 2g )=v (f 3g )=$0;v (f 1;2;3g )=$7:This de…nition of the function v is pretty intuitive.If players 1and 2come together and transact,their total gain is the di¤erence between the buyer’s willingness-to-pay and the seller’s cost,namely $5.Likewise,if players 1and 3come together,their total gain is the again the di¤erence between willingness-to-pay and cost,which is now $7.Players 2and 3cannot create any value by coming together;each is looking for the seller,not another buyer.Next,no player can create value on his or her own,since no transaction can then take place.Finally,note that v (f 1;2;3g )is set equal to $7,not $5+$7=$12.The reason is that the player 1has only one unit to sell and so,even though there are two buyers in the set f 1;2;3g ,player 1can transact with only one of them.It is a modeling choice–but the natural one–to suppose that in this situation player 1transacts with the buyer with the higher willingness-to-pay,namely player 3.That is the reason for setting v (f 1;2;3g )equal to $7rather than $5.13Marginal ContributionGiven a cooperative game (N;v ),the quantity v (N )speci…es the overall amount of value created.(In the example above,this quantity was v (f 1;2;3g )=$7.)1Formore discussion of this last,somewhat subtle point,see “Value-Based Business Strat-egy,”by Adam Brandenburger and Harborne Stuart,Journal of Economics &Management Strategy ,Spring 1996,Section 7.1(“Unrestricted Bargaining”),pp.18-19.3An important question is then:How is this overall value divided up among the various players?(Referring again to the example above,the question becomes: How does the$7of value get split among the three players?)The intuitive answer is that bargaining among the players in the game de-termines the division of overall value v(N).This bargaining in typically‘many-on-many.’Sellers can try to play one buyer o¤against another,buyers can try to do the same with sellers.Intuitively,a player’s‘power’in this bargaining will depend on the extent to which that player needs other players as compared with the extent to which they need him or her.Brie‡y put,the issue is:Who needs whom more?The analytical challenge is to formalize this intuitive line of reasoning.This is what the concept of marginal contribution does.To de…ne marginal contribution,a piece of notation is needed:Given the set of players N and a particular player i,let N nf i g denote the subset of N consisting of all the players except player i.De…nition1The marginal contribution of player i is v(N) v(N nf i g),to be denoted by MC i.In words,the marginal contribution of a particular player is the amount by which the overall value created would shrink if the player in question were to leave the game.Example1Contd.To practice this de…nition,let us calculate the marginal contributions of the players in the example above:MC1=v(f1;2;3g) v(f2;3g)=$7 $0=$7;MC2=v(f1;2;3g) v(f1;3g)=$7 $7=$0;MC3=v(f1;2;3g) v(f1;2g)=$7 $5=$2:We will return to this example once more below,to use these marginal-contribution numbers to deduce something about the division of the overall value created in this particular game.Before that,we need to state and justify a principle about the division of value in a cooperative game.(Later on,we will examine a stricter principle than this one.)De…nition2Fix a cooperative game(N;v).An allocation is a collection (x1;x2;:::;x n)of numbers.4The interpretation is easy:An allocation is simply a division of the overall value created,and the quantity x i denotes the value received by player i. De…nition3An allocation(x1;x2;:::;x n)is individually rational if x i v(f i g)for all i.De…nition4An allocation(x1;x2;:::;x n)is e¢cient if P n i=1x i=v(N).These two de…nitions are quite intuitive.Individual rationality says that a division of the overall value(i.e.an allocation)must give each player as much value as that player receives without interacting with the other players.E¢-ciency says that all the value that can be created,i.e.the quantity v(N),is in fact created.Unless otherwise noted,all allocations from now on will be assumed to be individually rational and e¢cient.De…nition5An(individually rational and e¢cient)allocation(x1;x2;:::;x n) satis…es the Marginal-Contribution Principle if x i MC i for all i.The argument behind the Marginal-Contribution Principle is simple,almost tautological sounding.First observe that the total value captured by all the players is v(N).It therefore follows from the de…nition of MC i that if some player i were to capture more than MC i,the total value captured by all the players except i would be less than v(N nf i g).But v(N nf i g)is the amount of value that these latter players can create among themselves,without player i. So,they could do better by coming together without player i,creating v(N nf i g) of value,and dividing this up among themselves.The putative division of value in which player i captured more than MC i would not hold up.The Marginal-Contribution Principle,while indeed almost obvious at some level,turns out to o¤er a single,far-reaching method of analyzing the division of value in bargaining situations.The power of the principle should become apparent as we explore some applications.Example1Contd.As a…rst application,return one more time to Exam-ple1above.The overall value created was$7.Let us now use the marginal-contribution calculations above to deduce something about the division of this value among players1,2,and3.Since player2has zero marginal contribution, the Marginal-Contribution Principle implies that player2won’t capture any value.Player3has a marginal contribution of$2,and so can capture no more5than this.This implies that player1will capture a minimum of$7 $2=$5. The remaining$2of value will be split somehow between players1and3.The Marginal-Contribution Principle does not specify how this‘residual’bargaining between the two players will go.This answer is very intuitive.In this game,the buyers(players2and3)are in competition for the single unit that the seller(player1)has on o¤er.The competition is unequal,however,in that player3has a higher willingness-to-pay than player2,and is therefore sure to win.The operative question is:On what terms will player3win?The answer is that player2will be willing to pay up to$9for player1’s product,so player3will have to pay at least that to secure the product.The e¤ect of competition,then,is to ensure that player1receives a price of at least$9(hence captures at least$9 $4=$5of value);player3 pays a price of at least$9(hence captures at most$11 $9=$2of value);and player2captures no value.Will the price at which players1and3transact be exactly$9?Not necessarily.At this point,the game is e¤ectively a bilateral negotiation between players1and3,in which player1won’t accept less than $9and player3won’t pay more than$11.The Marginal-Contribution Principle doesn’t specify how this residual$2of value will be divided.It allows that player3might pay as little as$9,or as much as$11,or any amount in-between.A reasonable answer is that the residual$2will be split evenly,with player1 capturing a total of$5+$1=$6of value,and player3capturing$1of value (but other answers within the permissible range are equally acceptable).We see that the cooperative game-theoretic analysis captures in an exact fashion the e¤ect of competition among the players in a bargaining situation. It makes precise the idea that the division of value should somehow re‡ect who needs whom more.But the analysis is(sensibly)agnostic on where the bar-gaining over residual value–what remains after competition has been accounted for–will end up.After all,where this leads would seem to depend on‘intan-gibles’such as how skilled di¤erent players are at persuasion,blu¢ng,holding out,and so on.These are factors external to the game as described in coopera-tive theory.Thus,an indeterminacy in the theory at this point is a virtue,not a vice.6。

英语第一章阅读 game theory 原文及翻译

都具有相互依赖的共同特征。也就是说，每个参与者的结果取决于所有人的选择（策略）。在所谓的零和游戏中，玩家的利益是完全冲突的博弈论是战略的科学。它试图从数学和逻辑上确定 “玩家”应采取的行动，以确保他们在各种“游戏”中获得最佳成果。所研究的游戏包括从国际象棋到儿童饲养，从网球到收购。但是这些游戏，所以一个人的收益总是另一个人的损失。更典型的是有相互收益（正数）或相互伤害（负数）的博弈，以及一些冲突。
The essence of a game is the interdependence of player strategies. There are two distinct types of strategic interdependence: sequential and simultaneous. In the former the players move in sequence, each aware of the others’ previous actions. In the latter the players act at the same time, each ignorant of the others’ actions.
Game theory was pioneered by Princeton mathematician john von Neumann. In the early years the emphasis was on games of pure conflict (zero-sum games). Other games were considered in a cooperative form. That is, the participants were supposed to choose and implement their actions jointly. Recent research has focused on games that are neither zero sum nor purely cooperative. In these games the players choose their actions separately, but their links to others involve elements of both competition and cooperation.

合作博弈_精品文档

哥本哈根气候峰会博弈
1 发达国家欧、美、日为代表
2 发展中国家中、印、巴西、印尼
3 气候敏感国家和贫穷国家图瓦卢、马尔代夫、斐济等太平洋小岛国；非洲
各国的立场
中国，到2020年单位国内生产总值二氧化碳排放比2005年下降40％－45％
美国将在哥本哈根气候变化大会上承诺 2020年温室气体排放量在2005年基础上减少17％。
Shapley 值是其中重要的解概念之一
Shapley 值
Shapley公理 Shapley 提出了看上去比较合理的几个公理假设
在这些假设下，Shapley 证明了任何合作博弈 (N, v)存在唯一的Shapley值。可作为合作分配的一个解概念。
Shapley 值
参与人集合N的一个置换 (permutation)，是任一函数π：N N，使得对于N中的每个j, N 中恰好存在一个i, 使得π(i) =j（ π是单射，又是满射）
英国：承诺到2020年和2050年分别减排 2005年的34%和80%，
各国立场
欧盟：通过包括气候与能源一揽子计划和各种能效措施，无条件承诺到2020年较1990年减排20%以上。同时承诺抬高减排幅度至30%，前提是各工业化国家同意相当水平的减排力度，同时发展中国家做出重大贡献，共同促成国际条约的签署。
给定上述置换π和任一联盟博弈v, 令πv为满足 π v （{π (i) | i∈S}）=v (S), S为N的任一子集
的联盟博弈。
Shapley 值
Shapley 公理1（对称性）对于合作博弈 (N, v), 在任一参与人的置换映射π(i) 下，分配结果应保持不变，即有
φπ(i) (πv) = φi(v) 公理1表明：一个参与人在博弈中的角

夸美纽斯的游戏理论

夸美纽斯的游戏理论Kuhn's Game Theory is a mathematical approach to studying the interactions between two or more players. It is based on the idea that each player has a set of strategies that they can use to maximize their chances of winning in a given situation. The theory is used to analyze the decisions that players make in a game, and to determine the optimal strategy for each player to maximize their chances of winning. This theory has been applied to a wide variety of games, including poker, chess, and Go. It has also been used to study economic and political interactions.Krashen's Game Theory is a theory of second language acquisition developed by Stephen Krashen, a linguist and educational researcher. The theory posits that language acquisition is a subconscious process that occurs when learners are exposed to comprehensible input. It suggests that learners can acquire language when they are exposed to meaningful input that they can understand, even if they are not actively attempting to learn the language. Krashen's Game Theory proposes that the best way to learn a second language is to play games in the target language. Games provide an enjoyable and engaging way for learners to interact with the language and learn it in a natural way. Games also provide an opportunity for learners to practice using the language in a low-stakes environment. Krashen's Game Theory suggests that playing games in the target language can be an effective way to learn a second language.Kuhn's game theory is a theory that explains how players in a game interact with each other. It is based on the idea that players are motivated by a desire to maximize their own benefit, and that they will make decisions based on their own interests. The theory states that players will make decisions that are in their own best interest, regardless of the consequences for other players. The theory also suggests that players will try to anticipate the moves of their opponents and adjust their strategies accordingly. This theory is used to explain a wide range of phenomena in economics, politics, and other fields.KMUNS's game theory is a theory of strategic interaction between two or more players. It is based on the idea that players choose strategies that maximize their benefits given the strategies chosen by other players. The theory has been applied to a wide range of fields, including economics, politics, and military strategy. KMUNS's game theory is a powerful tool for understanding the behavior of individuals and organizations in situations where the outcomes depend on the decisions of multiple players. It allows us to analyze how different strategies can lead to different outcomes, and how players can use different strategies to achieve their goals.Kleiner-Minsky's game theory is a mathematical approach to understanding how different players interact and make decisions in a game. It is based on the idea that players have different objectives and will make decisions based on their own preferences. The theory is used to analyze the behavior of players in a game, and to predict how they will act in different situations. It canalso be used to develop strategies for players to maximize their chances of winning. Kleiner-Minsky's game theory has been used in a variety of fields, including economics, political science, and artificial intelligence.Kauffman's Game Theory is a theory of evolutionary dynamics that was developed by American biologist and complexity theorist Stuart Kauffman. The theory is based on the idea that complex systems can self-organize and evolve over time in response to their environment. Kauffman's Game Theory is used to explain how complex systems such as ecosystems, social networks, and markets can emerge and evolve without the need for outside intervention. The theory suggests that the emergence of complexity is a result of the interactions between the elements of the system, and that the system is capable of self-organization and adaptation. Kauffman's Game Theory has been used to explain a wide range of phenomena, from the evolution of species to the emergence of new technologies.。

Game Theory Introduction

7

In this course we focus on Non-cooperative games:
◦ These games relate to situations where the players compete with each other and can neither enter into binding agreements (contracts) nor negotiate ◦ Players make decisions independently
8

In this lecture we focus on one-short games
◦ These games relate to situations where the players interact with each other only once
E.g. Two firms make a one-short decision about their prices in a particular market
13
A firm has a dominant strategy when
it has one action that WORKS BEST
(that maximises its payoff) NO MATTER what its rival does.
14
Firm B Advertise
Advertise
• Game theory is used to study how individuals and firms make their decisions when they need to take into account the actions of others. • The theory retains the assumptions of traditional microeconomics (of self interest and maximising behaviour).

Decisions(策略决策)

One that is optimal no matter what an opponent does.
An Example
A & B sell competing products They are deciding whether to undertake
advertising campaigns
The optimal decision of a player without a dominant strategy will depend on what the other player does.
15
Modified Advertising Game
Firm B Don’t
Advertise
5
Gaming and Strategic Decisions
Noncooperative versus Cooperative Games
“The strategy design is based on understanding your opponent’s point of view, and (assuming you opponent is rational) deducing how he or she is likely to respond to your actions”
（威慑、承诺与可信性） Entry Deterrence（进入阻止，进入威慑） Bargaining Strategy（讨价还价策略）
2
Gaming and Strategic Decisions
“If I believe that my competitors are rational and act to maximize their own profits, how should I take their behavior into account when making my own profit-maximizing decisions?”

博弈论

Day 1
Day 2
Day 3
分析
如果是情况（2），2红1黑

那么在第一天，红头发的人会看到1红1黑，他会考虑如果自己头发颜色是黑的，那么为情况（1），他所见的红发人会在第一天黄昏自杀，如果他头发为红，为情况（2），他所见的红发人不会自杀。黑头发人看到2红，那么可排除情况（1），如果他头发为黑，则为情况（2），否则为情况（3）。到了第二天，没有人自杀。那么两个红发人都认定此为情况（2），知道自己头发为红，于第二天晚自杀。黑发人第三天发现这是情况（2），知道自己头发为黑，于当晚自杀。
分析
我们从1个海盗的情况开始讨论。（1）如果只有1个海盗，那么他显然会把 10个金币都分给自己。此时最佳方案为{10}。
分析

（2）如果有2个海盗，那么2号来制定方案。但是他无论怎么制定，1号海盗都投反对票，根据规则2号海盗会被丢入大海，并且金币被1号海盗独享。最佳方案为{死，10}。
2 1
分析

（3）如果有3个海盗，那么3号无论怎么制定方案，2号必同意（因为如果只剩2人了那么2号必死，他保命要紧），而1号必反对（因为如果只剩 2人，他将独享10金币并搞死2号）。所以3号可以给自己分10个，依然能通过。最佳方案为{10， 0，0}。 3 2 1
分析

（4）如果有4个海盗，那么4号除自己需要2票，此时3号必反对提议（因为如果到3海盗情况他将得10金币，就算现在给他 10金币他也反对因为他还想搞死4号），那么此时需要1、2号各一票。如果到3海盗情况，那么1、2号会颗粒无收。若不给他们金币让他们同样颗粒无收，他们将反对（同样都一无所获那为什么不让你死），但若给他们1人1金币，他们就会同意。所以最佳方案为{8，0，1，1}。

控制自动化专业词汇

天线指向控制抗积分饱卷+• ? 非周期分解后验估计？- 近似推理…可扩充性自动化专业英语词汇（A —E ）accelerati on tran sducer力廿速度传感器 … accepta nee testi ng验收测试一 accessibility 可及性 -訐 accumulated error 累积误差繹 AC-DC-AC freque ncy con verter交-直-交变频器 …筄 AC (alternati ng curre nt) electric drive交流电子传动 active attitude stabilizati on主动姿态稳定澡 actuator 驱动器，执行机构… adali ne 线性适应元 “adaptation layer适应层… adaptive telemeter system 适应遥测系统 -adjoint operator伴随算子“ admissible error 容许误差- aggregati on matrix 集结矩阵AHP (an alytic hierarchy process)层次分析法 amplifyi ng eleme nt 放大环节 …an alog-digital con version模数转换- annun ciator 信号器antenna poin ti ng controlan ti-i ntegral win dupaperiodic decompositi ona posteriori estimateapproximate reas oninga priori estimate 先验估计 - articulated robot 关节型机器人assig nment problem 配置问题，分配问题attractor 吸引子 augme ntability augme ntedsystem automaticman ual stati on automaton 自动机 backlash characteristicsbase coord in ate system增广系统…？自动-手动操作器间隙特性RX 基座坐标系…associative memory model associatron 联想机…臔联想记忆模型asymptotic stability atta ined pose drift attitude acquisiti on 渐进稳定性实际位姿漂移姿态捕获？ • AOCS (attritude and orbit con trol system) 姿态轨道控制系统 attitude an gular velocity 姿态角速度 … attitude disturba neeattitude man euver 姿态扰动姿态机动Bayes classifier 贝叶斯分类器bearing alignment 方位对准biological feedback systemblack box testi ng approachbli nd search 盲目搜索 block diago nalizati on Boltzma n mach ine生物反馈系统黑箱测试法bottom-up developme ntbou ndary value an alysisbra in storm ing methodbreadth-first searchbutterfly valve 蝶阀块对角化… 玻耳兹曼机自下而上开发边界值分析头脑风暴法” 广度优先搜索&誡计算机辅助工程& 计算机辅助制造规范化状态变量聚类分析- 粗-精控制蛛网模型- 系数矩阵- 认知科学… 单调关联系统bellows pressure gauge波纹管压力表 •诹 ben efit-cost an alysis收益成本分析 … bili near system 双线性系统？ biocybernetics生物控制论…？CAE (computer aided engin eeri ng)CAM (computer aided man ufacturi ng)Camflex valve 偏心旋转阀 “ canoni cal state variable capacitive displaceme nt tran sducer 电容式位移传感器capsule pressure gauge膜盒压力表 - CARD 计算机辅助研究开发…？ Cartesian robot 直角坐标型机器人 … cascade compe nsati on串联补偿••- catastrophe theory 突变论？•• cen trality 集中性?-cha ined aggregati on 链式集结 … chaos 混沌… characteristic locus 特征轨迹-■chemical propulsi on 化学推进- calrity 清晰性 - classical in formation patter n经典信息模式 - classifier 分类器扟郹 cli nical con trol system 临床控制系统 -closed loop pole 闭环极点 •closed loop tra nsfer fun cti on 闭环传递函数cluster an alysiscoarse-fi ne con trol cobweb modelcoefficie nt matrixcog nitive scie neecog nitro n 认知机cohere nt systemcomb in ati on decisi on 组合决策组合爆炸 comb in atorial explosi on comb ined pressure and vacuum gauge comma nd pose 指令位姿压力真空表 compa nion matrix 相伴矩阵 compartme ntal model 房室模型 compatibility 相容性，兼容性 compe nsat ing n etwork 补偿网络 compe nsati on 补偿，矫正 complia nee 柔顺，顺应composite con trol 组合控制computable gen eral equilibrium model con ditio nally in stability 条件不稳定性组态… 连接机制可计算一般均衡模型 con figurati on conn ecti onism conn ectivity con servative system con siste ncy —致性连接性守恒系统con stra int con diti on con sumpti on fun cti on 约束条件消费函数 con text-free grammar con ti nuous discrete eve nt hybrid system simulation contin uous duty 上下文无关语法连续离散事件混合系统仿真 con trol accuracy con trol cab inet 连续工作制控制精度控制柜 con trollability in dex con trollable canoni cal form [con trol] pla nt 可控指数可控规范型控制对象，被控对象 con troll ing in strume nt 控制仪表 con trol mome nt gyro 控制力矩陀螺 con trol pa nel 控制屏，控制盘control synchro 控制［式］自整角机con trol system syn thesis 控制系统综合控制时程合作对策 con trol time horiz on cooperative game coordinability condition coord ination strategy coord inator 协调器可协调条件协调策略corner freque ncy costate variable 转折频率共态变量 cost-effective ness an alysis coupli ng of orbit and attitudecritical damp ing 临界阻尼 critical stability 临界稳定性费用效益分析轨道和姿态耦合cyli ndrical robot damped oscillati on damper 阻尼器圆柱坐标型机器人阻尼振荡…damp ing ratio data acquisiti on data en crypti on data preprocess ingdata processor 阻尼比数据采集数据加密数据预处理数据处理器cross-over freque ncy 穿越频率，交越频率current source inverter 电流［源］型逆变器cut-off freque ncy 截止频率cybernetics 控制论瀛cyclic remote con trol 循环遥控&櫗'decentralitydece分散随机控制 decisi on support system decompositi on-aggregati on approach decoupli ngparameter 解耦参数决策支持系统分解集结法deductive-inductive hybrid modeling method delayed telemetry 延时遥测 derivati on tree 导岀树演绎与归纳混合建模法 derivative feedback微分反馈describ ing fun cti on扌描述函数desired value 希望值 desp determi nistic automat on deviati on 偏差棛偏差报警器 deviati on alarmDFD 数据流图 diag no 诊断模型diag on ally dominant matrix diaphragm pressure gauge differe neeequation differe ntial pressure level meterdiffere ntial pressure tran smitter 确定性自动机对角主导矩阵膜片压力表差分方程模型微分动力学系统差压液位计差压变送器differe ntial tran sformer displaceme nt transducerdiffere ntiati on eleme nt 微分环节差动变压器式位移传感器 DC gen erator-motor set driveD co ntroller微分控制器直流发电机-电动机组传动digital filer 数字滤波器…digital sig nal process ing 数字信号处理馶digitizati on 数字化鹅逭digitizer 数字化仪湹-dime nsion tra nsducer 尺度传感器direct coord ination 直接协调…disaggregation 解裂<■discoord in ati on 失协调-+•■discrete eve nt dyn amic system 离散事件动态系统…discrete system simulation Ianguage 离散系统仿真语言--discrim inant fun cti on 判别函数…displaceme nt vibrati on amplitude tran sducer 位移振幅传感器效益理论需求弹性电动执行机构 electric con ducta nee levelmeter electric drive con trol gear electric hydraulic con verter electric pn eumatic con verter electrohydraulic servo vale electromag netic flow tra nsducer 电导液位计 “ %电动传动控制设备 “电-液转换器-dissipative structure 耗散结构- distributed parameter control system 分布参数控制系统 distrubanee 扰动- disturba nee compe nsati on 扰动补偿•■? diversity 多样性… divisibility 可分性嗾諐 doma in kno wledge 领域知识 • dominant pole 主导极点 … dose-resp onse model 剂量反应模型 - dual modulati on telemeteri ng system 双重调制遥测系统 dual pri nciple 对偶原理•)• dual spin stabilizati on 双自旋稳定 - duty ratio 负载比-■ dyn amic braking 能耗制动 … dyn amic characteristics 动态特性- dyn amic deviati on 动态偏差- dyn amic error coefficie nt 动态误差系数 ”? dyn amic exact ness 动它吻合性 … dyn amic in put-output model 动态投入产岀模型 econo metric model 计量经济模型-鞨 econo mic cyber netics 经济控制论哤■"- econo mic effective ness 经济效益 … econo mic evaluati on 经济评价■- econo mic in dex 经济指数••- • econo mic in dicator 经济指标- eddy curre nt thick ness meter 电涡流厚度计 effectiveness 有效性恐鮪 effective ness theory elasticity of de ma nd electric actuator electr onic batchi ng scale 电子配料秤 …electr onic belt con veyor scale 电子皮带秤electro nic hopper scale 电子料斗秤 -elevation 仰角-emerge ncy stop 异常停止緼-empirical distributi on 经验分布 …en doge nous variable 内生变量equilibrium growth 均衡增长L〃equilibrium point 平衡点…equivale nee partiti等价类划分oningerg ono mics 工效学error 误差“error-correcti on parsing 纠错剖析estimate 估计量…estimati on theory 估计理论…evaluati on tech ni que 评价技术 ieve nt cha in 事件链evoluti onary system 进化系统…exoge nous variable 外生变量 -expected characteristics 希望特性■-exter nal disturba nee 外扰accelerati on tran sducer 力口速度传感器accepta nee testi ng 验收测试accessibility 可及性accumulated error 累积误差AC-DC-AC frequency converter 交-直-交变频器AC (alternating current) electric drive 交流电子传动active attitude stabilizati on 主动姿态稳定actuator驱动器，执行机构adali ne线性适应元adaptati on layer 适应层adaptive telemeter system 适应遥测系统adjoint operator 伴随算子admissible error 容许误差aggregati on matrix 集结矩阵AHP (analytic hierarchy process) 层次分析法amplifying element 放大环节analog-digital conversion 模数转换annunciator 信号器antenna pointing control 天线指向控制anti-integral windup 抗积分饱卷aperiodic decomposition 非周期分解 a posteriori estimate 后验估计approximate reasoning 近似推理 a priori estimate 先验估计articulated robot 关节型机器人assignment problem 配置问题，分配问题associative memory model 联想记忆模型associatron 联想机asymptotic stability 渐进稳定性attained pose drift 实际位姿漂移attitude acquisition 姿态捕获AOCS (attritude and orbit control system) 姿态轨道控制系统attitude angular velocity 姿态角速度attitude disturbance 姿态扰动attitude maneuver 姿态机动attractor 吸引子augment ability 可扩充性augmented system 增广系统automatic manual station 自动-手动操作器automaton 自动机backlash characteristics 间隙特性base coord in ate system 基座坐标系Bayes classifier 贝叶斯分类器bearing alignment 方位对准bellows pressure gauge 波纹管压力表benefit-cost analysis 收益成本分析bilinear system 双线性系统biocybernetics 生物控制论biological feedback system 生物反馈系统black box testing approach 黑箱测试法blind search 盲目搜索block diagonalization 块对角化Boltzman machine 玻耳兹曼机bottom-up development 自下而上开发boundary value analysis 边界值分析brainstorming method 头脑风暴法breadth-first search 广度优先搜索butterfly valve 蝶阀CAE (computer aided engineering) 计算机辅助工程CAM (computer aided manufacturing) 计算机辅助制造Camflex valve 偏心旋转阀canonical state variable 规范化状态变量capacitive displacement transducer 电容式位移传感器capsule pressure gauge膜盒压力表CARD 计算机辅助研究开发Cartesian robot 直角坐标型机器人cascade compe nsati on 串联补偿catastrophe theory 突变论centrality 集中性chained aggregation 链式集结chaos 混沌characteristic locus 特征轨迹chemical propulsion 化学推进calrity 清晰性classical information pattern 经典信息模式classifier 分类器clinical control system 临床控制系统closed loop pole 闭环极点closed loop transfer function 闭环传递函数cluster analysis 聚类分析coarse-fine control 粗-精控制cobweb model 蛛网模型coefficient matrix 系数矩阵cognitive science 认知科学cognitron 认知机coherent system 单调关联系统combination decision 组合决策combinatorial explosion 组合爆炸comb ined pressure and vacuum gauge压力真空表command pose 指令位姿companion matrix 相伴矩阵compartmental model 房室模型compatibility 相容性，兼容性compensating network 补偿网络compensation 补偿，矫正compliance 柔顺，顺应composite control 组合控制computable general equilibrium model 可计算一般均衡模型conditionally instability 条件不稳定性configuration 组态connectionism 连接机制connectivity 连接性conservative system 守恒系统consistency 一致性constraint condition 约束条件consumption function 消费函数context-free grammar 上下文无关语法continuous discrete event hybrid system simulation 连续离散事件混合系统仿真continuous duty 连续工作制control accuracy 控制精度control cabinet 控制柜controllability index 可控指数controllable canonical form 可控规范型[control] plant 控制对象,被控对象controlling instrument 控制仪表control moment gyro 控制力矩陀螺control panel 控制屏，控制盘control synchro 控制[ 式] 自整角机control system synthesis 控制系统综合control time horizon 控制时程cooperative game 合作对策coordinability condition 可协调条件coordination strategy 协调策略coordinator 协调器corner frequency 转折频率costate variable 共态变量cost-effectiveness analysis 费用效益分析coupling of orbit and attitude 轨道和姿态耦合critical damping 临界阻尼critical stability 临界稳定性cross-over frequency 穿越频率，交越频率current source inverter 电流［源］型逆变器cut-off frequency 截止频率cybernetics 控制论cyclic remote control 循环遥控cylindrical robot 圆柱坐标型机器人damped oscillation 阻尼振荡damper 阻尼器damping ratio 阻尼比data acquisition 数据采集data encryption 数据加密data preprocessing 数据预处理data processor 数据处理器DC generator-motor set drive 直流发电机-电动机组传动D controller 微分控制器decentrality 分散性decentralized stochastic control 分散随机控制decision space 决策空间decision support system 决策支持系统decomposition-aggregation approach 分解集结法decoupling parameter 解耦参数deductive-inductive hybrid modeling method 演绎与归纳混合建模法delayed telemetry 延时遥测derivation tree 导出树derivative feedback 微分反馈describing function 描述函数desired value 希望值despinner 消旋体destination 目的站detector 检出器deterministic automaton 确定性自动机deviation 偏差舱deviation alarm 偏差报警器DFD 数据流图diagnostic model 诊断模型diagonally dominant matrix 对角主导矩阵diaphragm pressure gauge 膜片压力表difference equation model 差分方程模型differential dynamical system 微分动力学系统differential game 微分对策differential pressure level meter 差压液位计differential pressure transmitter 差压变送器differential transformer displacement transducer 差动变压器式位移传感器differentiation element 微分环节digital filer 数字滤波器digital signal processing 数字信号处理digitization 数字化digitizer 数字化仪dimension transducer 尺度传感器direct coordination 直接协调disaggregation 解裂discoordination 失协调discrete event dynamic system 离散事件动态系统discrete system simulation language 离散系统仿真语言discriminant function 判别函数displacement vibration amplitude transducer 位移振幅传感器dissipative structure 耗散结构distributed parameter control system 分布参数控制系统distrubance 扰动disturbance compensation 扰动补偿diversity 多样性divisibility 可分性domain knowledge 领域知识dominant pole 主导极点dose-resp onse mode I剂量反应模型dual modulation telemetering system 双重调制遥测系统duaI principIe 对偶原理duaI spin stabiIization 双自旋稳定duty ratio 负载比dynamic braking 能耗制动dynamic characteristics 动态特性dynamic deviation 动态偏差dynamic error coefficient 动态误差系数dynamic exactness 动它吻合性dynamic input-output modeI 动态投入产出模型econometric modeI 计量经济模型economic cybernetics 经济控制论economic effectiveness 经济效益economic evaIuation 经济评价economic index 经济指数economic indicator 经济指标eddy current thickness meter 电涡流厚度计effectiveness 有效性effectiveness theory 效益理论elasticity of demand 需求弹性electric actuator 电动执行机构electric conductance levelmeter 电导液位计electric drive control gear 电动传动控制设备electric hydraulic converter 电-液转换器electric pneumatic converter 电-气转换器electrohydraulic servo vale 电液伺服阀electromagnetic flow transducer电磁流量传感器electronic batching scale 电子配料秤electronic beltconveyor scale 电子皮带秤electronic hopper scale 电子料斗秤elevation 仰角emergency stop 异常停止empirical distribution 经验分布endogenous variable 内生变量equilibrium growth 均衡增长equilibrium point 平衡点equivalence partitioning 等价类划分ergonomics 工效学error 误差error-correction parsing 纠错剖析estimate 估计量estimation theory 估计理论evaluation technique 评价技术event chain 事件链evolutionary system 进化系统exogenous variable 外生变量expected characteristics 希望特性external disturbance 外扰fact base 事实failure diagnosis 故障诊断fast mode 快变模态feasibility study 可行性研究feasible coordination 可行协调feasible region 可行域feature detection 特征检测feature extraction 特征抽取feedback compensation 反馈补偿feedforward path 前馈通路field bus 现场总线finite automaton 有限自动机FIP (factory information protocol) 工厂信息协议first order predicate logic 一阶谓词逻辑fixed sequence manipulator 固定顺序机械手fixed set point control 定值控制FMS (flexible manufacturing system) 柔性制造系统flow sensor/transducer 流量传感器flow transmitter 流量变送器fluctuation 涨落forced oscillation 强迫振荡formal language theory 形式语言理论formal neuron 形式神经元forward path 正向通路forward reasoning 正向推理fractal 分形体，分维体frequency converter 变频器frequency domain model reduction method 频域模型降阶法frequency response 频域响应full order observer 全阶观测器functional decomposition 功能分解FES (functional electrical stimulation) 功能电刺激functional simularity 功能相似fuzzy logic 模糊逻辑game tree 对策树gate valve 闸阀general equilibrium theory 一般均衡理论gen eralized least squares estimation 广义最小二乘估计generation function 生成函数geomagnetic torque 地磁力矩geometric similarity 几何相似gimbaled wheel 框架轮global asymptotic stability 全局渐进稳定性global optimum 全局最优globe valve 球形阀徢goal coordination method 目标协调法grammatical inference 文法推断graphic search 图搜索gravity gradient torque 重力梯度力矩group technology 成组技术guidance system 制导系统gyro drift rate 陀螺漂移率gyrostat 陀螺体Hall displacement transducer 霍尔式位移传感器hardware-in-the-loop simulation 半实物仿真harmonious deviation 和谐偏差harmonious strategy 和谐策略heuristic inference 启发式推理hidden oscillation 隐蔽振荡hierarchical chart 层次结构图hierarchical planning 递阶规划hierarchical control 递阶控制homeostasis 内稳态homomorphic model 同态系统horizontal decomposition 横向分解hormonal control 内分泌控制hydraulic step motor 液压步进马达hypercycle theory 超循环理论I controller 积分控制器identifiability 可辨识性IDSS (intelligent decision support system) 智能决策支持系统image recognition 图像识别impulse 冲量impulse function 冲击函数，脉冲函数inching 点动incompatibility principle 不相容原理incremental motion control 增量运动控制index of merit 品质因数inductive force transducer 电感式位移传感器inductive modeling method 归纳建模法industrial automation 工业自动化inertial attitude sensor 惯性姿态敏感器inertial coordinate system 惯性坐标系inertial wheel 惯性轮inference engine 推理机infinite dimensional system 无穷维系统information acquisition 信息采集infrared gas analyzer 红外线气体分析器inherent nonlinearity 固有非线性inherent regulation 固有调节initial deviation 初始偏差initiator 发起站injection attitude 入轨姿势input-output model 投入产出模型instability 不稳定性instruction level language 指令级语言integral of absolute value of error criterion 绝对误差积分准则integral of squared error criterion 平方误差积分准则integral performance criterion 积分性能准则integration instrument 积算仪器integrity 整体性intelligent terminal 智能终端interacted system 互联系统，关联系统interactive prediction approach 互联预估法，关联预估法interconnection 互联intermittent duty 断续工作制internal disturbance 内扰ISM (interpretive structure modeling) 解释结构建模法invariant embedding principle 不变嵌入原理inventory theory 库伦论inverse Nyquist diagram 逆奈奎斯特图inverter 逆变器investment decision 投资决策isomorphic model 同构模型iterative coordination 迭代协调jet propulsion 喷气推进job-lot control 分批控制joint 关节Kalman-Bucy filer 卡尔曼-布西滤波器knowledge accomodation 知识顺应knowledge acquisition 知识获取knowledge assimilation 知识同化KBMS (knowledge base management system) 知识库管理系统瓢knowledge representation 知识表达ladder diagram 梯形图lag-lead compensation 滞后超前补偿Lagrange duality 拉格朗日对偶性Laplace transform 拉普拉斯变换large scale system 大系统lateral inhibition network 侧抑制网络least cost input 最小成本投入least squares criterion 最小二乘准则level switch 物位开关libration damping 天平动阻尼limit cycle 极限环linearization technique 线性化方法linear motion electric drive 直线运动电气传动linear motion valve 直行程阀linear programming 线性规划LQR (linear quadratic regulator problem) 线性二次调节器问题load cell 称重传感器local asymptotic stability 局部渐近稳定性local optimum 局部最优log magnitude-phase diagram 对数幅相图long term memory 长期记忆lumped parameter model 集总参数模型Lyapunov theorem of asymptotic stability 李雅普诺夫渐近稳定性定理macro-economic system 宏观经济系统magnetic dumping 磁卸载magnetoelastic weighing cell 磁致弹性称重传感器magnitude-frequency characteristic 幅频特性magnitude margin 幅值裕度magnitude scale factor 幅值比例尺manipulator 机械手man-machine coordination 人机协调manual station 手动操作器MAP (manufacturing automation protocol) 制造自动化协议marginal effectiveness 边际效益Mason''s gain formula 梅森增益公式master station 主站matching criterion 匹配准则maximum likelihood estimation 最大似然估计maximum overshoot 最大超调量maximum principle 极大值原理mean-square error criterion 均方误差准则mechanism model 机理模型meta-knowledge 元知识metallurgical automation 冶金自动化minimal realization 最小实现minimum phase system 最小相位系统minimum variance estimation 最小方差估计minor loop 副回路missile-target relative movement simulator 弹体- 目标相对运动仿真器modal aggregation 模态集结modal transformation 模态变换MB (model base) 模型库model confidence 模型置信度model fidelity 模型逼真度model reference adaptive control system 模型参考适应控制系统model verification 模型验证modularization 模块化MEC (most economic control) 最经济控制motion space 可动空间MTBF (mean time between failures) 平均故障间隔时间MTTF (mean time to failures) 平均无故障时间multi-attributive utility function 多属性效用函数multicriteria 多重判据multilevel hierarchical structure 多级递阶结构multiloop control 多回路控制multi-objective decision 多目标决策multistate logic 多态逻辑multistratum hierarchical control 多段递阶控制multivariable control system 多变量控制系统myoelectric control 肌电控制Nash optimality 纳什最优性natural language generation 自然语言生成nearest-neighbor 最近邻necessity measure 必然性侧度negative feedback 负反馈neural assembly 神经集合neural network computer 神经网络计算机Nichols chart 尼科尔斯图noetic science 思维科学noncoherent system 非单调关联系统noncooperative game 非合作博弈nonequilibrium state 非平衡态nonlinear element 非线性环节nonmonotonic logic 非单调逻辑nonparametric training 非参数训练nonreversible electric drive 不可逆电气传动nonsingular perturbation 非奇异摄动non-stationary random process 非平稳随机过程nuclear radiation levelmeter 核辐射物位计nutation sensor 章动敏感器Nyquist stability criterion 奈奎斯特稳定判据objective function 目标函数observability index 可观测指数observable canonical form 可观测规范型on-line assistance 在线帮助on-off control 通断控制open loop pole 开环极点operational research model 运筹学模型optic fiber tachometer 光纤式转速表optimal trajectory 最优轨迹optimization technique 最优化技术orbital rendezvous 轨道交会orbit gyrocompass 轨道陀螺罗盘orbit perturbation 轨道摄动order parameter 序参数orientation control 定向控制originator 始发站oscillating period 振荡周期output prediction method 输出预估法oval wheel flowmeter 椭圆齿轮流量计overall design 总体设计overdamping 过阻尼overlapping decomposition 交叠分解Pade approximation 帕德近似Pareto optimality 帕雷托最优性passive attitude stabilization 被动姿态稳定path repeatability 路径可重复性pattern primitive 模式基元PR (pattern recognition) 模式识别P control 比例控制器peak time 峰值时间penalty function method 罚函数法perceptron 感知器periodic duty 周期工作制perturbation theory 摄动理论pessimistic value 悲观值phase locus 相轨迹phase trajectory 相轨迹phase lead 相位超前photoelectric tachometric transducer 光电式转速传感器phrase-structure grammar 短句结构文法physical symbol system 物理符号系统piezoelectric force transducer 压电式力传感器playback robot 示教再现式机器人PLC (programmable logic controller) 可编程序逻辑控制器plug braking 反接制动plug valve 旋塞阀pneumatic actuator 气动执行机构point-to-point control 点位控制polar robot 极坐标型机器人pole assignment 极点配置pole-zero cancellation 零极点相消polynomial input 多项式输入portfolio theory 投资搭配理论pose overshoot 位姿过调量position measuring instrument 位置测量仪posentiometric displacement transducer 电位器式位移传感器positive feedback 正反馈power system automation 电力系统自动化predicate logic 谓词逻辑pressure gauge with electric contact 电接点压力表pressure transmitter 压力变送器price coordination 价格协调primal coordination 主协调primary frequency zone 主频区PCA (principal component analysis) 主成分分析法principle of turnpike大道原理priority 优先级process-oriented simulation 面向过程的仿真productionbudget 生产预算production rule 产生式规则profit forecast 利润预测PERT (program evaluation and review technique) 计划评审技术program set station 程序设定操作器proportional control 比例控制proportional plus derivative controller 比例微分控制器protocol engineering 协议工程prototype 原型pseudo random seque nee伪随机序歹U pseudo-rate-increment control 伪速率增量控制pulse duration 脉冲持续时间pulse frequeney modulation eontrol system 脉冲调频控制系统pulsewidth modulation eontrol system 脉冲调宽控制系统PWM inverter 脉宽调制逆变器pushdown automaton 下推自动机QC (quality control) 质量管理quadratic performance index 二次型性能指标qualitative physical model 定性物理模型quantized noise 量化噪声quasilinear characteristics 准线性特性queuing theory 排队论radio frequency sensor 射频敏感器ramp function 斜坡函数random disturbance 随机扰动random process 随机过程rate integrating gyro 速率积分陀螺ratio station 比值操作器reachability 可达性reaction wheel control 反作用轮控制realizability 可实现性,能实现性real time telemetry 实时遥测receptive field 感受野rectangular robot 直角坐标型机器人rectifier 整流器recursive estimation 递推估计reduced order observer 降阶观测器redundant information 冗余信息reentry control 再入控制regenerative braking 回馈制动，再生制动regional planning model 区域规划模型regulating device 调节装载regulation 调节relational algebra 关系代数relay characteristic 继电器特性remote manipulator 遥控操作器remote regulating 遥调remote set point adjuster 远程设定点调整器rendezvous and docking 交会和对接reproducibility 再现性resista nee thermometer sen sor热电阻resolution principle 归结原理resouree alloeation 资源分配response eurve 响应曲线returndifferenee matrix 回差矩阵return ratio matrix 回比矩阵reverberation 回响reversible eleetrie drive 可逆电气传动revolute robot 关节型机器人revolution speed transducer 转速传感器rewriting rule 重写规则rigid spacecraft dynamics 刚性航天动力学risk decision 风险分析robotics 机器人学robot programming language 机器人编程语言robust control 鲁棒控制robustness 鲁棒性roll gap measuring instrument 辊缝测量仪root locus 根轨迹roots flowmeter 腰轮流量计rotameter 浮子流量计，转子流量计rotary eccentric plug valve 偏心旋转阀rotary motion valve 角行程阀rotating transformer 旋转变压器Routh approximation method 劳思近似判据routing problem 路径问题sampled-data control system 采样控制系统sampling control system 采样控制系统saturation characteristics 饱和特性scalar Lyapunov function 标量李雅普诺夫函数SCARA (selective compliance assembly robot arm) 平面关节型机器人scenario analysis method 情景分析法scene analysis 物景分析s-domain s 域self-operated controller 自力式控制器self-organizingsystem 自组织系统self-reproducing system 自繁殖系统self-tuningcontrol 自校正控制semantic network 语义网络semi-physicalsimulation 半实物仿真sensing element 敏感元件sensitivity analysis 灵敏度分析sensory control 感觉控制sequential decomposition 顺序分解seque ntial least squares estimation序贯最小二乘估计servo control 伺服控制，随动控制servomotor 伺服马达settling time 过渡时间sextant 六分仪short term planning 短期计划short time horizon coordination 短时程协调signal detection and estimation 信号检测和估计signal reconstruction 信号重构similarity 相似性simulated interrupt 仿真中断simulation block diagram 仿真框图simulation experiment 仿真实验simulation velocity 仿真速度simulator 仿真器single axle table 单轴转台single degree of freedom gyro 单自由度陀螺single level process 单级过程single value nonlinearity 单值非线性singular attractor 奇异吸引子singular perturbation 奇异摄动sink 汇点slaved system 受役系统slower-than-real-time simulation 欠实时仿真slow subsystem 慢变子系统socio-cybernetics 社会控制论socioeconomic system 社会经济系统software psychology 软件心理学solar array pointing control 太阳帆板指向控制solenoid valve 电磁阀source 源点specific impulse 比冲speed control system 调速系统spin axis 自旋轴spinner 自旋体stability criterion 稳定性判据stability limit 稳定极限stabilization 镇定，稳定Stackelberg decision theory 施塔克尔贝格决策理论state equation model 状态方程模型state space description 状态空间描述static characteristics curve 静态特性曲线station accuracy 定点精度stationary random process 平稳随机过程statistical analysis 统计分析statistic pattern recognition 统计模式识别steady state deviation 稳态偏差steady state error coefficient 稳态误差系数step-by-step control 步进控制step function 阶跃函数stepwise refinement 逐步精化stochastic finite automaton 随机有限自动机strain gauge load cell 应变式称重传感器strategic function 策略函数strongly coupled system 强耦合系统subjective probability 主观频率suboptimality 次优性supervised training 监督学习supervisory computer control system 计算机监控系统sustained oscillation 自持振荡swirlmeter 旋进流量计switching point 切换点symbolic processing 符号处理synaptic plasticity 突触可塑性synergetics 协同学syntactic analysis 句法分析system assessme n係统评价systematology 系统学system homomorphism 係统同态system isomorphism 係统同构system engineering 係统工程tachometer 转速表target flow transmitter 靶式流量变送器task cycle 作业周期teaching programming 示教编程telemechanics 远动学telemetering system of frequency division type 频分遥测系统telemetry 遥测teleological system 目的系统teleology 目的论temperature transducer 温度传感器template base 模版库tensiometer 张力计texture 纹理theorem proving 定理证明therapy model 治疗模型thermocouple 热电偶thermometer 温度计thickness meter 厚度计three-axis attitude stabilization 三轴姿态稳定three state controller 三位控制器thrust vector control system 推力矢量控制系统thruster 推力器time constant 时间常数time-invariant system 定常系统，非时变系统time schedule controller 时序控制器time-sharing control 分时控制time-varying parameter 时变参数top-down testing 自上而下测试topological structure 拓扑结构TQC (total quality control) 全面质量管理tracking error 跟踪误差trade-off analysis 权衡分析transfer function matrix 传递函数矩阵transformation grammar 转换文法transient deviation 瞬态偏差transient process 过渡过程transition diagram 转移图tran smissible pressure gauge 电远传压力表transmitter 变送器trend analysis 趋势分析triple modulation telemetering system 三重调制遥测系统turbine flowmeter 涡轮流量计Turing machine 图灵机two-time scale system 双时标系统ultrasonic levelmeter 超声物位计unadjustable speed electric drive 非调速电气传动unbiased estimation 无偏估计underdamping 欠阻尼uniformly asymptotic stability 一致渐近稳定性uninterrupted duty 不间断工作制，长期工作制unit circle 单位圆unit testing 单元测试unsupervised learing 非监督学习upper level problem 上级问题urban planning 城市规划utility function 效用函数value engineering 价值工程variable gain 可变增益，可变放大系数variable structure control system 变结构控制vector Lyapunov function 向量李雅普诺夫函数velocity error coefficient 速度误差系数velocity transducer 速度传感器vertical decomposition 纵向分解vibrating wire force transducer 振弦式力传感器vibrometer 振动计viscous damping 粘性阻尼voltage source inverter 电压源型逆变器vortex precession flowmeter 旋进流量计vortex shedding flowmeter 涡街流量计WB (way base) 方法库weighing cell 称重传感器weighting factor 权因子weighting method 加权法Whittaker-Shannon sampling theorem 惠特克-香农采样定理Wiener filtering 维纳滤波work station for computer aided design 计算机辅助设计工作站w-plane w 平面zero-based budget 零基预算zero-input response 零输入响应zero-state resp onse 零状态响应zero sum game model 零和对策模型z-transform z 变换。

GAME THEORY

其次，剔除新博弈中某个参与人的严格劣策略；重复上述过程，直到只剩下唯一的策略组合。我们认为这个唯一所剩的策略组合是稳定的。
1.2.2 重复剔除的占优均衡
Definition：In a normal-form game, if for each player i , si" is i‟s dominant strategy, than we call the strategies profile (s1″, …, sn" ) the „dominantstrategy equilibrium‟.
1.2.1占优战略均衡
定义2：一个博弈G,若对博弈方i及所用s-i都有 ui (si*,s-i) > ui (si ‟,s-i)，则称si*是si ‟的严格上策， si ‟是si*的严格下策。定义3：若在博弈G中对每个博弈方i都存在策略si*是其它所有策略的严格上策,则称策略组合s*=(s1*,s2*, … ,sn*)是G的上策均衡。
In the normal-form representation of a game ,each
player simultaneously chooses a strategy, and the combination of strategies chosen by the players determines a payoff for each player. Definition: The normal-form representation of an-n-player game specifies the players‟ strategy spaces S1 , … , Sn and their payoff functions u1 ,…, un. We denote this game

指南中关于合作游戏的阐述

指南中关于合作游戏的阐述英文回答：Cooperative games, also known as co-op games, are a type of game where players work together towards a common goal. Unlike competitive games where players compete against each other, cooperative games encourage collaboration and teamwork. In these games, players must communicate, strategize, and coordinate their actions in order to succeed.One of the key elements of cooperative games is the shared objective. All players have a common goal that they must work towards achieving. This can be anything from solving a puzzle, completing a mission, or surviving against a common enemy. The shared objective creates a sense of unity among the players and fosters a cooperative mindset.Communication is crucial in cooperative games. Playersmust constantly communicate with each other to share information, coordinate their actions, and plan strategies. Effective communication can greatly enhance the team's chances of success. It allows players to share their ideas, discuss different approaches, and make informed decisions together.Another important aspect of cooperative games is the distribution of roles and responsibilities. Each player may have a unique role or set of abilities that contribute to the team's overall success. For example, one player may be responsible for healing, while another player focuses on dealing damage. By assigning specific roles, players can maximize their efficiency and complement each other's strengths and weaknesses.Cooperative games also often incorporate elements of challenge and difficulty. The game may present obstacles or enemies that require the collective effort of the team to overcome. This can create a sense of excitement and accomplishment when the team successfully overcomes these challenges together.Cooperative games can be enjoyed by players of allskill levels and ages. They provide a platform for players to work together, build relationships, and develop problem-solving and communication skills. These games can also be a great way to foster teamwork and cooperation in various settings, such as classrooms, workplaces, or family gatherings.中文回答：合作游戏，也被称为合作性游戏，是一种玩家共同合作达到共同目标的游戏类型。

博弈论-Game Theory

game models to describepracticalproblems, use game thinking to analyse and deal with practical problems.
4.Understand the application of game theory in economics, management, computer science and other disciplines through group cooperation and topical discussion.
5.Apply the theory in the course to solve a variety of problems at an appropriate level of difficulty.
6.Demonstrate skills in communicating mathematics.
Pre-requisites
Advanced Algebra, Mathematical Analysis, Probability Theory, Operations Research
Intended Learning Outcomes
On successful completion of this course, students will be able to:
Syllabus ofMathematics and Applied Mathematicsat Haide College
Introduction to Game Theory
Description
Game theory is a theory that studies the decision-maker's strategic choice and related equilibrium problems under the conditions of competition or conflict factors and mutual dependence of interests. It has extensive and profound applications in economics, management, political science, computer science, military strategy and many other disciplines. This course mainly introduces the mathematical models, equilibrium theory and applications of game theory. The content includes: the basic concept of game theory, static and dynamic game theory (complete information static game, incomplete information static game, complete information dynamic game, incomplete information dynamic game), cooperative game theory, etc. Through the study of this course, students can understand the background, establishment and analysis of various game models, master the basic theories and methods of game theory, think and explore with the ideological methods of game theory, and improve the ability to analyze practical problems by establishing corresponding mathematical models and solving them.

合作博弈论 Cooperative Game Theory

Cooperative Game TheoryR.Chandrasekaran,Most of this follows Owen and Shubik and Wooldridge et al.When we extend two person game theory to consider n person games for n≥3,there is little diﬀerence from non-cooperative game theory point of view.Existence of Nash equilibrium follows from similar arguments and all the diﬃculties we had with two person nonzero sum games show up here as well.But there is a new phenomenon here that must be taken into account:—that of coalition formation.Subsets of players could form a"cartel"and act in unison to gain more than they could if they acted independently.This forms one essential aspect of the game here.And this requires having binding contracts,using correlated mixed strategies,and transferable utility(so that the gain could be shared between the colluders in some way that all agree to). The main study here is to model the coalition formation,and gain sharing process.So we abstract away details and concentrate on important parts of the game.Game Representation:Characteristic Function Forms Let N= {1,2,...,n}be the set of players.Any nonempty subset S of N is called a coalition.Deﬁnition1By a characteristic function of an n-person game we mean a function v that assigns a value to each subset of players;i.e v:2N→R. We think of v(S)as the payoﬀto the subset S of N if it acts in unison;some times it is also assumed that this is maximin payoﬀin that we also think all of N−S act in unison(against S).v(S)is called the value of the coalition S.When we go from games in extensive forms to normal forms,we abstract some details and only look at strategies to obtain a(mixed)equilibrium(for which we do not need the details that have been abstracted away).Similarly,1in n person cooperative games where the study focuses on stable coalition formations,we abstract away even further and look only at the characteristic function form.It is implicitly assumed that a coalition S can distribute its value v(S)to its members in any way they choose.Hence these are also called transferable utility games(TU games for short).How the distribution takes place is the main interest in these games.It is generally assume that v({φ})=0;v(S)≥0∀S⊆N.Outcomes/Solutions An outcome of a game in characteristic form con-sists of:(i)A partition of N into coalitions,called a coalition structure,and(ii)a payoﬀvector,whic distributes the value of each coalition to its members.A coalition structure CS over N is a nonempty collection of nonempty subsets CS={S1,S2,...,S k}satisfying the relations:∪k i=1S i=N;S i∩S j=φif i=jThe set of all coalition structures for a given set N of players is denoted by CS N.v(CS)denotes the sum k j=1v(S j).A vector x=(x1,x2,...,x n)is payoﬀvector for a coalition structure CS={S1,S2,...,S k},over N={1,2,...,n}ifx i≥0∀i∈Nx i≤v(S j)1≤j≤ki∈S jAn outcome is a apir[CS,x].x(S)= i∈S x i is called the payoﬀfor the coalition S under x.x is said to be eﬃcient in the outcome[CS,x]ifx i=v(S j)1≤j≤ki∈S jA payoﬀvector x for a coalition structure CS N is called an imputation if it is eﬃcent and individually rational.x i≥v({i})∀i∈Nx i=v(S j)1≤j≤ki∈S j2The set of all imputations for a coalition structure CS∈CS N is denoted by E(CS).If CS={N},then this is denoted by E(N)or E(v).If a payoﬀvector is an imputation,then each player prefers this to being alone.Howver, a group of players may want to deviate since it might be better for them and this would result in unstable conditions.Subclasses of games in characteristic form:Monotone Games:A game[N,v]in characteristic form is monotone if[S⊆T]⇒v(S)≤v(T)Most games are montone;nonmonotonicuty may arise because some players intesely dislike each other or becuase of the overhead charges for communi-cation increase nonlinearly with size of the coaltion.Superadditive Games:A game[N,v]in characteristic form is said to be superadditive if[S∩T=φ]⇒v(S∪T)≥v(S)+v(T)It comes from the fact that S can assure itself v(S)without help from any one and so also T can assure itself v(T),then S∪T can assure itself the sum.Since we have assumed that characteristic function is nonnengative,it follows that superadditivity implies monotonicity.Most games are superadditive;indeed older books did not consider any others.Non-superadditive games arise from anit-trust or anti-monopoly regualtions.In superadditive games,there is no compelling reason for players to form any coalition structure except CS={N}called the"grand"coalition.Hence the outcome for such a game is of the form[N,x]wherex i=v(N)A non-superaddtive game cna be transformed into a superadditive game by the following process:Let T⊆N be any coalition.Let CS T denote all coalition structures over T.Given a game[N,v]we deﬁne a new game [N∗,v∗]byv∗(T)=maxv(CS)CS∈CS T3G∗is called the superadditive cover of the game G.v∗(T)is the maximum that the players in set T cna achive by forming their own coalition structure in G.Convex(Supermodualr)Games:A game is said to be convex or supermodular ifv(S∪T)+v(s∩T)≥v(S0+v(T)∀S,T⊆NTheorem2A game G=[N,v]is convex iﬀ[T⊂S;i/∈S]⇒[v(S∪{i})−v(S)≥v(T∪{i})−v(T)]A convex game is superadditive.Deﬁnition3A game v in characteristic function form is called a constant sum game ifv(S)+v(N−S)=v(N)∀S⊆NIt is clear from the super-additivity condition that the maximum the entire set of players can get is v(N).Now we look into the questions of how to divide this total—it what does each player get—in a stable situation.Let (x1,x2,...,x n)denote the payoﬀto the players.Clearly no player will accept less than what he can get for himself with no help from others.Hence one condition that this vector must satisfy(called individual rationality)isx i≥v({i})∀iThe second condition that is normally imposed(known as pareto-optimality) is to requireni=1x i=v(N)Any vector that satisﬁes these two conditions is called an imputation.The main question now is which of these in the setE(v)={x:x i≥v({i});1≤i≤n;ni=1x i=v(N)}should the predicted outcome of this game be?The answer is easy in one case(this is the most uninteresting case!)4Deﬁnition4A game is said to be inessential if v(N)= n i=1v({i}). By superadditivity,we have v(N)≥ n i=1v({i}).If equality holds,E(v) contains only one point—x i=v({i})∀iHence this the outcome of such games.From now on,we are interested only in essential games where v(N)> n i=1v({i}).Deﬁnition5Let x,y∈E(v).We say that x dominates y via the coalition S[denoted by x≻S y]ifx i>y i∀i∈Sx i≤v(S)i∈SEach player in S gets more under x than in y and the coalition S has enough to give its members the amount speciﬁed in x.Deﬁnition6We say x dominates y if the above is true for some S.If x dominates y then y is not stable.Games with same domination structure are in some sense equivalent and we make this precise by:Deﬁnition7Two n-person games u and v are said to be isomorphic if there is a function f:E(u)→E(v)such that[x,y∈E(u);x≻S y]⇔[f(x)≻S f(y)]We are preserving the domination structure.Deﬁnition8Two n−person games u and v are S−equivalent if there exists numbers(a1,a2,...,a n)andβ>0such thatv(S)=βu(S)+ i∈S a i∀S⊆NTheorem9If u and v are S-equivalent,then they are isomorphic.The converse is true for all constant sum games.5e the function f(x)=βx+a.Since S-equivalence is indeed an equivalence relations,it is suﬃcient to study one member of each of its equivalence classes.Such representatives are called normalized games.Deﬁnition10An essential(characteristic function)game is said to be(0,1)-normalized ifv({i)}=0∀iv(N)=1Lemma11A game is S−equivalent to exactly one game in(0,1)normalized form.Another normalization used in the literature is the(−1,0)normalization wherev({i})=−1∀iv(N)=0We use the(0,1)normalization.Thus,the set of all(0,1)normalized games consist of v∈2N that satisfyv(φ)=0v({i})=0∀iv(N)=1[S∩T=φ]⇒v(S∪T)≥v(S)+v(T)If the game is also a constant sum game it satisﬁes the relationv(S)+v(N−S)=v(N)Any(n−1)−person game u in(0,1)normalization can be converted to an equivalent n-person constant sum game v in(0,1)normalization as follows:v(S)=u(S)1−u(N−S)if n/∈Sif n∈SHere N={1,2,...,n}.6Deﬁnition12A game v is symmetric if v(S)depends only on|S|.Deﬁnition13A game v in(0,1)normalization is called a simple game ifv(S)∈{0,1}∀SCoalitions S with v(S)=1are called winning coalitions and those with v(S)=0are called losing coalitions.Deﬁnition14Let(p1,p2,..,p n)be a nonnegative vector and let q satisfy therelation0<q<n i=1p iThe weighted majority game(q;p1,p2,...,p n)is deﬁned as a simple game v in(0,1)normalization wherev(S)=1if i∈S p i≥qelseDeﬁnition15The set of undominated imputations C(v)of a game v is called the core of a game.Theorem16C(v)is the set of n-vectors x satisfying the relations;i∈Sx i≥v(S)∀S⊆Nni=1x i=v(N)Proof.Clearly,theﬁrst condition implies the result thatx i≥v({i})∀iHence any vector that satisﬁes both relations above is an imputation.Suppose x satisﬁes both relations.Let y be an n-vector satisfying the relationy i>x i∀i∈S7for some S⊆N.Theni∈Sy i> i∈S x i≥v(S)Hence there is no vector y that dominates x.Hence vectors that satisfy both relations are undominated.Conversely,suppose we have an n-vector y that does not satisfy both re-lations.Ifni=1y i=v(N)then y is not an imputation and hence not in the core.Supposeni=1y i=v(N)i∈Sy i=v(S)−ǫfor someǫ>0and some nonempty set S⊂N.By superadditivity it follows thatα=v(N)−v(S)− i∈N−S v({i})≥0Let|S|=s;[note that0<s<n].Consider an n-vector z deﬁned as follows:z i=y i+ǫv({i})+αn−sIt is easy to verify that z is an imputation and that z≻S y and hence y can not be in the core.This result shows that the core is a closed convex polyhedral set. Example1Player1(seller)has a horse which is of no value to him.There are two buyers#2,#3who want to buy the horse.#2has a value of$90 and#3has value of100for the horse.The characteristic function form for this game isv({i})=0∀iv({2,3})=0v({1,2})=90v({1,3})=v({1,2,3})=1008Hence the core consists of vectors x satisfying the relations:x1+x2≥90x1+x3≥100x1+x2+x3=100x i≥0∀iThe core for this game is given byC(v)={(t,0,100−t):90≤t≤100} Exercise17What is the non-cooperative solution to this game?9。

博弈论用英文怎么说如何拼写

博弈论用英文怎么说如何拼写博弈论主要研究公式化了的激励结构间的相互作用，是研究具有斗争或竞争性质现象的数学理论和方法。

那么你知道博弈论的英文怎么说吗?下面店铺为大家带来博弈论的英文说法，供大家参考学习。

博弈论的英文说法：game theory英 [ɡeim ˈθiəri]美 [ɡem ˈθiəri]博弈论相关英文表达：博弈论算法 Algorithmic Game Theory合作博弈论 Cooperative Games Theory经济博弈论 Economic Game Theory重复博弈论 repeated game approach博弈论英文说法例句：1. Game theory is a powerful weapon to decision - making of multi - person.博弈论是解决多人竞争决策问题的有利武器.2. Game theory is an equilibrium problem in decision influence.博弈论是在选择中的决策影响和均衡问题.3. Conflict and cooperation are the two fundamental issues in game theory.冲突与合作是博弈论研究的两大基本问题.4. The main research way is the analytical method of Game Theory.研究方法主要是博弈论中的博弈分析方法.5. Game theory; High - tech SMEs; principal - agent; performance management; incentive mechanism.博弈论; 高新技术中小企业; 委托—代理; 绩效管理; 激励机制.6. Textbook farce and textbook game theory – how delightful!经典的闹剧,经典的博弈论——多有趣啊 !7. Contract Theory, Information Economics, Applied Game Theory, Corporate Finance.契约理论, 信息经济学, 应用博弈论, 公司财务,政治经济学.8. This story illustrates an important distinction between ordinary decision theory and theory.这个故事说明了普通决策理论和博弈论之间的一个重要的区别.9. The backward induction is an important reasoning method in game theory.逆向归纳法(倒推法)是博弈论中的一种重要的推理方法.10. What's the definition of the game theory?[灌水]博弈论的定义是什么 ?11. Game theory studies mutual roles among rational agents.博弈论是研究理性的行动者相互作用的理论.12. So the penalty kick, for instance, is like this laboratory mile of game theory.打个比方, 罚点球, 就像博弈论里面的实验室.13. Based on principal - agency, the thesis analyzes budget management system from the angle of game theory.本文以委托代理理论为基础, 从博弈论视角对企业预算管理制度进行了分析.14. Evolutionary game theory provides a uniform frame to study the evolution of cooperation.进化博弈论为理解合作行为的演化提供了一个统一的框架.15. Proving the possibility and inevitability of the tax evasion by the basic theory of GAME.用博弈论的基本理论证明企业偷税的可能性和必然性.。

Cooperative Game Theory and Solution Concepts

Agreeing to Cooperate:Cooperative Game Theory and Solution ConceptsMPhil Microeconomics III:Game TheoryD AVID P.M YATTD EPARTMENT OFE CONOMICS,U NIVERSITY OF O XFORD/dpm/mailto:david.myatt@C ONTENTS1.Cooperative Game Theory22.Coalitional Games with Transferable Payoffs33.Payoff Proﬁles and the Core44.Example:Treasure Hunting55.Application:Intra-Firm Bargaining66.The Core of the Firm77.A Production Example88.Marginal Contributions and the Shapley Value99.Expected Marginal Contributions1010.Application:The Shapley Value and a Worker1111.The Shapley Value for a Worker:The Easy Way1212.Application:The Shapley Value and the Firm1313.The Shapley Value for a Firm:The Easy Way1414.Justifying the Shapley Value1515.Behaviour and Scope of the Firm1616.The Over-Hiring of Labour1717.Investment Incentives and Frontload Factors1818.Economies of Scope and the Effect of Synergies19Page2of19Agreeing to Cooperate1.C OOPERATIVE G AME T HEORY•Non-cooperative game theory(or just game theory)maps out:–The participants(players)in a strategic scenario.–Who can do what and when,and what they know when they do it.–The payoffs of players as a function of the choices of all players.•Our“solutions”focus on Nash and related concepts:–Players are required to play optimally,and have mutually consistent expectations.–This precludes single player deviations•By contrast,cooperative-game theory maps out:–The participants(players)in a scenario.–What subsets of players—coalitions—can jointly achieve.•Cooperative“solutions”require stability from the deviations of coalitions of players.•Moreover,the focus is on what players can achieve rather than do.Notes:Agreeing to CooperatePage 3of 192.C OALITIONAL G AMES WITH T RANSFERABLE P AYOFFS•A coalitional game with transferable payoffs consists of:–A set S of players.–A function v (S ),the worth of any coalition S ⊂S •A coalitional game is cohesive if v (S )≥ v (S k )for any partition {S k }of S .•Hence a coalitional game speciﬁes what different groups of people can jointly achieve.•It is cohesive if the whole can achieve more than the individual parts.Examples of coalitional games include:Treasure Hunting:The players are a group of treasure seekers.Their worth is the amount of treasure they can carry.Intra-Firm Bargaining:They players are a ﬁrm and group of workers.Their worth is either their outside option (for workers only)or the amount that they can produce in the ﬁrm.Production:They players are a group of people owning endowments of inputs and pro-duction technologies.Their worth is the amount of output they can produce given their constraints.Notes:Page4of19Agreeing to Cooperate3.P AYOFF P ROFILES AND THE C ORE•Deﬁne payoff proﬁles as follows–A payoff proﬁle is a set of payoffs{x i}for all i∈S.–A proﬁle is S-feasible if:x i=v(S)i∈S–It is feasible if it is S-feasible,or:x i=v(S)i∈S•The core of a coalitional game is deﬁned as follows:–A set of feasible payoff proﬁles x,for which:x i=v(S)i∈S–There must be no S-feasible alternative y,for which y i>x i for all i∈S and:y i=v(S)i∈S•Hence the core is robust to deviations by coalitions of players.Notes:Agreeing to CooperatePage 5of 194.E XAMPLE :T REASURE H UNTING An expedition of n people discover some treasure in the mountains.Each pair can carry out a single piece of treasure.Players:These are S ={1,2,...,n },the treasure seekers.Worths:The worth of a coalition S ⊂S is:v (S )= |S |/2if |S |is even (|S |−1)/2if |S |is odd•Suppose that n =|S |is even,and n ≥4.If there are unequal payoffs,then the two players with the lowest payoffs may deviate and obtain more.Hence the core entails payoffs of 12for everyone.•Suppose that n =|S |is odd.The core is empty.If all players receive something,then n −1could choose to abandon the n th.But any zero-payoff player can form a coalition with the lowest positive payoff player,and obtain a better payoff for both.•Notice that for n odd,the core is too restrictive —it is empty!Notes:Page 6of 19Agreeing to Cooperate5.A PPLICATION :I NTRA -F IRM B ARGAINING •There is a ﬁrm and a pool of n workers.Workers have a reservation wage of w L .Binding contracts are not possible.•Production with i workers yields revenue,net of non-labour costs,of F (i ).•Write the marginal product of the i th employee as:F (i )=F (i )−F (i −1)•Assume that this is decreasing in i —a concave production function.•Translate this to a cooperative game with transferable utility:Players:These are S =Firm ∪{n workers }.Worths:The worth of a coalition S ⊂S is:v (S )= 0S ={Firm }iw L S ={i workers }F (i )S ={Firm }∪{i workers }Notes:Agreeing to Cooperate Page7of196.T HE C ORE OF THE F IRM•We must have x i≥w L otherwise a single worker could deviate.•We must have x i≤ F(n)otherwise teh reaminder could abandon the worker.•This is sufﬁcient:Suppose that k workers are removed:kx i≤k F(n)≤F(n)−F(n−k)i=1•Hence any payoffs such that:nx i≤F(n)and w L≤x i≤ F(n)i=1are in the core,with the remainder accruing to theﬁrm are in the core.•This suggests that workers are paid above their transfer earnings w L,but below their marginal productivity F(n).•There is no sharp prediction—the core is too weak in this case.Notes:Page8of19Agreeing to Cooperate7.A P RODUCTION E XAMPLE•Consider a market with transferable payoffs.This consists of:–A set of N players and M input goods.–For each agent i an endowment ofωi∈R M+.–For each agent i,a nicely behaved production function f i(x).•This can be converted into a coalitional game with transferable payoffs:v(S)=max{z i}:i∈Si∈Sf i(z i)such that z i∈R M+andi∈Sz i=i∈Sωi•Every market game such as this has a non-empty core.•Every proﬁle of competitive payoffs(i.e.mimicking a competitive equilibrium)is in the core.•This extends to the core of exchange economies.•As the number of agents increases by replication,the core shrinks to the set of competi-tive equilibria.Notes:Agreeing to Cooperate Page9of198.M ARGINAL C ONTRIBUTIONS AND THE S HAPLEY V ALUE•The core has some problems in general coalitional games:–Sometimes the core is empty,and sometimes it is large.–In does not consider the credibility of deviating coalitions.•Hence we require a cooperative solution in which any deviations are themselves robust.•Hence we are examining“off the equilibrium coalition”consistency.•Require a payoff proﬁle to be deﬁned for all coalitions.Hence obtain the value:ψi(S):2S→R•Possibilities are the bargaining set,the nucleolus,the kernel and vNM stable sets.•We will consider the Shapley value.This incorporates:–A player is paid their marginal contribution to a coalition.–This contribution depends on their position in the coalition.–Hence pay them their expected marginal contribution.Notes:Page10of19Agreeing to Cooperate9.E XPECTED M ARGINAL C ONTRIBUTIONS•Suppose that player i is the last member of a coalition S.What is her marginal contri-bution?m i(S)=v(S)value with i −v(S\{i})value without iwhere i∈S⊂S•Now arrange all of the agents at random.Consider the following arrangement:–Suppose that the group S occursﬁrst,with player i at the end.–There are(|S|−1)!ways of arranging the other members of S before i,and(|S|−|S|)!ways of arranging non-members S\S after i.–There are|S|!ways of arranging people in total.–Hence the probability that i is marginal to coalition S is:p i(S)=(|S|−1)!(|S|−|S|)!|S|!•Hence player i’s expected marginal contribution is:ψi(S)=S∈2S:i∈S p i(S)m i(S)=S∈2S:i∈S(|S|−1)!(|S|−|S|)!|S|![v(S)−v(S\{i})]•This is the Shapley value.Notice thati∈S=v(S).•Put simply,the Shapley value is a player’s expected marginal contribution to a ran-domly ordered set of players.•The formula above seems complex,but individual applications can be simpler. Notes:10.A PPLICATION:T HE S HAPLEY V ALUE AND A W ORKER•Let us calculate the Shapley value for a particular worker i.There are n+1possible positions for this worker.•Consider a coalition S of j workers.Apart from the worker in focus,there are j−1others.Thus there are:n−1j−1=(n−1)!(j−1)!(n−j)!possible coalitions we can form.•The worker’s marginal contribution to such a coalition is:i∈S={j workers}⇒m i(S)=w L •Consider a coalition of j−1workers,plus aﬁrm.There are:n−1 j−2=(n−1)!(j−2)!(n−j+1)!possible coalitions of this type.•The worker’s marginal contribution to such a coalition is:i∈S={Firm∪j−1workers}⇒m i(S)= F(j−1)•Hence we can assemble the expected marginal contribution:ψworker=nj=1(n−1)!(j−1)!(n−j)!(j−1)!(n+1−j)!(n+1)!w L+n+1j=2(n−1)!(j−2)!(n−j+1)!(j−1)!(n+1−j)!(n+1)!F(j−1)•Cancelling where appropriate leave us with:ψworker=nj=1n+1−jn(n+1)w L+n+1j=2j−1n(n+1)F(j−1)=w L2+1n(n+1)nj=1j F(j)Notes:11.T HE S HAPLEY V ALUE FOR A W ORKER:T HE E ASY W AY•A worker takes one out of n+1positions.•There is a possibility that he is marginal to a coalition of workers:–This must be because theﬁrm comes after him in the line up.–Theﬁrm comes after rather than before with probability1/2.–The expected marginal contribution is w L/2.•There is a possibility that he is marginal to a coalition involving theﬁrm.–The probability that he takes position j+1is1/(n+1).–There are n remaining places,and j places before him.–The probability that theﬁrm takes one of the places before him is j/n.–In this case,he adds to a workingﬁrm as the j th worker a contribution of F(j).–This yields an expected contribution of:1 n+1×jn× F(j)•Assembling these elements we have:ψworker=w L2+1n(n+1)nj=1j F(j)Notes:12.A PPLICATION :T HE S HAPLEY V ALUE AND THE F IRM •There are n +1positions for a ﬁrm.Suppose it is at position j ,so that |S |=j .–The ﬁrm requires j −1workers before it.There are: n j −1 =n !(j −1)!(n −j +1)!such sets S .–The ﬁrm’s marginal contribution is:i ∈S ={Firm ∪j −1workers }⇒m i (S )=F (j −1)−(j −1)w L•Hence we can assemble the expected marginal contribution:ψﬁrm =n +1j =1n !(j −1)!(n −j +1)!(j −1)!(n +1−j )!(n +1)![F (j −1)−(j −1)w L ]•Simplifying,this becomes:ψﬁrm =1n +1nj =0[F (j )−jw L ]•Recall that a “neoclassical”ﬁrm with j employees makes proﬁts:π(j )=F (j )−jw L•Hence the “bargaining”ﬁrm enjoys the average neoclassical proﬁts:˜π(n )=1n +1n j =0π(i )≈1n n0π(j )dj Notes:13.T HE S HAPLEY V ALUE FOR A F IRM:T HE E ASY W AY•Aﬁrm takes one out of n+1positions.•It takes any particular position j+1with probability1/(n+1)•Suppose it takes position j+1:–There are j workers before it.–Its membership of the coalition means that the workers are no longer earning their outside wage,a loss of jw L–Its membership of the coalition enables production to take place,yielding F(j).–Hence the net gain is F(j)−jw L•Assembling these elements we have:ψﬁrm=nj=0F(j)−jw L•Recall that a“neoclassical”ﬁrm with j employees makes proﬁts:π(j)=F(j)−jw L•Hence the“bargaining”ﬁrm enjoys the average neoclassical proﬁts:˜π(n)=1n+1nj=0π(i)≈1nnπ(j)djNotes:14.J USTIFYING THE S HAPLEY V ALUE•Suppose that in a j-workerﬁrm,the workers andﬁrm agree to payoffs of˜w(j)and˜π(j).•Suppose that a worker threatens to leave:–Consider their payoffs inside and outside the relationship:Firm WorkerAgree F(j)−j˜w(j)˜w(j)Disagree F(j−1)−(j−1)˜w(j−1)w L–They bargain to“equalise the gains from trade”:˜w(j)−w L=[F(j)−j˜w(j)]−[F(j−1)−(j−1)˜w(j−1)]= F(j)−j˜w(j)+(j−1)˜w(j−1)⇔(j+1)˜w(j)=w L+ F(j)+(j−1)˜w(j−1)⇔˜w j=w L+ F(j)+(j−1)˜w(j−1)j+1–This is the balanced contributions condition.The same condition for aﬁrm of size j=1yields:w(1)= F(1)+w L2–The wage paid in j personﬁrm depends on the marginal product F(j).But it also depends on the wage paid in aﬁrm of size j−1,which in turn depends upon F(j−1).Hence infra-marginal products matter for wage determination.–Solve the equations by repeated substitution and obtain:˜w(n)=1n(n+1)nj=0j F(j)+w L2˜π(n)=nj=01−jn+1F(j)−nw L2=1n+1nj=0[F(j)−jw L]–Of course,these are just the Shapley values. Notes:15.B EHAVIOUR AND S COPE OF THE F IRM •Recalling that neoclassical proﬁts areπ(j)=F(j)−jw L we can employ˜w(n)=w L+π(n)−˜π(n)nand˜π(n)=1n+1nj=0π(j)average of neoclassicalﬁrm proﬁts•Hence the proﬁts of an infra-marginal neoclassicalﬁrm matter with non-binding con-tracts.•Consider the optimal scale of theﬁrm,choosing n to maximise˜π(n)=1nnπ(s)ds•Take theﬁrst order condition and re-arrange:˜π (n)=1nπ(n)−1n2nπ(s)ds=0⇔˜π(n∗)=π(n∗)•Notice thatπ(n)=F(n)−nw L and˜π(n)=F(n)−n˜w(n).Hence at n∗we have ˜w(n∗)=w L—theﬁrm over-hires labour to bid-down the wage paid.Notes:16.T HE O VER -H IRING OF L ABOUR ......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................˜w (n )>w L ←−n ∗−→˜w (n )<w Lπ(x )˜π(x )..........................................................Notes:17.I NVESTMENT I NCENTIVES AND F RONTLOAD F ACTORS•Suppose that production,and hence proﬁts,depends on investment x :–A with a neoclassical ﬁrm,the proﬁts of a ﬁrm of size n are π(x,n ).Comparing incentives:∂2π(x,s )∂x∂s>0⇒∂π(x,n )∂x >1n n 0∂π(x,s )∂x ds –Hence,for ﬁxed n ,if investment and labour are complements,there is an reducedincentive to invest.–If investment and labour are substitutes,there is an enhanced incentive to invest.•Consider the proﬁts of the bargaining ﬁrm.–Integrate proﬁts ˜π(n )by parts to obtain:˜π(n )=1n n0π(s )ds =1n [sπ(s )]n 0−1n n 0sdπ(s )=π(n )−1n n 0sπ (s )ds –Write this as ˜π(n )=π(n )γ(F,n )as a measure of the loading of technology:˜π(n )=π(n )× 1−1π(n ) n 0s n π (s )ds γ(F,n )=Frontload Factor –This is a measure of the degree to which returns are gained early in the technology.Notes:18.E CONOMIES OF S COPE AND THE E FFECT OF S YNERGIES•Suppose that their are two divisions,of size n and m:–A neoclassicalﬁrm with such employees has proﬁts:π(n,m)=F(n,m)−nw L,1+mw L,2–By contrast,bargainingﬁrm can be shown to have proﬁts:˜π(n,m)=1n+m+1ni=0mj=0nimjn+mi+jπ(i,j)•Suppose that the reservation wage is zero,and that m=n=1:–Writing F(n,m)=F nm,a neoclassicalﬁrm will integrate divisions whenever:F11−F00Combined Firm ≥F10−F00Division1+F01−F00Division2or F11+F00−(F01+F10)S F=Measure of Synergies Between Divisions≥0–With intra-ﬁrm bargaining,the integrated proﬁts are:˜π(1,1)=13F00+F10+F012+F11=12[F00+F11]−16S F–Paradoxically,decreasing the efﬁciency of individual divisions harms theﬁrm—complementarity( S F)strengthens the bargaining of the employees.Notes:。

指南中关于合作游戏的阐述

指南中关于合作游戏的阐述英文回答：Cooperative Gameplay.Cooperative gameplay, also known as co-op, allows multiple players to work together to achieve a common goal. This mode of play can be found in a variety of genres, from first-person shooters to role-playing games. In cooperative games, players must coordinate their actions and communicate effectively in order to succeed. This can lead to a more challenging and engaging experience than playing alone.There are many benefits to cooperative gameplay. First, it allows players to socialize with others and build relationships. Second, it can help players learn new skills and strategies. Third, it can provide a more challenging and rewarding experience than playing alone.There are a few things to keep in mind when playing cooperative games. First, it is important to communicate effectively with your teammates. Second, it is important to be patient and understanding. Third, it is important to be willing to compromise.Cooperative gameplay can be a great way to experience video games with friends. It can be a challenging and rewarding experience that can help players build relationships and learn new skills.中文回答：合作模式。

合作博弈代码

合作博弈代码合作博弈（Cooperative game）是博弈论中的一个重要分支，研究的是参与者通过合作来实现组织目标的博弈模型。

在合作博弈中，参与者之间通过协商、合作来达成最优解，共同分享收益或承担风险。

为了解决这类问题，人们开发了各种合作博弈模型和相应的求解方法。

本文将介绍一种常见的合作博弈代码实现方法。

合作博弈模型可以用一个特征函数（characteristic function）来表示。

特征函数描述了博弈参与者之间的合作关系以及相应的收益分配方式。

以合作博弈中的N人问题为例，特征函数可以表示为：v(S)：对于任意的联盟S，v(S)表示这个联盟合作所能获得的总收益。

基于这个特征函数，我们可以使用Shapley值（Shapley value）来确定参与者的个人收益。

Shapley值是一个有理分配方式，可以确保参与者之间的收益是公平和合理的。

为了实现合作博弈的代码，我们可以按照以下步骤进行：第一步：定义特征函数根据实际情况，我们可以首先定义特征函数v(S)。

这个函数可以是一个字典或一个矩阵，用来表示各个联盟合作所能获得的总收益。

第二步：计算Shapley值根据定义的特征函数，我们可以使用迭代的方法计算每个参与者的Shapley值。

Shapley值的计算方式如下所示：1. 初始化参与者的Shapley值为0；2. 对于每个参与者i，依次计算他参与所有可能的联盟所能获得的平均边际值；3. 将每个参与者的平均边际值累加到其对应的Shapley值上。

具体而言，我们可以使用以下伪代码来实现Shapley值的计算：```pythondef shapley_value(v):n = len(v) # 参与者的个数shapley = [0] * n # 初始化Shapley值为0for i in range(n):for j in range(2 ** n):if (j >> i) % 2 == 1:coalition = [k for k in range(n) if (j >> k) % 2 == 1]m = len(coalition)marginal_value = (v[coalition + [i]] - v[coalition]) / b(n - 1, m)shapley[i] += marginal_valuereturn shapley```第三步：应用代码在得到了Shapley值之后，我们可以根据实际需要进行进一步的分析和应用。