10 Dynamic Games of incomplete information=Axelrod 竞赛PPT课件
lecture12Extensive-Form Representation(博弈论,Carnegie Mellon University)
information Game tree
June 4, 2003
73-347 Game Theory--Lecture 12
3
Entry game
An incumbent monopolist faces the possibility of entry by a
challenger. The challenger may choose to enter or stay out. If the challenger enters, the incumbent can choose either to accommodate or to fight. The payoffs are common knowledge.
Dynamic games of complete information Extensive-form representation Dynamic games of complete and perfect information Game tree Subgame-perfect Nash equilibrium Backward induction Applications Dynamic games of complete and imperfect information More applications Repeated games
June 4, 2003
73-347 Game Theory--Lecture 12
8
Game tree
A game tree has a set
of nodes and a set of edges such that
a path from x0 to x4
第十一讲最优资本结构
一个例子 考虑一个每年EBIT为100元的公司 （不存在经营决策改进所导致的现金流增 长） 公司希望发行最大限度的债务（等于每年 的EBIT）以抵税 以10%的利率发行债务1000元
不存在现金流增长的公司现金流量
时期 EBIT 利息 1 100 2 100 3 100 4 100 … …
（100） （100） （100） （100） … 0 0 0 …
Case2：个人税率不相同的情形 假设股利个人税TS为10%，利息个人税TB为50%
股利 股利个人税 个人税后股利剩余 利息 利息个人税 个人税后利息剩余 个人税后总现金流 计划1 650 （65） 585 0 0 0 585 计划2 390 （39） 351 400 （200） 200 551
Preface to the handbook
Organization
The organization of the Handbook of Industrial Organization reflects our perspectives on the principal topics in the field that have recently received intensive research attention or that otherwise are most needful of a new integrative survey. Each of the chapters in the Handbook can be read independently, though they are organized into Parts with some logic, and many pairs are close complements. Part 1 begins the Handbook with four chapters on the firm. In much of economics, the firm has been viewed as just a black box that maximizes profits subject to an exogenous production or cost function. Because firm behavior is so important in industrial organization, scholars in this field have been productively working to open that box. John Panzar (Chapter 1) focuses on the impact of costs and technology on the organization of production among firms in an industry. He surveys the body of theoretical results on the connections between detailed properties of multiproduct cost functions and details of firm and market structure, and discusses methods of applying these results in empirical analyses of such industries as electric power and telecommunications. Bengt Holmstrom and Jean Tirole (Chapter 2) consider the implications of imperfect information for the behavior of firms viewed as organizations of self-interested owners, managers, and employees. They summarize the burgeoning body of research that formally analyzes from this perspective the existence, scope, financing, internal structure, control, and objectives of firms. In a complementary chapter, Oliver Williamson (Chapter 3) analyzes the consequences of the minimization of transactions costs for the structures of firms and for the locations of boundaries between firms and markets. Martin Perry (Chapter 4) focuses on vertical integration as an important dimension of firm structure. His presentation surveys the long line of research on the incentives for and effects of
重要课件 Lecture-13
LECTURE 13LEARNING OUTCOMESBy the end of this lecture, students will be able to:∙Understand what is meant by Perfect Bayesian Equilibrium (PBE)∙Understand how a PBE relates to the other equilibrium concepts studied so far∙Understand how to find a PBEINTRODUCTIONSo far we have studied three equilibrium concepts:-Nash equilibrium in static games of complete information.-SPNE in dynamic games of complete information.-Bayesian Nash Equilibrium in static games of incomplete information.In this lecture, we will introduce a new equilibrium concept:-Perfect Bayesian Equilibrium (PBE) in dynamic games of incomplete information.Why do we require a “new” equilibrium concept for each class of games?The equilibrium concepts above are closely related – they are not new per se. We also need to strengthen our equilibrium concept, as we consider progressively richer games. For example, a SPNE eliminates Nash equilibria that involve non-credible threats. Similarly, a Perfect Bayesian Equilibrium can be thought of as a refinement of a Bayesian Nash EquilibriumAlso, a Perfect Bayesian Equilibrium strengthens the requirements of SPNE (see example below) by considering explicitly the players’ beliefs. (Recall that beliefs are important in the context of games characterized by incomplete information.)MOTIVATION FOR THE USE OF A PBEConsider the following dynamic game (characterized by complete but imperfect information).2,1Normal form Representation:2L’R’1 LM RIt is easy to see that, in the normal form game above, there are 2 (pure strategy) Nash equilibria: (L, L’) and(R, R’).Are these Nash equilibria subgame-perfect?The answer is yes. The reason is that the only subgame is the entire game. (Recall that a SPNE is a Nash equilibrium in every subgame.)However, there is a problem with the equilibrium (R, R’), as it involves a non-credible threat: For player 2, L’ dominates R’ (so player 2 would not play R’).Thus, we need to strengthen our equilibrium concept to eliminate the SPNE (R, R’). This is the reason why we need to consider a PBE – not just a SPNE.REFINING OUR EQUILIBRIUM PREDICTIONSA PBE imposes 3 requirements on our equilibrium predictions, 2 of which a presented below:Requirement 1 (“Beliefs”)At each information set, the player with the move must have a belief about which node in the information set has been reached.∙Non-singleton information set: belief = probability distribution.∙Singleton information set: probability 1 is assigned to the single decision node.Based on our example above, requirement 1 is represented by the probabilities p and l-p(see Figure).Requirement 2 (“Sequential Rationality”)Players act optimally given their beliefs and the other players’ strategy.Based on our example aboveThus, Requirement 2 pre vents player 2 from choosing R’ becauseIn consequence, requiring that each player has a belief and acts optimally given this belief suffices to eliminate (R, R’).That is, player 2 won't play R’, so player 1 won’t be induced to play R. Thus, we are left with (L, L’) as our unique SPNE outcome.ANOTHER EXAMPLE TO ILLUSTRATE “SEQUENTIAL RATIONALITY”3, 01∙ Suppose that player 2 assigns probability 2/3 to history C ∙ Suppose that player 2 assigns probability 1/3 to history DSequential rationality requires that player 2’s strategy be optimal, given the subsequent behavior specified by player 1's strategy: i.e.Thus, Sequential Rationality requires that player 2 chooses G.Sequential rationality also requires that player 1’s strategy is optimal at her two information sets, given player 2’s strategy: i.e. ∙ after history (C, F) J optimal∙ at the beginning of the gameD, E optimal, given GThus, there are 2 optimal strategies for player 1: DJ, EJ; given G. (Recall that a strategy is complete plan of action, specifying what the player is going to do at each decision node she may be called upon to decide –so we need to specify an action at each of player 1’s decision nodes.)REQUIREMENT 3Requirement 3 says: Each player’s belief is consistent with the equilibrium strategy profile (“consistency of beliefs with equilibrium strategies”).Based on our initial example, requirement 3 simply says that, in the SPNE (L, L’), player 2's belief is p=1.This completes our analysis of the 3 requirements related to a PBE.CALCULATING BELIEFS – A GENERAL APPROACHExample: Entry GameConsider the following entry game:Suppose that the Challenger attaches probability P R, P U and P O to “Ready”, “Unready” and “Out”, respectively. The Incumbent’s probabilities that “Ready” and “Unready” will occur are p and 1-p, respectively.We have the following possibilities:∙ If , then Requirement 3 does not restrict the Incumbent’s belief.∙ If , then Requirement 3 says that the Incumbent assigns probabilityto “Ready” and probabilityto “Unready”.Both of the last 2 probabilities are consistent with Bayes’ rule.Thus we have arrived at the following definition of a PBE:EXAMPLEConsider the game tree below. Find the PBE.subgameThe subgame identified above can be translated into the following normal form game:L’R’LMIt is easy to see that this game has a unique Nash equilibrium: (L, R’).Using backward induction, we can now identify the optimal action of player 1, given (L, R’). Thus, it is optimal for player 1 to choose D. In consequence, there is a unique SPNE in this game: (D, L, R’).What is the PBE of the game?Requirement 1: Implies beliefs p and 1-p for player 3.Requirement 2: It is fulfilled because the strategies (D, L, R’) have been chosen optimally.Requirement 3: It is fulfilled because p=1 for player 3 is consistent with L chosen by player 2.Thus we can state that: According to the definition of a PBE, the strategies (D, L, R’) and belief p=1 for player 3 satisfy requirements 1-3 – and therefore constitute a PBE.SUMMARYIn this lecture, we saw that all equilibrium concepts studied so far are closely related. We noted that, as we progressively consider richer game, we need to strengthen our equilibrium concept. For example, a Perfect Bayesian Equilibrium can be thought of as a refinement of a Bayesian Nash Equilibrium in the sense that it considers explicitly the players’ beliefs.We examined 3 requirements implied by a Perfect Bayesian Equilibrium: in brief, (i) beliefs, (ii) sequential rationality and (iii) consistency of beliefs with equilibrium strategies. We defined a PBE as strategies and beliefs satisfying requirements 1-3. Through a series of examples, we studied how the 3 requirements can be applied so as to obtain a PBE.。
S315大学高数第10章 博弈论初步
20
第十章 博弈论初步 第二节 同时博弈：纯策略均衡
条件策略下划线法： 用下划线分别来表示甲厂商和乙厂商的条件策略。 在甲厂商的支付矩阵中，找出每一列的最大者；在乙
厂商的支付矩阵中，找出每一行的最大者。 都有划线的支付组合为条件均衡策略。
甲厂商的策略
的个体，至少有两个，有时可以引入一个虚拟的参与 人如“自然” 。 策略（Strategies/actions） ：是一项规则，一组可选择 的行动集合。 参与人应该在什么条件下选择什么样的 行动，以保证自身利益最大化。 支付（Payoffs） ：参与人得到的报酬，所得到的支付 都是所有策略共同作用的结果——支付组合。
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第十章 博弈论初步 第一节 博弈论和策略行为
博弈论重要性 20世纪70 年代以后，博弈论形成了一个完整的体系；从80 年代
开始，博弈论逐渐成为主流经济学的一部分，甚至成为微观经济学的 基础。
1994年：纳什（Nash）、泽尔腾（Selten）和海萨尼（Harsanyi） 3位数学家因在非合作博弈的均衡分析理论方面作出了开创性的贡献， 对博弈论和经济学产生了重要影响而获得了诺贝尔经济学奖。
1950年，22岁的纳什获得博士学位。博士论文为“非 合作的赛局”(后被称为“纳什均衡”) ，该论文仅28 页。
18
第十章 博弈论初步 第二节 同时博弈：纯策略均衡
1958年，纳什得了严重的精神分裂症。他的妻子艾莉 西亚，一直守护在纳什身边，并走过了唯一的儿子同 样罹患精神分裂症的震惊与哀伤……漫长的岁月证明， 与艾莉西亚结婚，也许是纳什一生中比获得诺贝尔奖 更重要的事情。
12
第十章 博弈论初步
第二节 同时博弈：纯策略均衡
HP Color LaserJet Enterprise MFP M776用户指南说明书
Legal informationCopyright and License© Copyright 2019 HP Development Company, L.P.Reproduction, adaptation, or translation without prior written permission is prohibited, except as allowedunder the copyright laws.The information contained herein is subject to change without notice.The only warranties for HP products and services are set forth in the express warranty statementsaccompanying such products and services. Nothing herein should be construed as constituting anadditional warranty. HP shall not be liable for technical or editorial errors or omissions contained herein.Edition 1, 10/2019Trademark CreditsAdobe®, Adobe Photoshop®, Acrobat®, and PostScript® are trademarks of Adobe Systems Incorporated.Apple and the Apple logo are trademarks of Apple Inc., registered in the U.S. and other countries.macOS is a trademark of Apple Inc., registered in the U.S. and other countries.AirPrint is a trademark of Apple Inc., registered in the U.S. and other countries.Google™ is a trademark of Google Inc.Microsoft®, Windows®, Windows® XP, and Windows Vista® are U.S. registered trademarks of MicrosoftCorporation.UNIX® is a registered trademark of The Open Group.iiiT able of contents1 Printer overview (1)Warning icons (1)Potential shock hazard (2)Printer views (2)Printer front view (2)Printer back view (4)Interface ports (4)Control-panel view (5)How to use the touchscreen control panel (7)Printer specifications (8)T echnical specifications (8)Supported operating systems (11)Mobile printing solutions (12)Printer dimensions (13)Power consumption, electrical specifications, and acoustic emissions (15)Operating-environment range (15)Printer hardware setup and software installation (16)2 Paper trays (17)Introduction (17)Load paper to Tray 1 (multipurpose tray) (17)Load Tray 1 (multipurpose tray) (18)Tray 1 paper orientation (19)Use alternative letterhead mode (24)Enable Alternative Letterhead Mode by using the printer control-panel menus (24)Load paper to Tray 2 (24)Load Tray 2 (24)Tray 2 paper orientation (26)Use alternative letterhead mode (29)Enable Alternative Letterhead Mode by using the printer control-panel menus (29)Load paper to the 550-sheet paper tray (30)Load paper to the 550-sheet paper tray (30)550-sheet paper tray paper orientation (32)Use alternative letterhead mode (35)Enable Alternative Letterhead Mode by using the printer control-panel menus (35)ivLoad paper to the 2 x 550-sheet paper trays (36)Load paper to the 2 x 550-sheet paper trays (36)2 x 550-sheet paper tray paper orientation (38)Use alternative letterhead mode (41)Enable Alternative Letterhead Mode by using the printer control-panel menus (41)Load paper to the 2,700-sheet high-capacity input paper trays (41)Load paper to the 2,700-sheet high-capacity input paper trays (41)2,700-sheet HCI paper tray paper orientation (43)Use alternative letterhead mode (45)Enable Alternative Letterhead Mode by using the printer control-panel menus (45)Load and print envelopes (46)Print envelopes (46)Envelope orientation (46)Load and print labels (47)Manually feed labels (47)Label orientation (48)3 Supplies, accessories, and parts (49)Order supplies, accessories, and parts (49)Ordering (49)Supplies and accessories (50)Maintenance/long-life consumables (51)Customer self-repair parts (51)Dynamic security (52)Configure the HP toner-cartridge-protection supply settings (53)Introduction (53)Enable or disable the Cartridge Policy feature (53)Use the printer control panel to enable the Cartridge Policy feature (54)Use the printer control panel to disable the Cartridge Policy feature (54)Use the HP Embedded Web Server (EWS) to enable the Cartridge Policy feature (54)Use the HP Embedded Web Server (EWS) to disable the Cartridge Policy feature (55)Troubleshoot Cartridge Policy control panel error messages (55)Enable or disable the Cartridge Protection feature (55)Use the printer control panel to enable the Cartridge Protection feature (56)Use the printer control panel to disable the Cartridge Protection feature (56)Use the HP Embedded Web Server (EWS) to enable the Cartridge Protection feature (56)Use the HP Embedded Web Server (EWS) to disable the Cartridge Protection feature (57)Troubleshoot Cartridge Protection control panel error messages (57)Replace the toner cartridges (58)T oner-cartridge information (58)Remove and replace the cartridges (59)Replace the imaging drums (62)Imaging drum information (62)Remove and replace the imaging drums (63)Replace the toner-collection unit (66)T oner-collection unit information (66)vRemove and replace the toner-collection unit (67)Replace the staple cartridge (M776zs model only) (70)Staple cartridge information (70)Remove and replace the staple cartridge (71)4 Print (73)Print tasks (Windows) (73)How to print (Windows) (73)Automatically print on both sides (Windows) (74)Manually print on both sides (Windows) (74)Print multiple pages per sheet (Windows) (75)Select the paper type (Windows) (75)Additional print tasks (76)Print tasks (macOS) (77)How to print (macOS) (77)Automatically print on both sides (macOS) (77)Manually print on both sides (macOS) (77)Print multiple pages per sheet (macOS) (78)Select the paper type (macOS) (78)Additional print tasks (79)Store print jobs on the printer to print later or print privately (79)Introduction (79)Create a stored job (Windows) (79)Create a stored job (macOS) (80)Print a stored job (81)Delete a stored job (81)Delete a job that is stored on the printer (81)Change the job storage limit (82)Information sent to printer for Job Accounting purposes (82)Mobile printing (82)Introduction (82)Wi-Fi, Wi-Fi Direct Print, NFC, and BLE printing (82)Enable wireless printing (83)Change the Wi-Fi Direct name (83)HP ePrint via email (83)AirPrint (84)Android embedded printing (85)Print from a USB flash drive (85)Enable the USB port for printing (85)Method one: Enable the USB port from the printer control panel (85)Method two: Enable the USB port from the HP Embedded Web Server (network-connectedprinters only) (85)Print USB documents (86)Print using high-speed USB 2.0 port (wired) (86)Method one: Enable the high-speed USB 2.0 port from the printer control panel menus (86)Method two: Enable the high-speed USB 2.0 port from the HP Embedded Web Server (network-connected printers only) (87)vi5 Copy (88)Make a copy (88)Copy on both sides (duplex) (90)Additional copy tasks (92)6 Scan (93)Set up Scan to Email (93)Introduction (93)Before you begin (93)Step one: Access the HP Embedded Web Server (EWS) (94)Step two: Configure the Network Identification settings (95)Step three: Configure the Send to Email feature (96)Method one: Basic configuration using the Email Setup Wizard (96)Method two: Advanced configuration using the Email Setup (100)Step four: Configure the Quick Sets (optional) (104)Step five: Set up Send to Email to use Office 365 Outlook (optional) (105)Introduction (105)Configure the outgoing email server (SMTP) to send an email from an Office 365 Outlookaccount (105)Set up Scan to Network Folder (108)Introduction (108)Before you begin (108)Step one: Access the HP Embedded Web Server (EWS) (108)Step two: Set up Scan to Network Folder (109)Method one: Use the Scan to Network Folder Wizard (109)Method two: Use Scan to Network Folder Setup (110)Step one: Begin the configuration (110)Step two: Configure the Scan to Network Folder settings (111)Step three: Complete the configuration (118)Set up Scan to SharePoint (118)Introduction (118)Before you begin (118)Step one: Access the HP Embedded Web Server (EWS) (118)Step two: Enable Scan to SharePoint and create a Scan to SharePoint Quick Set (119)Scan a file directly to a SharePoint site (121)Quick Set scan settings and options for Scan to SharePoint (122)Set up Scan to USB Drive (123)Introduction (124)Step one: Access the HP Embedded Web Server (EWS) (124)Step two: Enable Scan to USB Drive (124)Step three: Configure the Quick Sets (optional) (125)Default scan settings for Scan to USB Drive setup (126)Default file settings for Save to USB setup (126)Scan to email (127)Introduction (127)Scan to email (127)Scan to job storage (129)viiIntroduction (129)Scan to job storage on the printer (130)Print from job storage on the printer (132)Scan to network folder (132)Introduction (132)Scan to network folder (132)Scan to SharePoint (134)Introduction (134)Scan to SharePoint (134)Scan to USB drive (136)Introduction (136)Scan to USB drive (136)Use HP JetAdvantage business solutions (138)Additional scan tasks (138)7 Fax (140)Set up fax (140)Introduction (140)Set up fax by using the printer control panel (140)Change fax configurations (141)Fax dialing settings (141)General fax send settings (142)Fax receive settings (143)Send a fax (144)Additional fax tasks (146)8 Manage the printer (147)Advanced configuration with the HP Embedded Web Server (EWS) (147)Introduction (147)How to access the HP Embedded Web Server (EWS) (148)HP Embedded Web Server features (149)Information tab (149)General tab (149)Copy/Print tab (150)Scan/Digital Send tab (151)Fax tab (152)Supplies tab (153)Troubleshooting tab (153)Security tab (153)HP Web Services tab (154)Networking tab (154)Other Links list (156)Configure IP network settings (157)Printer sharing disclaimer (157)View or change network settings (157)Rename the printer on a network (157)viiiManually configure IPv4 TCP/IP parameters from the control panel (158)Manually configure IPv6 TCP/IP parameters from the control panel (158)Link speed and duplex settings (159)Printer security features (160)Introduction (160)Security statements (160)Assign an administrator password (160)Use the HP Embedded Web Server (EWS) to set the password (160)Provide user access credentials at the printer control panel (161)IP Security (161)Encryption support: HP High Performance Secure Hard Disks (161)Lock the formatter (161)Energy-conservation settings (161)Set the sleep timer and configure the printer to use 1 watt or less of power (161)Set the sleep schedule (162)Set the idle settings (162)HP Web Jetadmin (163)Software and firmware updates (163)9 Solve problems (164)Customer support (164)Control panel help system (165)Reset factory settings (165)Introduction (165)Method one: Reset factory settings from the printer control panel (165)Method two: Reset factory settings from the HP Embedded Web Server (network-connectedprinters only) (166)A “Cartridge is low” or “Cartridge is very low” message displays on the printer control panel (166)Change the “Very Low” settings (166)Change the “Very Low” settings at the control panel (166)For printers with fax capability (167)Order supplies (167)Printer does not pick up paper or misfeeds (167)Introduction (167)The printer does not pick up paper (167)The printer picks up multiple sheets of paper (171)The document feeder jams, skews, or picks up multiple sheets of paper (174)Clear paper jams (174)Introduction (174)Paper jam locations (174)Auto-navigation for clearing paper jams (175)Experiencing frequent or recurring paper jams? (175)Clear paper jams in the document feeder - 31.13.yz (176)Clear paper jams in Tray 1 (13.A1) (177)Clear paper jams in Tray 2 (13.A2) (182)Clear paper jams in the fuser (13.B9, 13.B2, 13.FF) (188)ixClear paper jams in the duplex area (13.D3) (194)Clear paper jams in the 550-sheet trays (13.A3, 13.A4) (199)Clear paper jams in the 2 x 550 paper trays (13.A4, 13.A5) (206)Clear paper jams in the 2,700-sheet high-capacity input paper trays (13.A3, 13.A4, 13.A5, 13.A7) (213)Resolving color print quality problems (220)Introduction (220)Troubleshoot print quality (221)Update the printer firmware (221)Print from a different software program (221)Check the paper-type setting for the print job (221)Check the paper type setting on the printer (221)Check the paper type setting (Windows) (221)Check the paper type setting (macOS) (222)Check toner-cartridge status (222)Step one: Print the Supplies Status Page (222)Step two: Check supplies status (222)Print a cleaning page (222)Visually inspect the toner cartridge or cartridges (223)Check paper and the printing environment (223)Step one: Use paper that meets HP specifications (223)Step two: Check the environment (223)Step three: Set the individual tray alignment (224)Try a different print driver (224)Troubleshoot color quality (225)Calibrate the printer to align the colors (225)Troubleshoot image defects (225)Improve copy image quality (233)Check the scanner glass for dirt and smudges (233)Calibrate the scanner (234)Check the paper settings (235)Check the paper selection options (235)Check the image-adjustment settings (235)Optimize copy quality for text or pictures (236)Edge-to-edge copying (236)Improve scan image quality (236)Check the scanner glass for dirt and smudges (237)Check the resolution settings (238)Check the color settings (238)Check the image-adjustment settings (239)Optimize scan quality for text or pictures (239)Check the output-quality settings (240)Improve fax image quality (240)Check the scanner glass for dirt and smudges (240)Check the send-fax resolution settings (242)Check the image-adjustment settings (242)Optimize fax quality for text or pictures (242)Check the error-correction setting (243)xSend to a different fax machine (243)Check the sender's fax machine (243)Solve wired network problems (244)Introduction (244)Poor physical connection (244)The computer is unable to communicate with the printer (244)The printer is using incorrect link and duplex settings for the network (245)New software programs might be causing compatibility problems (245)The computer or workstation might be set up incorrectly (245)The printer is disabled, or other network settings are incorrect (245)Solve wireless network problems (245)Introduction (245)Wireless connectivity checklist (245)The printer does not print after the wireless configuration completes (246)The printer does not print, and the computer has a third-party firewall installed (246)The wireless connection does not work after moving the wireless router or printer (247)Cannot connect more computers to the wireless printer (247)The wireless printer loses communication when connected to a VPN (247)The network does not appear in the wireless networks list (247)The wireless network is not functioning (247)Reduce interference on a wireless network (248)Solve fax problems (248)Checklist for solving fax problems (248)What type of phone line are you using? (249)Are you using a surge-protection device? (249)Are you using a phone company voice-messaging service or an answering machine? (249)Does your phone line have a call-waiting feature? (249)Check fax accessory status (249)General fax problems (250)The fax failed to send (250)No fax address book button displays (250)Not able to locate the Fax settings in HP Web Jetadmin (250)The header is appended to the top of the page when the overlay option is enabled (251)A mix of names and numbers is in the recipients box (251)A one-page fax prints as two pages (251)A document stops in the document feeder in the middle of faxing (251)The volume for sounds coming from the fax accessory is too high or too low (251)Index (252)xiPrinter overview1Review the location of features on the printer, the physical and technical specifications of the printer,and where to locate setup information.For video assistance, see /videos/LaserJet.The following information is correct at the time of publication. For current information, see /support/colorljM776MFP.For more information:HP's all-inclusive help for the printer includes the following information:●Install and configure●Learn and use●Solve problems●Download software and firmware updates●Join support forums●Find warranty and regulatory informationWarning iconsUse caution if you see a warning icon on your HP printer, as indicated in the icon definitions.●Caution: Electric shock●Caution: Hot surface●Caution: Keep body parts away from moving partsPrinter overview1●Caution: Sharp edge in close proximity●WarningPotential shock hazardReview this important safety information.●Read and understand these safety statements to avoid an electrical shock hazard.●Always follow basic safety precautions when using this product to reduce risk of injury from fire orelectric shock.●Read and understand all instructions in the user guide.●Observe all warnings and instructions marked on the product.●Use only a grounded electrical outlet when connecting the product to a power source. If you do notknow whether the outlet is grounded, check with a qualified electrician.●Do not touch the contacts on any of the sockets on the product. Replace damaged cordsimmediately.●Unplug this product from wall outlets before cleaning.●Do not install or use this product near water or when you are wet.●Install the product securely on a stable surface.●Install the product in a protected location where no one can step on or trip over the power cord.Printer viewsIdentify certain parts of the printer and the control panel.Printer front viewLocate features on the front of the printer.2Chapter 1 Printer overviewPrinter front view3Printer back viewLocate features on the back of the printer.Interface portsLocate the interface ports on the printer formatter. 4Chapter 1 Printer overviewControl-panel viewThe control panel provides access to the printer features and indicates the current status of the printer.NOTE:Tilt the control panel for easier viewing.The Home screen provides access to the printer features and indicates the current status of the printer.screens.NOTE:The features that appear on the Home screen can vary, depending on the printerconfiguration.Control-panel view5Figure 1-1Control-panel view?i 12:42 PM6Chapter 1 Printer overviewHow to use the touchscreen control panelPerform the following actions to use the printer touchscreen control panel.T ouchT ouch an item on the screen to select that item or open that menu. Also, when scrolling T ouch the Settings icon to open the Settings app.How to use the touchscreen control panel 7SwipeT ouch the screen and then move your finger horizontally to scroll the screen sideways.Swipe until the Settings app displays.Printer specificationsDetermine the specifications for your printer model.IMPORTANT:The following specifications are correct at the time of publication, but they are subject to change. For current information, see /support/colorljM776MFP .T echnical specificationsReview the printer technical specifications.Product numbers for each model ●M776dn - #T3U55A ●Flow M776z - #3WT91A ●Flow M776zs - #T3U56APaper handling specificationsPaper handling features Tray 1 (100-sheet capacity)Included Included Included Tray 2 (550-sheet capacity)IncludedIncludedIncluded8Chapter 1 Printer overview550-sheet paper trayOptional Included Not included NOTE:The M776dn models accept one optional550-sheet tray.Optional Included Included2 x 550-sheet paper tray and standNOTE:The M776dn models accept one optional550-sheet tray that may be installed on top of thestand.Optional Not included Not included2,700-sheet high-capacity input (HCI) paper trayand standNOTE:The M776dn models accept one optional550-sheet tray that may be installed on top of theoptional printer stand.Printer standOptional Not included Not included NOTE:The M776dn models accept one optional550-sheet tray that may be installed on top of theoptional printer stand.Inner finisher accessory Not included Not included Included Automatic duplex printing Included IncludedIncludedIncluded Included Included10/100/1000 Ethernet LAN connection with IPv4and IPv6Hi-Speed USB 2.0Included Included IncludedIncluded Included IncludedEasy-access USB port for printing from a USBflash drive or upgrading the firmwareIncluded Included Included Hardware Integration Pocket for connectingaccessory and third-party devicesHP Internal USB Ports Optional Optional OptionalOptional Optional OptionalHP Jetdirect 2900nw Print Server accessory forWi-Fi connectivity and an additional Ethernet portOptional IncludedIncludedHP Jetdirect 3100w accessory for Wi-Fi, BLE, NFC,and proximity badge readingPrints 45 pages per minute (ppm) on Letter-sizepaper and 46 ppm on A4-size paperEasy-access USB printing for printing from a USBIncluded Included Includedflash driveT echnical specifications9Included Included Included Store jobs in the printer memory to print later orprint privatelyScans 100 pages per minute (ppm) on A4 andIncluded Included Included letter-size paper one-sidedIncluded Included Included 200-page document feeder with dual-headscanning for single-pass duplex copying andscanningNot included Included Included HP EveryPage T echnologies including ultrasonicmulti-feed detectionNot included Included Included Embedded optical character recognition (OCR)provides the ability to convert printed pages intotext that can be edited or searched using acomputerIncluded Included Included SMART Label feature provides paper-edgedetection for automatic page croppingIncluded Included Included Automatic page orientation for pages that haveat least 100 characters of textIncluded Automatic tone adjustment sets contrast,Included Includedbrightness, and background removal for eachpageIncluded Included Includedfolders on a networkIncludedSend documents to SharePoint®Included IncludedIncluded Included Included NOTE:Memory reported on the configurationpage will change from 2.5 GB to 3 GB with theoptional 1 GB SODIMM installed.Mass storage: 500 GB hard disk drive Included Included IncludedSecurity: HP Trusted Platform Module (TPM)Included Included IncludedT ouchscreen control panel Included Included IncludedRetractable keyboard Not included Included Included 10Chapter 1 Printer overviewFax Optional Included IncludedSupported operating systemsUse the following information to ensure printer compatibility with your computer operating system.Linux: For information and print drivers for Linux, go to /go/linuxprinting.UNIX: For information and print drivers for UNIX®, go to /go/unixmodelscripts.The following information applies to the printer-specific Windows HP PCL 6 print drivers, HP print driversfor macOS, and to the software installer.Windows: Download HP Easy Start from /LaserJet to install the HP print driver. Or, go tothe printer-support website for this printer: /support/colorljM776MFP to download the printdriver or the software installer to install the HP print driver.macOS: Mac computers are supported with this printer. Download HP Easy Start either from /LaserJet or from the Printer Support page, and then use HP Easy Start to install the HP print driver.1.Go to /LaserJet.2.Follow the steps provided to download the printer software.Windows 7, 32-bit and 64-bit The “HP PCL 6” printer-specific print driver is installed for this operating system aspart of the software installation.Windows 8.1, 32-bit and 64-bit The “HP PCL-6” V4 printer-specific print driver is installed for this operating systemas part of the software installation.Windows 10, 32-bit and 64-bit The “HP PCL-6” V4 printer-specific print driver is installed for this operating systemas part of the software installation.Windows Server 2008 R2, SP 1, 64-bit The PCL 6 printer-specific print driver is available for download from the printer-support website. Download the driver, and then use the Microsoft Add Printer tool toinstall it.Windows Server 2012, 64-bit The PCL 6 printer-specific print driver is available for download from the printer-support website. Download the driver, and then use the Microsoft Add Printer tool toinstall it.Windows Server 2012 R2, 64-bit The PCL 6 printer-specific print driver is available for download from the printer-support website. Download the driver, and then use the Microsoft Add Printer tool toinstall it.Windows Server 2016, 64-bit The PCL 6 printer-specific print driver is available for download from the printer-support website. Download the driver, and then use the Microsoft Add Printer tool toinstall it.Windows Server 2019, 64-bit The PCL 6 printer-specific print driver is available for download from the printer-support website. Download the driver, and then use the Microsoft Add Printer tool toinstall it.Supported operating systems11macOS 10.13 High Sierra, macOS 10.14 MojaveDownload HP Easy Start from /LaserJet , and then use it to install the print driver.NOTE:Supported operating systems can change.NOTE:For a current list of supported operating systems and HP’s all-inclusive help for the printer, go to /support/colorljM776MFP .NOTE:For details on client and server operating systems and for HP UPD driver support for this printer, go to /go/upd . Under Additional information , click Specifications .●Internet connection●Dedicated USB 1.1 or 2.0 connection or a network connection● 2 GB of available hard-disk space ●1 GB RAM (32-bit) or2 GB RAM (64-bit)●Internet connection●Dedicated USB 1.1 or 2.0 connection or a network connection●1.5 GB of available hard-disk spaceNOTE:The Windows software installer installs the HP Smart Device Agent Base service. The file size is less than 100 kb. Its only function is to check for printers connected via USB hourly. No data is collected. If a USB printer is found, it then tries to locate a JetAdvantage Management Connector (JAMc) instance on the network. If a JAMc is found, the HP Smart Device Agent Base is securelyupgraded to a full Smart Device Agent from JAMc, which will then allow printed pages to be accounted for in a Managed Print Services (MPS) account. The driver-only web packs downloaded from for the printer and installed through the Add Printer wizard do not install this service.T o uninstall the service, open the Control Panel , select Programs or Programs and Features , and then select Add/Remove Programs or Uninstall a Programto remove the service. The file name isHPSmartDeviceAgentBase.Mobile printing solutionsHP offers multiple mobile printing solutions to enable easy printing to an HP printer from a laptop, tablet, smartphone, or other mobile device.T o see the full list and to determine the best choice, go to /go/MobilePrinting .NOTE:Update the printer firmware to ensure all mobile printing capabilities are supported.●Wi-Fi Direct (wireless models only, with HP Jetdirect 3100w BLE/NFC/Wireless accessory installed)●HP ePrint via email (Requires HP Web Services to be enabled and the printer to be registered with HP Connected)●HP Smart app ●Google Cloud Print12Chapter 1 Printer overview。
Lec10
Existence of NE
• Since any dynamic game has a (unique) normal-form representation, at least one NE exist as long as a game is finite, i.e., finite number of players and strategies. • If some of the paths in the game tree involve infinite stages (information set), then the corresponding normal-form game is no longer finite. The dynamic game may not have a NE!
SPNE
• A subgame perfect Nash equilibrium (SPNE) is a combination of strategies in a extensive-form which constitutes a Nash equilibrium in every subgame. Since the entire game itself is a subgame, it is obvious that a SPNE is a NE, i.e., SPNE is stronger solution concept than NE.
ECO290E: Game Theory
Lecture 10 Examples of Dynamic Games
Review of Lec. 8 & 9
• A strategy in a dynamic game is a complete plan of actions, i.e., specifying what she will do in every her information set. • Dynamic games may have many Nash equilibria, but some of these may involve non-credible threats or promises. The subgame perfect Nash equilibria are those that pass a credibility test.
第三章 完全信息动态博弈
定义：一个扩展式博弈的子博弈 由一个决策结 定义 一个扩展式博弈的子博弈G由一个决策结 一个扩展式博弈的子博弈 x和所有该决策结的后续结 和所有该决策结的后续结T(x)（包括终点结） 和所有该决策结的后续结 （包括终点结） 组成，它满足下列条件： 组成，它满足下列条件： 是一个单结信息集， （1）x是一个单结信息集，即h(x)={x} ） 是一个单结信息集 （2）对于所有的 1∈T(x), ）对于所有的x 如果x＂ 如果 ＂∈h(x1)，那么 ＂∈T(x) ，那么x＂
（一）纯战略均衡
如果对于任意一个参与人i，si*使ui(si，s*-i)取 得极大值，即
s ∈ arg max u( si , s ), ∀i
* i si ∈Si * −i
那么，战略组合s*是扩展式博弈的一个纳什 均衡。
（二）行为战略均衡
1、“行为战略”（behavior strategies）
A 开发 N 大 1/2 B 小 1/2 不开发 N 大 1/2 B 小 1/2 B
不开发 B 不开发 开发 不开发 开发 开发 开发 不开发 (0, 1) (0, 0) (4, 4) (8, 0) (0, 0) (-3, -3) (1, 0) (0, 8) 图2.1 房地产开发博弈
（一）博弈树的构件 1、结(nodes)
同一信息集的表示法：知道自然的选择，但不知道参与人A的选 择
用数学式表述
– H代表所有信息集的集合； – h代表一个特定的信息集，即h∈H； – h(x)表示包含决策结x的信息集，它表示在x点决策 的参与人i不确定他是处在x，还是处在其它 x ’∈h(x)。如果x’∈h(x)，那么x∈h(x ’)。 同一信息集满足下列条件 ：
3、等价性定理（Kuhn,1953）：
Gam混合策略纳什均衡求解
STATIC GAME THEORY
Solution using equilibrium
Finding pure-strategy Nash equilibriums: a) Stage 1: Identify each player’s optimal strategy in response to what the other player might do. b) Stage 2: A Nash equilibrium is identified when all players are playing their optimal strategies simultaneously.
INTRODUCTION
What is game theory?
Game theory is a mathematical theory that
deals with the general features of competitive situations, such as military battles, political campaigns, advertising and marketing campaigns by competing business firms.
STATIC GAME THEORY
Mixed-strategy of Nash equilibrium (v=4, w=3,
g=2, h=1)
x
Shirk
Agent 1
1- x
Work
Principal 2 y Inspect
-1,0
0, 1
1- y Not Inspect
-3, 3
博弈论最全完整-讲解
“乘客侧前轮”看起来是一个合乎逻辑的选择。 但真正起作用的是你的朋友是否使用同样的
逻辑，或者认为这一选择同样显然。并且是 否你认为这一选择是否对他同样显然；反之， 是否她认为这一选择对你同样显然。……以 此类推。 也就是说，需要的是对这样的情况下该选什 么的预期的收敛。这一使得参与者能够成功 合作的共同预期的策略被称为焦点。心有灵 犀一点通。
例3：为什么教授如此苛刻？
问题是，一个好心肠的教授如何维持如 此铁石心肠的承诺？
他必须找到某种使拒绝变得强硬和可信 的方法。
拿行政程序或者学校政策来做挡箭牌 在课程开始时做出明确和严格的宣布 通过几次严打来获得“冷面杀手”的声
誉
导论
博弈均衡与一般均衡 博弈论与诺贝尔经济学奖获得者
博弈论的基本概念与类型 主要参考文献
即使决策或行动有先后，但只要局中人 在决策时都还不知道对手的决策或者行 动是什么，也算是静态博弈
完全信息博弈与不完全信息博弈
(games of complete information and games of incomplete information)
按照大家是否清楚对局情况下每个 局中人的得益。
“各种对局情况下每个人的得益是 多少” 是所有局中人的共同知识 （common knowledge）。
据“共同知识”的掌握分为完全信 息与不完全信息博弈。
完美信息博弈与不完美信息博弈
(games with perfect information and games with imperfect information)
了解自己行动的限制和约束，然后以精心策划的方式 选择自己的行为，按照自己的标准做到最好。 • 博弈论对理性的行为又从新的角度赋予其新的含义— —与其他同样具有理性的决策者进行相互作用。 • 博弈论是关于相互作用情况下的理性行为的科学。
博弈论最全完整-讲解
问题是，大家都这么做。这样一来，所有人 的成绩都不比大家遵守协议来得高。而且， 大家还付出了更多的功夫。
正因为这样的博弈对所有参与者存在着或大 或小的潜在成本，如何达成和维护互利的合 作就成为一个值得探究的重要问题。
存在双赢的博弈吗？实用文档
6
例2：焦点博弈 “We Can’t Take the Exam,
获奖理由：在非合作博弈的均衡分析理 论方面做出了开创性的贡献，对博弈论 和经济学产生了重大影响 。
实用文档
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约翰·纳什 1928年生于美国
莱因哈 德·泽 尔腾， 1930 年生于 德国
实用文档
约翰· 海萨尼 1920年 生于美 国
18
1996年诺贝尔经济学奖获得者
英国人詹姆斯·莫里斯 (James A. Mirrlees)和美国人威廉-维克瑞 (William Vickrey)
获奖理由：前者在信息经济学理论领域做 出了重大贡献，尤其是不对称信息条件 下的经济激励理论的论述；后者在信息 经济学、激励理论、博弈论等方面都做 出了重大贡献。
实用文档
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威廉·维克瑞， 1914-1996， 生于美国
詹姆斯·莫里斯 1936年生于英 国
实用文档
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2001年诺贝尔经济学奖获得者
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第一章 完全信息静态博弈
博弈论的基本概念及战略式表述 纳什均衡
纳什均衡应用举例 混合战略纳什均衡 纳什均衡的存在性与多重性
实用文档
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第一节 博弈论的基本概念
与战略式表述
Байду номын сангаас
实用文档
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博弈论的基本概念与战略式表述
博弈论（game theory）是研究决策主体的行 为发生直接相互作用时候的决策以及这种 决策的均衡问题。
博弈论第二章——博弈规则
U1f(f,z)=1 盖 U1f(f,f)=-1 硬
▪ U2z(z,z)=-1
币 方
-1
U2z(f,z)=1
U2f(z,f)=1
U2f(f,f)=-1
猜硬币游戏
猜硬币方-2 正面z 反面f
正面z -1,1 1,-1 反面f 1，-1 -1,1
Uz= U1z+ U2z=-1+1-1+1=0
Uf= U1f+ U2f=1-1+1-1=0
2.2.1 博弈中的博弈方
博弈方（player/ players） 博弈中独立决策、独立承担博弈结
果的个人或组织称为博弈方。 1.单人博弈 2.双人博弈 3.多人博弈
1.单人博弈
设有一商人要从A地运输一批货物， 从A地到B地有水、陆两条路线， 走陆路运输成本10 000元，而走水 路运输成本只要7000元。但非常危 险，出现坏天气的概率为0.25，此 时会损失10%的货物。货物总价值 90 000元。
参考书目
1. [美]阿维纳什·K ·迪克西特.策略思维.中国人民大 学出版社，2002
2. 王则柯. 新编博弈论平话. 中信出版社，2003 3. 谢识予.经济博弈论(第二版) .复旦大学
出版社，2002
4. [美]埃里克·拉斯缪森.博弈与信息：博弈论概论. 北京大学出版社，2003
5.张维迎.博弈论与信息经济学.上海三联书店， 2004
第二章 博弈论基本知识
2.1 什么是博弈论 2.2 博弈的结构和分类 2.3 博弈的表达方式 2.4 几类经典的博弈模型
第一节 什么是博弈论
2.1.1 从游戏到博弈 2.1.2 一个非技术性的定义 2.1.3 博弈论模型简介
2.1.1 从游戏到博弈
博弈论完整课件浙江大学Game Chapter5博弈论经典
Definition 满足要求1-4的策略和推断构成博弈 的完美贝叶斯均衡〔PBE〕。Gibbons
PBE:Consider a strategy profile for the players, As well as beliefs over the nodes at all informa -tion sets.These are called a perfect Bayesian equilibrium(PBE) if:(1)each player’s strategy specifies optimal actions, given his beliefs and the strategies of the other players and (2)the
“萨摩亚岛居民以文身的好差作为挑选武士 的标准〞
在波纳佩岛上，谁能种出特别大的山药，谁 的社会地位就高，谁就能赢得人们的尊敬并可 担任公共职务。
Signals:经济或其他活动中具有信息传递作用 的行为。
Signaling Mechanism:通过信号传递信息的过程。
Pooling-strategy separating-strategy Hybrid-strategy
Game Theory(5)
Dynamic Games of Incomplete Information PERFECT BAYESIAN EQUILIBRIUM
PBE<BNE <SNE<NE
在完全信息静态博弈中，有 PBE=BNE=SNE=NE
一、Introduction to PBE
如果一个博弈没有子博弈，那么子博弈精炼 的要求〔参与人的策略在每一个子博弈中 君构成NE的要求〕自然就得到满足，从 而在任何没有子博弈的博弈中，SNE=NE。
博弈论第五讲
information
• Harsanyi transformation (nature and types)
• Bayesian Nash Equilibrium • Mechanism design (*)
• Revelation principle • screening
Signaling Games:
Figure Illustrations
Yongqin Wang CCES, Fudan
Beer – Quiche
2
A Pooling equilibrium
3
A Separating equilibrium
4
A hybrid equilibrium
5
Job Market Signaling
11
A separating equilibrium
12
An intuitive separating equilibrium
(Cho-Kreps, 1987)
13
Costless signaling: cheap talk
Heuristics: for cheap talk to be informative:
17
Course review
Dynamic game of incomplete information
• Perfect Bayesian Equilibrium
• Requirements and definition
• Continuation equilibrium • The importance of beliefs
不完全信息动态博弈
不完全信息动态博弈不完全信息动态博弈（Dynamic Games with Incomplete Information）[编辑]什么是不完全信息动态博弈在动态博弈中，行动有先后次序；在不完全信息条件下，博弈的每一参与人知道其他参与人的有哪几种类型以及各种类型出现的概率，即知道“自然”参与人的不同类型与相应选择之间的关系，但是，参与人并不知道其他的参与人具体属于哪一种类型。
由于行动有先后顺序，后行动者可以通过观察先行动者的行为，获得有关先行动者的信息，从而证实或修正自己对先行动者的行动。
在不完全信息动态博弈一开始，某一参与人根据其他参与人的不同类型及其所属类型的概率分布，建立自己的初步判断。
当博弈开始后，该参与人就可以根据他所观察到的其他参与人的实际行动，来修正自己的初步判断。
并根据这种不断变化的判断，选择自己的策略。
[编辑]相关例子以下是几个关于不完全信息动态博弈的例子：1.黔驴技穷精炼贝叶斯均衡是完全信息动态博弈的子博弈精炼纳什均衡与不完全信息静态博弈的贝叶斯纳什均衡的结合。
贝叶斯方法是概率统计中的一种分析方法。
它是指根据所观察到现象的有关特征，并对有关特征的概率分布的主观判断（即先验概率）进行修正的标准方法。
中国著名成语故事黔驴技穷，就是贝叶斯方法思想的一个典型表达。
老虎没有见过驴子，因而不知道自己比驴子强还是弱。
老虎的战略是：如果自己弱，那就只能躲，如果自己强，那就吃驴子。
对于自己并不了解驴子，老虎的做法是不断试探，通过试探，修改自己对驴子的看法。
如果驴子表现温顺无能，老虎就认为驴子是美食的概率比较大，起初驴子没有反应，老虎认为驴子不像强敌，胆子越来越大。
后来驴子大叫，老虎以为驴子要吃它，吓的逃走，但后来想想，又觉得不一定，于是继续试探，直到驴子踢老虎，老虎才觉得驴子“仅此技耳”，于是采取自己强时的最优行动——吃驴子。
2.信号传递由于信息不完全，每个人都希望向对方传递对自己有利的信号。
比如，在招聘时，应聘者总是显示自己最好的一面。
（2，2）贝叶斯理性秘密共享方案
（2，2）贝叶斯理性秘密共享方案刘海;彭长根;田有亮;吕桢;刘荣飞【摘要】在理性秘密共享协议中，自利性目标可能会驱使理性参与者偏离协议，从而影响协议的公平性。
在（t， n）门限理性秘密共享方案中，其特殊情形（2，2）理性秘密共享方案的公平性较难实现。
在同时考虑理性参与者的眼前利益和长远利益的基础上，基于不完全信息动态博弈模型，通过分析理性参与者在（2，2）秘密重构阶段可能采取的策略和信念系统，引入理性参与者的期望收益，研究了（2，2）理性秘密共享重构阶段的完美贝叶斯均衡问题。
进一步结合机制设计理论中的VCG（Vickrey-Clarke-Groves）机制，设计激励相容的交互记录机制来约束理性参与者的行为，在不需要秘密分发者保持在线的情形下，提出一个适用于异步通信的公平的（2，2）理性秘密共享方案。
%The rational secret sharing isan intersection direction between the traditional secret sharing and game theory .In the rational secret sharing scheme,the selfishness maybe impels rational players to deviate from the protocols so as to influence the fairness of scheme .In the existing threshold rational secret sharing schemes,the fairness of (2,2)rational secret sharing scheme, which is a special case,is hard to be realized,especially implementing on the asynchronous communication channel .To achieve fair-ness of (2,2)rational secret sharing over the asynchronous communication channel,this paper firstly analyzes rational players’utili-ty by simultaneously discussing their short-term interest and long-term interest .Then through illustratingra tional players’available actions and belief systems,and computing their expected utilities with the dynamic games of incomplete information,theperfect Bayesian equilibrium for reconstruction phase of (2,2)rational secret sharing is studied.Furthermore,combining with the VCG (Vickrey-Clarke-Groves)mechanism of design theory,the incentive compatibility mechanism,which is named recording interaction, is designed to restrict the behavior of rational players.Consequently,the fair (2,2)rational secret sharing scheme is presented, which does not need the dealer to keep on-line over the asynchronous communication channel .【期刊名称】《电子学报》【年(卷),期】2014(000)012【总页数】8页(P2481-2488)【关键词】理性秘密共享;不完全信息;信念系统;完美贝叶斯均衡;机制设计【作者】刘海;彭长根;田有亮;吕桢;刘荣飞【作者单位】贵州大学理学院，贵州贵阳550025; 贵州大学密码学与数据安全研究所，贵州贵阳550025;贵州大学理学院，贵州贵阳550025; 贵州大学密码学与数据安全研究所，贵州贵阳550025;贵州大学理学院，贵州贵阳550025; 贵州大学密码学与数据安全研究所，贵州贵阳550025; 中国科学院信息工程研究所信息安全国家重点实验室，北京 100093;贵州大学理学院，贵州贵阳550025; 贵州大学密码学与数据安全研究所，贵州贵阳550025;贵州大学理学院，贵州贵阳550025; 贵州大学密码学与数据安全研究所，贵州贵阳550025【正文语种】中文【中图分类】TP309;TN9181 引言（t，n）门限秘密共享是针对密钥管理中密钥的泄露问题和遗失问题提出的一种分发、保存和恢复密钥的方法.它最早是于1979年由Shamir［1］和Blakey［2］分别基于拉格朗日插值法和几何空间中点的性质提出的.在传统的秘密共享方案中，参与者都被假设为诚实的或恶意的.2004年，Halpern 和 Teague［3］将博弈论与秘密共享相结合，首次提出理性秘密共享的概念.在理性秘密共享方案中，参与者都是“理性”的.他们提出了基于随机交互次数的（t，n）理性秘密共享方案.但是，该方案不适用于（2，2）门限情况.2006年，Gordon和 Kazt［4］改进了Halpern和Teague的方案，引入活跃参与者，通过适当选取秘密分发者分发正确共享主秘密的概率，首次基于同步信道实现（2，2）理性秘密共享.随后，关于理性秘密共享的研究也取得了一定的成果［5～9］.然而，这些研究都是基于完全信息博弈模型展开的.2011年，Tian等［10］用贝叶斯博弈研究理性秘密共享方案中理性参与者不合作的问题，提出一个基于同步信道的一次理性秘密共享方案.2013年，Zhang等［11］首次将不完全信息博弈模型与理性秘密共享相结合，引入序贯均衡的概念用于设计理性秘密共享方案.然而，在他们的方案中，依然采用了同步信道，并要求秘密分发者保持在线.机制设计是考虑构造怎样的博弈，使得该博弈的均衡解是社会目标，主要涉及信息效率和激励相容两个方面的问题.激励相容是指在给定机制下，真实报告自己的个人信息是参与者的占优策略均衡.机制设计已被广泛的运用到计算机领域［12～14］.然而，在现有的理性秘密共享方案［15，16］的研究中，虽已多次使用“机制”一词，但都还未将机制设计的相关理论运用到理性秘密共享的研究中.本文首先结合文献［3］和文献［17］中两种不同的理性参与者偏好模型，同时考虑理性参与者的眼前利益和长远利益，分析理性参与者在既希望获得眼前利益又希望获得长远利益时的偏好收益.结合不完全信息动态博弈模型中的完美贝叶斯均衡，研究异步信道中，（2，2）不完全信息理性秘密共享重构阶段中参与者的信念系统，计算期望收益，分析完美贝叶斯均衡策略.引入VCG（Vickrey-Clarke-Groves）机制，设计一个有效约束理性参与者“自利性”行为的激励相容的交互记录机制，并基于该机制提出一个公平的（2，2）贝叶斯理性秘密共享方案.在该方案中利用拉格朗日插值法将子秘密拆分为影子秘密进行交互的方法，解决现有方案中要求理性秘密分发者保持在线的问题.2 准备知识2.1 完美贝叶斯均衡一个策略—信念系统组合（pure-s；ρ）是一个完美贝叶斯均衡［18］，如果它满足：（1）在每一个信息集中，行动的参与者必须对博弈进行到该信息集中的哪个节点有一个“推断”；（2）给定参与者的推断，参与者的策略必须满足序贯理性的要求；（3）在处于均衡路径之上的信息集中，由贝叶斯法则及参与者的均衡策略给出“推断”；（4）对处于均衡路径之外的信息集，由贝叶斯法则以及可能情况下的参与者的均衡战略决定“推断”.2.2 VCG机制VCG机制［19］是一类在拟线性效用环境下满足个人理性的策略一致机制.3 （2，2）理性秘密共享重构阶段的贝叶斯分析令P＝｛P1，P2｝为理性参与者集合，R＝｛r1，r2｝是参与者信誉值集合，其中ri是参与者Pi的信誉值.在本文中，假设理性参与者Pi拥有足够的耐性追求自己利益的最大化.假设理性参与者使用拉格朗日插值法将子秘密拆分成影子秘密后进行交互.当参与者Pi收到子秘密Si后，利用拉格朗日插值法将子秘密Si拆分成影子秘密si1和si2.若ri≤r－i，此时在秘密重构阶段参与者Pi率先将自己拥有的影子秘密传递给参与者P－i.当秘密重构完成后由P－i率先对ri进行修改（把P－i不改变ri认为是降低ri的一种特殊情况）.3.1 参与者偏好收益本文同时考虑理性参与者的眼前利益（是否获得共享主秘密）和长远利益（信誉值是否得到提高）.假设理性参与者Pi的收益如表1所示：表1 理性参与者的偏好收益Pi的收益 Pi是否获得秘密P－i是否获得秘密ri是否获提高r－i是否获提高Pi的收益Pi是否获得秘密P－i是否获得秘密ri是否获提高r－i是否获提高u（1）i 是否提高降低u（9）i 否否提高降低u（2）i 是否提高提高u（10）i 否否提高提高u（3）i 是是提高降低u（11）i 否是提高降低u（4）i 是是提高提高u（12）i 否是提高提高u（5）i 是否降低降低u（13）i 否否降低降低u（6）i 是否降低提高u（14）i 否否降低提高u（7）i 是是降低降低u（15）i 否是降低降低u（8）i 是是降低提高u（16）i 否是降低提高则对于参与者Pi来说，其偏好收益为：3.2 参与者类型令Θ＝Θ1×Θ2是理性参与者类型组合，其中Θi＝｝，表示参与者Pi（1≤i≤2）的类型空间.θhi 表示参与者Pi的类型是诚实的，θdi表示参与者Pi的类型是不诚实的.假设μi是理性参与者Pi（1≤i≤2）类型空间Θi的概率分布，则有：3.3 参与者策略和信念系统令A＝｛A1，A2｝表示理性参与者的行为集合，其中Ai＝｛ai1，ai2，ai3，ai4，ai5，ai6｝表示参与者 Pi 的行为集合.aij（1≤i，j≤2）表示参与者Pi传递正确的影子秘密sij给Pj；ai3（1≤i≤2）表示参与者Pi传递完整的子秘密Si给Pj；ai4（1≤i≤2）表示参与者Pi 退出协议；ai5（1≤i≤2）表示参与者Pi提高理性参与者Pj的信誉值；ai6（1≤i≤2）表示参与者Pi传递错误的影子秘密si1给Pj.用〈aik，ail〉表示参与者Pi在选择行为aik后，又立即选择行为ail.在（2，2）理性秘密共享重构博弈阶段中，不妨设r1≤r2，则（2，2）理性秘密共享重构阶段博弈如图1所示，其中“●”表示博弈终止.理性参与者P1的纯策略为：构阶段Stage 4采取的行为.利用“海萨尼转换”分析上述博弈.令“自然”N（用“○”表示）首先确定理性参与者P1的类型（如图2所示）.在上述贝叶斯博弈中，P2的信念是关于P1的行为的概率分布：3.4 理性参与者的期望收益令EU（θi，pure-si）表示理性参与者Pi 在其采用纯策略pure-si时的期望收益.则参与者P1在Stage 1时选择行为a11和a16的期望收益为：显然，.所以理性参与者P1 在Stage 1时将不会选择行为a16.同理，理性参与者P2在Stage 2时将不会选择行为a26.在（2，2）贝叶斯理性秘密共享重构博弈Stage 3时理性参与者P1的期望收益为：“≈”表示理性参与者的纯策略推论1 在上述（2，2）贝叶斯理性秘密共享博弈上述博弈中，将会选择行为a12；否则，就会选择行为a14.证明由上述式（1）和式（3）知，当 EU（θh1，｛a11，者P1由于其“自利性”，将会选择行为a12.在（2，2）贝叶斯理性秘密共享重构博弈Stage 4时理性参与者P2的期望收益为：推论2 在上述（2，2）贝叶斯理性秘密共享重构博，则理性参与者P2在上述博弈Stage 4时，将会选择行为〈a22，a25〉；否则，就会选择行为a24.证明由上述式（4）和式（8）知，当时，理性参与者由于其“自利性”，将会选择行为〈a22，a25〉；否则，就会选择行为a24.3.5 （2，2）贝叶斯理性秘密共享重构博弈完美贝叶斯均衡（2，2）理性秘密共享重构博弈的完美贝叶斯均衡是使得对于理性参与者P1在信息集，理性参与者P2在信息集处的行为是对于其余参与者的任意行为都是最优反应.因此，当（pure- s＊；ρ＊）＝（｛（a11，a12，a15）h，（a11，a12，a14）d ｝，｛（a21，〈a22，a25〉）h，（a21，〈a22，a25〉）d｝；ρ＊）是一个候选的完美贝叶斯均衡；当满足式（2）、（5）、（6）、（7）、（9）、（10）、（11），ρ＊＝（pure-s°；ρ°）＝（｛（a14）h，（a14）d｝，｛（a14）h，（a14）d｝；ρ°）也是一个候选的完美贝叶斯均衡.定理1 策略和信念系统组合（pure-s＊；ρ＊）是（2，2）贝叶斯理性秘密共享重构博弈完美贝叶斯均衡.证明先证参与者在每个信息集合中都有一个“推断”.在（2，2）理性秘密共享重构博弈Stage 2时，理性参与者P2选择αh＊1和αd ＊1，使得：所以理性参与者在每一个信息集合都有一个“推断”.再证给定参与者的“推断”，其策略满足序贯理性.令BG（2）表示理性参与者P2到达信息集I2后的博时，由式（4）、（8）知：EU（θ2，a21，BG（2））＞EU（θ2，a26，BG（2））；在（2，2）理性秘密共享重构博弈Stage 2时，P2相信P1其类型是θh1时，在Stage 1选择行为a11的概率是σh，选择行为a16的概率是ζh，则其选择行为a14的概率是1－σh－ζh.其中，当P2类型是时，选择行为a21的概率为ξh，选择行为a26的概率为ψh；当P2类型是时，选择行为a21的概率为ξd，选择行为a26的概率为ψd；对于不处于均衡路径上的信息集当P1在信息集时也具有：所以，策略和信念系统组合（pure-s＊；ρ＊）是（2，2）贝叶斯理性秘密共享重构博弈完美贝叶斯均衡.4 交互记录机制定义1（交互记录机制）交互记录机制M＝（˜Aj，i，ej，i），其中：（1表示参与者Pj 所记录的Pi在此次交互活动中所采取的行为，其中是参与者Pj记录Pi在第l（1≤l≤k）轮中所采取是策略；（2）ej，i表示在每次交互活动完成后，参与者 Pj（i≠j）根据本次交互活动对Pi 的交互记录评价.该评价对于所有参与者是公开可见的，参与者Pi无权对其进行修改.当交互完成后，理性参与者Pj（i≠j）根据本次交互活动记录Pi的行为，并对其进行评价ej，i.令λ＞0为一定理2 交互记录机制M＝（˜Aj，i，ej，i）是激励相容机制.证明理性参与者Pi在该机制下的收益为vi（a，θi）＝ui（a，θi）＋wiej，i，其中 wi 表示理性参与者Pi 对参与者Pj的评价ej，i的看重程度.社会选择函数：Soc（ai，ej，i）＝ui（a，θ）.其中，参与者的目标函数为：使得：ui（a，θ）≥uj（a，θ）.因此，由式（12）、（13）可知机制M＝（˜Aj，i，ej，i）满足VCG机制的分配规则和支付规则.所以，交互记录机制M＝（˜Aj，i，ej，i）是激励相容机制5 （2，2）贝叶斯理性秘密共享方案本文利用承诺函数来构造公平的（2，2）贝叶斯理性秘密共享方案.承诺函数C（·）是一个单向函数，可在确保秘密信息不被泄露的情况下，为秘密信息的正确性提供验证.为了简单，假设共享秘密S＝S1⊕S2时，承诺函数C（S）＝C（S1）⊕C（S2）.（1）秘密分发协议πDisStep1 Dealer选择拉格朗日多项式，将S拆分成S1和S2，并计算C（S），C （S1）和C（S2）；Step2 Dealer将Si秘密地发送给参与者Pi，并广播C（S），C（S1）和C（S2）；（2）秘密重构协议πRecStep1 参与者Pi将收到的子秘密Si用拉格朗日插值法将子秘密Si拆分成影子秘密si1和si2；Step2 若ri＝min｛r1，r2｝，则参与者Pi将影子秘密si1传递P－i，否则，参与者P－i将影子秘密s－i1传递给Pi；Step3 参与者P－i收到Pi传递的影子秘密si1后，传递影子秘密s－i1给Pi，否则，使用交互记录机制M，并返回Step1；Step4 参与者Pi收到P－i传递的影子秘密s－i1后，传递影子秘密si2给P－i，否则，使用交互记录机制M，并返回Step1；Step5 参与者P－i收到影子秘密si2后，重构子秘密S′i，验证 C（S′i）：如果 C （Si）＝C（S′i），则传递影子秘密s－i2给Pi，提升ri，否则，就执行交互记录机制M，并返回Step1；Step6 参与者Pi收到s－i2后，重构子秘密S′－i，验证C（S′－i）：如果C（S －i）＝C（S′－i），则提升r－i，使用交互记录机制M，否则，使用交互记录机制M；Step7 参与者P－i使用交互记录机制M.下面给出方案的公平性分析：（1）若Pi不发送影子秘密si1，则P－i将执行交互记录机制M，且Pi和P－i都无法得到共享秘密S.此时，Pi（2）若Pi发送错误的影子秘密si1时，则P－i将执行交互记录机制M，且Pi和P－i都无法得到共享秘密S.（3）若Pi发送错误的影子秘密si2或不发送影子秘（4）若Pi发送正确的影子秘密si2后，P－i不发送影子秘密s－i2、发送错误的影子秘密s－i2，或发送正确的影子秘密但降低ri时，Pi将执行交互记录机制M.此时，（5）若P－i发送正确的影子秘密s－i2并提高ri后，Pi降低r－i，则P－i执行交互记录机制M.此时，Pi 和P－i的（6）若Pi和P－i都正确的执行协议，则Pi和P－i的通过上述分析，可以发现对于理性参与者Pi和P－i来说，只有正确执行协议时，得到的收益最大，符合理性参与者的自利性.此时，理性参与者Pi和P－i均可既获得共享秘密又可提升自己的信誉值.综上所述，可得：定理3 基于交互记录机制M＝（˜Aj，i，ej，i）的（2，2）贝叶斯理性秘密共享方案是公平的.6 结论公平的（2，2）理性秘密共享方案是构建适用于理性环境的各类安全协议的基础模块，如利用（2，2）理性秘密共享方案设计理性多方计算协议［20］，理性交换协议［21］.本文通过理性参与者利用拉格朗日插值法将子秘密拆分成影子秘密进行交互的方法，有效地解决理性秘密分发者保持在线的问题.并利用海萨尼转换，分析理性参与者类型不确定的情况下在异步信道进行交互的信念，计算其期望均衡，给出（2，2）贝叶斯理性秘密共享重构阶段的完美贝叶斯均衡.并初步探讨结合机制设计理论中VCG机制，设计激励相容的交互记录机制，提出一个公平的（2，2）贝叶斯理性秘密共享方案.参考文献【相关文献】［1］SHAMIR A.How to share asecret［J］.Communications of the ACM，1979，22（11）：612－613.［2］BLAKLEY GR.Safeguarding cryptographic keys［A］.Smith M.Proceedings of the 1979 AFIPS National Computer Conference［C］.New York：AFIPS Press，1979.313－317. ［3］HALPERN J，TEAGUE V.Rational secret sharing and multiparty computation：extended abstract［A］.Calinescu G.Proceedings of the 36th Annual ACM Symposium on Theory of Computing［C］.New York：ACM Press，2004.623－632.［4］GORDON S D，KATZ J.Rational secret sharing revisited［A］.Yung M.LNCS4116：Proceedings of the 5th International Conference on Security and Cryptography for Networks［C］.Berlin：Springer Press，2006.229－241.［5］ABRAHAM I，DOLEV D，GONENEN R，et a1.Distributed computing meets game theory：robust mechanisms for rational secret sharing and multiparty computation ［A］.Ruppert E.Proceedings of the 25th Annual ACM Symposium on Principles of Distributed Computing［C］.New York：ACM Press，2006.53－62.［6］KATZ J.Bridging game theory and cryptography：recent results and future directions ［A］.Canetti R.LNCS4948：Proceedings of the 5th Conference on Theory of Cryptography［C］.Berlin：Springer Press，2008.251－272.［7］MALEKA S，SHAREEF A，RANGAN C.P.Rational secret sharing with repeated games ［A］.Susilo W.LNCS4991：Proceedings of the 4th International Conference on Information Security Practice and Experience［C］.Berlin：Springer Press，2008.334－346. ［8］ASHAROV G，LINDELL Y.Utility dependence in correct and fair rational secret sharing［A］.Halevi S.LNCS5677：Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology［C］.Berlin：Springer Press，2009.559－576.［9］田有亮，马建峰，彭长根.秘密共享体制的博弈论分析［J］.电子学报，2011，39（12）：32－46.TIAN You-liang，MA Jian-feng，PENG Chang－gen.Game-theoretic analysis forthe secret sharing scheme［J］.Acta Electronica Sinica，2011，39（12）：32－46.（in Chinese）［10］TIAN You-liang，MA Jian-feng，PENG Chang－gen，et al.One-time rational secret sharing scheme based on Bayesian game［J］.Wuhan University Journal of NaturalSciences，2011，16（5）：430－434.［11］ZHANG Zhi-fang，LIU Mu-lan.Rational secret sharing as extensive game［J］.Science China Information Sciences，2013，56（3）：1-13.［12］FEIGENBAUM J，PAPADIMITRIOU C，SAMI R，et al.A bgp-based mechanism for lowest-cost routing［J］.Journal of Distributed Computing，2005，18（1）：61－72. ［13］FEIGENBAUM J，SHENKER S.Distributed algorithmic mechanism design：recent results and future directions［A］.Marathe M.Proceedings of the 6th International Workshop on Discrete Algorithms and Methods for Mobil Computing and Communication［C］.New York：ACM Press，2002.1－13.［14］PARKES D，SHEIDMAN J.Distributed implementations ofvickrey-clarke-groves mechanisms［A］.Scerri P.Proceedings of the 3rd International Joint Conference on Autonomous Agents and Multi-Agent Systems［C］.Washington：IEEE Computer Society Press，2004.261－268.［15］DANIV，MOVAHEDI M，SAIA J.Scalable mechanisms for rational secret sharing ［A］.Fraigniaud P.Proceedings of the 30th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing［C］.New York：ACM Press，2012.187－196. ［16］JOYEE D S，ASIM K P.Achieving correctness in fair rational secret sharing［A］.Kanade T.LNCS8257：Proceedings of the 12th International Conference on Cryptology and Network Security［C］.Berlin：Springer Press，2013.139－161.［17］NOJOUMIAN M，STINSON D，GRAINGER M.Unconditionally secure social secret sharing scheme［J］.IET Information Security，2010，4（4）：202－211.［18］OSBORNE M，RUBINSTEIN A.A Course in Game Theory［M］.Cambridge：MIT Press，2004.［19］NISAN N，RONEN A.Algorithmic mechanism design［J］.Games and Economic Behavior，2001，35（1／2）：166－196.［20］GROCE A，KATZ J.Fair computation with rational players［A］.JohanssonT.LNCS7237：Proceedings of the 31st Annual International Conference on the Theory and Applications of Cryptographic Techniques［C］.Berlin：Springer Press，2012.81－98. ［21］张恩.理性信息交换密码协议若干模型及应用研究［D］.北京：北京工业大学计算机学院，2013.。
博弈论英文课件 (1)
(R1, R2) (R1, R2) (R1, R2) (R1, R2)
(R1, R2) (R1, L2) (L1, L2) (L1, L2)
(R1, R2) (R1, L2) (L1, L2) (L1, L2)
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Trigger strategy: step 1 cont’d
Stage 1 2
P2: Trigger P2: deviate trigger at t
(R1, R2) (R1, R2)
(R1, R2) (R1, R2)
t-1 t t+1 t+2
Ø
Recall that every subgame of the infinitely repeated game is identical to the infinitely repeated game as a whole
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Step 2 cont’d: subgame
1 L1 2 L2 1 L1 2 L2 1 1 2 R2 L2 5 0 0 5 (1, 1) R1 2 R2 L2 4 4 1 1 R2 (5, 0) L1 1 R1 2 R2 L2 5 0 0 5 2 R2 L2 4 4 1 1 L1 2 R2 L2 1 L2 (0, 5) R1 2 R2 L2 1 1 R1 2 R2 (4, 4) L1 1 R1 2 R2 L2 5 0 0 5
Player 2
Player 1
L1 R1
1 , 0 ,
L2
1 5
5 , 4 ,
R2
0 4
4
Example: subgame
1 2 L2 (1, 1) L1 R2 (5, 0) L2 (0, 5) R1 2 R2 (4, 4)
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2020/9/16
张醒洲，大连
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针锋相对策略
• 针锋相对(Tit-for-Tat) 策略
– 它使重复博弈以相互合作开始并在其后模仿对方的行动
C: C
( ∙, C )
D: D
( ∙, D )
2020/9/16
The strategy with the highest payoff was tit-for-tat, submitted by Anatol Rapoport, a member of the Department of Psychology of the Univ. of Tornoto.
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• Kreps, Milgrom, Roberts, and Wilson (1982) 证明声誉模型能为此现 象提供合理的解释。
2020/9/16
张醒洲，大连
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Axelrod’s 竞赛: 第二轮
• Axelrod 接着又进行了第二轮竞赛。这一次，他同时邀请了第一轮 竞赛的参赛者以及通过杂志广告招募的计算机程序员参加竞赛。参赛 者分别通报了第一轮的结果，最后提交了62个策略。这一轮比赛较第 一轮在运行时间上有些许的差别：每个博弈的长度由一定的概率决定 。最后，第二轮竞赛获胜的策略仍然是Anatol Rapoport的针锋相对 策略。
非完全信息动态博弈
2020/9/16
张醒洲，大连
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概要
• Axelrod’s 竞赛 • 一个理性的参与人和从一组人中抽取的一个人
– 两阶段一般囚徒困境 – 三阶段一般囚徒困境
2020/9/16
张醒洲，大连
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Axelrod’s竞赛: 第一轮
Robert Axelrod is a political scientist at the Univ. of Michigan. In the late 1970s, he invited some economists, psychologists, mathematicians, and sociologists familiar with the repeated Prisoner’s Dilemma to submit strategies (written in computer code) for a finitely repeated Prisoner’s Dilemma with payoffs of (3,3) for (C,C),(5,0) for (F,C), (0,5) for (C,F) and (1,1) for (F,F).
He received 14 entries, which he pitted against each other and against a strategy that randomly chooses C and F each with probability 1/2, in 200-fold repetitions of the game.
• 这个实验结果表明，在有限重复囚徒困境中经常会出现合作结果，特 别是在距博弈结束比较远的阶段。
• Kreps, Milgrom, Roberts, and Wilson (1982) 证明声誉模型能为此现 象提供合理的解释。
He paired each strategy against each of the others five times. Strategies could involve random choices, so a pair of strategies could generate different outcomes when paired repeatedly.
• This experimental evidence suggests that cooperation occurs frequently during finitely repeated Prisoners’ Dilemmas, especially in stages that are not too close to the end.
张醒洲，大连
5
Axebsequently ran a second tournament. He invited the participants in the first tournament to compete again and also recruited entrants by advertising in journals read by microcomputer users (a relatively small crowed in the early 1980s). Contestants were informed of the results of the first round. Sixty-two strategies were submitted. The contest was run slightly different this time: the length of each game was determined probabilistically. Again tit-fortat (again submitted by Anatol Rapoport) won.
张醒洲，大连
3
Axelrod’s竞赛: 第一轮
20世纪70年代后期，密歇根大学的政治科学家Robert Axelrod邀请 了一些熟悉重复囚徒困境博弈的经济学家、心理学家、数学家和社会学 家进行一个竞赛，参与竞赛的人以计算机程序的形式提交自己的策略。
他收到了14个程序，自动运行这些程序，与其他程序进行博弈,包括 一个博弈，其中参与人分别以1/2的概率选择策略 C (合作)和 F(坦白) 。博弈重复进行200次，博弈的胜利者是所有博弈中的支付累计值最 高的策略。