第六章博弈论初步详解

L U Player A D (4,5) (3,3) R (2,3)
(3,2)
Different results
According to maxmin principle, the equilibria solution is (D,R); While the nash equilibria solution of this example is (D,L) Which is better?

Some Applications of Game Theory
The study of oligopolies (industries containing only a few firms) The study of cartels; e.g. OPEC The study of externalities; e.g. using a common resource such as a fishery. The study of military strategies.

An Example of a Two-Player Game
The players are called A and B. Player A has two strategies, called “Up” and “Down”. Player B has two strategies, called “Left” and “Right”. The table showing the payoffs to both players for each of the four possible strategy combinations is the game’s payoff matrix.

An Example of a Two-Player Game
Player B
L U Player A D (0,0) (2,1) R
(3,9) (1,8)
二、博弈的分类

以结果为依据：

零和博弈（zero sum game） 正和博弈（positive sum game） 负和博弈（negative sum game） 合作博弈（cooperative game） 非合作博弈（noncooperative game）

The Prisoner’s Dilemma

To see if Pareto-preferred outcomes must be what we see in the play of a game, consider a famous second example of a two-player game called the Prisoner’s Dilemma.
Player B L R U
(3,9) (1,8)
(0,0) (2,1)
Player A
D
Nash Equilibrium
A play of the game where each strategy is a best reply to the other is a Nash equilibrium. Our example has two Nash equilibria; (U,L) and (D,R).
第六章 博弈论初步
内容提要
概述 完全信息静态博弈 完全信息动态博弈 不完全信息静态博弈 不完全信息动态博弈

博弈论（Game Theory）

Game theory models strategic behavior by agents who understand that their actions affect the actions of other agents.

一、博弈的三要素

A game consists of

a set of players a set of strategies for each player the payoffs to each player for every possible list of str
J.Von.Neumann(1903-1957)
计算机之父； 天才的数学家； 数理经济学奠基人。 代表作品：《博弈论 与经济行为，经济学 领域的革命》，（与 摩根斯坦合著，1944）

John.Nash(1928_)
1948年进入普林斯顿 大学攻读数学博士学 位； 1950-51年提出纳什均 衡； 1958年患精神分裂症； 1994年获诺贝尔经济 学奖。

An Example of a Two-Player Game
Player B L R U Player A D
(3,9) (1,8)
(0,0) (2,1)
(U,L) and (D,R) are both Nash equilibria for the game.
An example
Player B

是否能达成协议

博弈的分类

博弈的次数

重复博弈 非重复博弈

博弈的次序


静态博弈（static game） 动态博弈（dynamic game）
完全信息 不完全信息

拥有的信息

三、均衡解
最大最小均衡 纳什均衡

An Example of a Two-Player Game
The Prisoner’s Dilemma
Clyde S S Bonnie (-5,-5) C (-30,-1)
C (-1,-30) (-10,-10)
What plays are we likely to see for this game?
Two-Player Games
A game with just two players is a twoplayer game. We will study only games in which there are two players, each of whom can choose between only two strategies.