＊Two suspects are arrested and charged with a crime. The police lack sufficient evidence to convict the suspects, unless at least one confesses.The police hold the suspects in separate cells and explain the consequences
＊理解完全信息静态博弈时要注意事项
１ Although we stated that in a normalform game the players choose their strategies simultaneously , this does not imply that the parties necessarily act simultaneously :it suffices that each choose his or her action without knowledge of the others’ choices, as would be the case “the prisoners’dilemma” if the prisoners reached decisions at arbitrary times (在任意时间)while in their separate cells.
that will follow from the actions they could take. If neither confesses then both will be convicted of a minor offense and sentenced to one year in jail. If both confess then both will be sentenced to jail five years. Finally, if one confesses but the other does not, then the confessor will be released immediately but the other will be sentenced to eight years in jail—five for the crime and a further three for obstructing justice(干扰司法)。
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 by G={S1, … ,Sn;u1, … , un}. 教材 Ｐ22
Chapter 1 完全信息静态博弈 Static Games of Complete Information In this chapter we consider games of the following simple form: first, the players simultaneously choose actions; then, the players receive payoffs that depend on the combination of actions just chosen. Within the class of such static (or simultaneous-move) games,we restrict attention to games of complete information. That
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We now turn to the general case. The normal-form representation of a game specifies: (1)the players in the game;(2)the strategies available to each player;(3)the payoff received by each player for each combination of strategies that could be chosen by the players.
is each player’s payoff function (the function that determines the players payoff from the combination of actions chosen by the players) is common knowledge among all the players. 教材P21
一、Normal-Form Representation of Games and Nash Equilibrium
(一)Normal-Form Representation of Games
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. We illustrate the normal-form representation with a classical example—The prisoners’ Dilemma.