Game theoretic approach , Microeconomics

Game Theoretic Approach

This approach shows that cooperation may emerge even within the framework of the prisoner's dilemma (PD) game, where there is repeated interaction over time between different actors. This is examined in the light of recent developments of non-cooperative game theory. Game theorists have found conditions under which the mutual defection outcome would cease to be a unique possible equilibrium even within the basic framework of the PD game. In other words, they have set about demonstrating the possibility of cooperation without giving up the payoff structure characteristic of the PD.

The reason why cooperation may be consistent with self-interested behaviour is that the repetition of the game opens the door to the possibility of conditional cooperation and punishment. More precisely, to show that cooperation is possible, the assumption must be made that the game is repeated infinitely or that information is incomplete - there is some uncertainty about the others' strategies or about the length of the game (the game horizon is finite or indefinite). The explanation of the cooperative outcome in a non-cooperative PD game is presented in three steps in the following.

1. Repetition of the PD game is not by itself sufficient to make cooperation a possible outcome. Unconditional defection at all periods is the dominant strategy of this game. Indeed, when the game has a finite length, non- cooperation is the unique equilibrium outcome.

2. If the length of the game is infinite, cooperation becomes possible. In this case, it may be worthwhile giving cooperation a try. A similar possibility obtains when the length of the game is finite but indefinite. Here, 'tit for tat' is an equilibrium strategy, where tit-for-tat is based on the principle: start by choosing to cooperate and thereafter choose the action that the other player chooses.

3. For cooperation to succeed in this kind of game, it is crucial to assume that if the player for whom there is doubts that he could follow a tit-for-tat strategy ever deviates from that strategy, then he would be immediately considered as being rational by the other player and non-operation would ensue. This conclusion may also be reached if the number of rounds in the game is rather small. Yet, The probability that the other player can play only tit-for-tat strategy must be large enough if cooperation is to occur in a game that is not long repeated. If this requirement is met, there exists an equilibrium in which both players can cooperate.

Thus, in a non-cooperative game theory, cooperation is a possible outcome, especially when interactions among group users are frequent. However, this outcome is possible in a small group. In a society of large groups there is no internal mechanism to induce and sustain collective action. In such a society, cooperation can effectively be sustained, provided that an effective authority structure exists to provide the required leadership.

 

Posted Date: 12/18/2012 12:44:37 AM | Location : United States







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