SchellingのkとESS

抄録

This paper is concerned withN-person Prisoners' Dilemma in which every player has a dominant strategyd (defecting) but if every player uses his dominant strategy the outcome is Pareto-inferior.
T. Schelling (1973) brought to attention the minimum size of any coalition that can gain by abstaining fromdin his definition ofN-person Prisoners' Dilemma and called this sizek. And he argued thatkplayers can be better off by abstaining from d, so they will cooperate.
M. Taylor (1987) criticized Schelling fo having removed the“dilemma”in the Prisoners' Dilemma and left open the question of whether the sizekinfluences a player's incerrtive to cooperate.
Cankinfluence a player's incentive to cooperate?
In pure strategykcannot influence a player's incentive. Becausedis a dominant strategy.
P. Molander (1992), on the other hand, showed in his theorem that the mixed strategy, consisting of both conditional cooperation influenced bykand unconditional defection, is Evolutionarily Stable Strategy (Maynard Smith (1974) ) in a dynamic model.
I show his theorem in a simplified model and make clear the role of Schelling'skin the process of reaching the equilibrium.
The results is as follows:
(1) Schelling's k influences a player's incentive to cooperate in mixed strategy and to take strategy containing cooperation is rational from the standpoint of payoff maximization.
(2) The equilibrium reached by the mixed strategies has robustness in that it resists invasion from other strategies.
This can be an answer to the open question that M. Taylor proposed.