Abstract
Infinite horizon discrete time non-cooperative games with observable actions of players and discounting of future single period payoffs are a suitable tool for analyzing emergence and sustainability of cooperation between all players because they do not contain the last period. A subgame perfect equilibrium is a standard solution concept for them. It requires only immunity to unilateral deviations in any subgame. It does not address immunity to deviations by coalitions. In particular, it does not rule out cooperation based on punishments of unilateral deviations that the grand coalition would like to forgive. We first briefly review concepts of renegotiation-proofness that rule out such forgiveness. Then we discuss the concept of strong perfect equilibrium that requires immunity to all deviations by all coalitions in all subgames. In games with only one level of players (e.g. members of the population engaged in the same type of competitive activity), it fails to exist when the Pareto efficient frontier of the set of single period payoff vectors has no sufficiently large flat portion. In such a case, it is not possible to punish unilateral deviations in a weakly Pareto efficient way. In games with two levels of players (e.g. members of two populations with symbiotic relationship, while activities within each population are competitive), it is possible to overcome this problem. The sum of benefits of all players during a punishment can be the same as when nobody is punished but its distribution between the two populations can be altered in favor of the punishers.
Highlights
IntroductionThe issue of emergence and sustainability of cooperation between human beings or animals (especially in populations whose members are originally quite egoistic) is one of the most interesting and important topics that can be studied using game theoretic models (see [1] for basic results in this field)
The issue of emergence and sustainability of cooperation between human beings or animals is one of the most interesting and important topics that can be studied using game theoretic models
A subgame perfect equilibrium developed by Selten [3] [4], is the standard solution concept used for infinite horizon discrete time non-cooperative games with discounting of future single period payoffs and observable actions
Summary
The issue of emergence and sustainability of cooperation between human beings or animals (especially in populations whose members are originally quite egoistic) is one of the most interesting and important topics that can be studied using game theoretic models (see [1] for basic results in this field). A stochastic game is the most complex case of an infinite horizon discrete time non-cooperative game In these games, the sets of players’ feasible actions and their payoff consequences in the future periods depend on players’ actions in the current period and on random factors. A subgame perfect equilibrium developed by Selten [3] [4], is the standard solution concept used for infinite horizon discrete time non-cooperative games with discounting of future single period payoffs and observable actions. It requires that no player can increase his average discounted single period payoff by a unilateral deviation in any subgame.
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