Resolving Social Dilemmas using Symmetry: The co-action solution for non-cooperative games

Is it rational for selfish individuals to cooperate? The conventional answer based on analysis of games such as the Prisoners Dilemma (PD) is that it is not, even though mutual cooperation results in a better outcome for all. This incompatibility between individual rationality and collective benefit lies at the heart of questions about the evolution of cooperation, as illustrated by PD and similar games. We have recently shown that this apparent incompatibility is due to an inconsistency in the standard Nash framework for analyzing non-cooperative games and proposed a new paradigm, that of the co-action equilibrium. As in the Nash solution, agents know that others are just as rational as them and taking this into account leads them to realize that others will independently adopt the same strategy, in contrast to the idea of unilateral deviation central to Nash equilibrium thinking. Co-action equilibrium results in better collective outcomes for games representing social dilemmas, with relatively “nicer” strategies being chosen by rational selfish individuals. In particular, the dilemma of PD gets resolved within this framework, suggesting that cooperation can evolve in nature as the rational outcome even for selfish agents, without having to take recourse to additional mechanisms for promoting it. When extended to an iterative situation, we show that even in the absence of initial symmetry agents can converge to cooperative state as a result of repeated interactions. In particular, the iterative PD for 2 players the co-action solution corresponds to a win-stay, lose-shift behavioral rule, thereby providing a rational basis for this Pavlovian strategy.