Understanding how cooperation can emerge in a population whose individual members are only interested in maximizing their personal well-being is one of the fundamental problems in economics, social sciences and evolutionary biology. The ever present temptation to not cooperate (thereby avoiding the associated cost) while enjoying the benefits of the cooperative acts of others appears to make it unlikely that cooperation will persist - even if it somehow arises occasionally by chance. Yet cooperation is seen to occur widely in society and forms the basis for complex economic organizations of the present era. The conventional theoretical approach to the problem, based on analysis of games such as the Prisoners Dilemma (PD), suggests that rational individuals will not cooperate even in situations where mutual cooperation may result in a better outcome for all. This incompatibility between individual rationality and collective benefit lies at the heart of the puzzle of evolution and robustness 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 have 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. The co-action equilibrium results in radically different collective outcomes (compared to Nash) 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 (such as reciprocity or reputation) for promoting it. When extended to an iterative situation, we show that even in the absence of initial symmetry among agents, their behavior can converge to cooperation as a result of repeated interactions. In particular, the co-action solution for the iterative PD between 2 players corresponds to a win-stay, lose-shift behavioral rule, thereby providing a rational basis for this Pavlovian strategy. 

References:

Sasidevan, V., and Sitabhra Sinha. "Symmetry warrants rational cooperation by co-action in Social Dilemmas." Scientific reports 5 (2015): 13071.

Sasidevan, V., and Sitabhra Sinha. "Co-action provides rational basis for the evolutionary success of Pavlovian strategies." Scientific Reports 6 (2016): 30831.

Sasidevan, V., and Sitabhra Sinha. "A Dynamical View of Different Solution Paradigms in Two-Person Symmetric Games: Nash Versus Co-action Equilibria." in F Abergel et al (Eds) Econophysics and Data Driven Modelling of Market Dynamics. Springer International Publishing, 2015: 213-223.

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