Cooperation among rational agents in co-action equilibrium of Prisoner's Dilemma and other single-stage symmetric games

The conventional solution concept used for solving non-cooperative games is that of the Nash equilibrium - a strategy choice by each player so that no player can do better by deviating unilaterally from it. In this paper, we propose an alternative framework referred to as the co-action equilibrium for solving such games. This equilibrium is guaranteed to exist for all games having a symmetric payoff structure. It also has the advantage of being unique for a given game. We analyze in detail three well-known two-person single-stage games, viz., Prisoner's Dilemma (PD), Chicken and Stag Hunt, to illustrate the differences between Nash and co-action solutions. The latter, in general, lead to "nicer" strategies being selected by the agents resulting in globally more efficient outcomes. For example, the co-action equilibrium in PD corresponds to full cooperation among agents at lower values of temptation to defect, while for higher temptation each agent employs a probabilistic (or mixed) strategy, thus essentially solving the dilemma. The key idea underlying the co-action solution is that agents make independent choices from the possible actions available, taking into account that other agents will behave the same way as them and they are also aware of this. It defines a new benchmark strategy for agents in non-cooperative games which is very different from the existing ones. The concept can be generalized to game situations where the symmetry assumption does not hold across all agents by clustering players into different symmetry groups that results in a novel class of games.