Reaching Pareto Optimality in Prisoner’s Dilemma Using Conditional Joint Action Learning

Dipyaman Banerjee and Sandip Sen

We consider a repeated Prisoner’s Dilemma game where two independent learning agents play against each other. We assume that the players can observe each others’ action but are oblivious to the payoff received by the other player. Multiagent learning literature has provided mechanisms that allow agents to converge to Nash Equilibrium. In this paper we define a special class of learner called a conditional joint action learner (CJAL) who attempts to learn the conditional probability of an action taken by the other given its own action and uses it to decide its next course of action. We prove that when played against itself, if the payoff structure of Prisoner’s Dilemma game satisfies certain conditions, using a limited exploration technique these agents can actually learn to converge to the Pareto optimal solution that dominates the Nash Equilibrium, while maintaining individual rationality. We analytically derive the conditions for which such a phenomenon can occur and have shown experimental results to support our claim.

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