Cooperative equilibria in the finite iterated prisoner's dilemma

Nash equilibria are defined using uncorrelated behavioural or mixed joint probability distributions effectively assuming that players of bounded rationality must discard information to locate equilibria. We propose instead that rational players will use all the information available in correlated distributions to constrain payoff function topologies and gradients to generate novel 'constrained' equilibria, each one a backwards induction pathway optimizing payoffs in the constrained space. In the finite iterated prisoner's dilemma, we locate constrained equilibria maximizing payoffs via cooperation additional to the unconstrained (Nash) equilibrium maximizing payoffs via defection. Our approach clarifies the usual assumptions hidden in backwards induction.