  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.
