Adaptation in a stochastic prisonerʹs dilemma with delayed information

Players in a Prisonerʹs Dilemma are modeled as learning automata that receive feedback from the environment and coadaptively adjust their strategies. Theory and simulations show the coevolutionary dynamics of the reward-inaction and reward-penalty schemes. The players are assumed to be physically distributed or, at least, in an environment where the effects of decisions are lagged. These systems include biological and social systems with constraints on instantaneous information or where environmental responses do not necessarily reflect the true state of the system. Linear stability analysis determines the conditions for persistent oscillations in the playersʹ mixed strategies. Using a parameterized stochastic version of the dilemma, the results indicate that if the environment modifies the payoffs, and thus ‘releases’ the prisoners from their dilemma, the prisoners become prone to instabilities in their strategies given sufficient delays. Again, the prisoners fail to coordinate their actions.