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This paper addresses a mathematically tractable model of the Prisoner'sDilemma using the framework of active inference. In this work, we design pairsof Bayesian agents that are tracking the joint game state of their and theiropponent's choices in an Iterated Prisoner's Dilemma game. The specification ofthe agents' belief architecture in the form of a partially-observed Markovdecision process allows careful and rigourous investigation into the dynamicsof two-player gameplay, including the derivation of optimal conditions forphase transitions that are required to achieve certain game-theoretic steadystates. We show that the critical time points governing the phase transitionare linearly related to each other as a function of learning rate and thereward function. We then investigate the patterns that emerge when varying theagents' learning rates, as well as the relationship between the stochastic anddeterministic solutions to the two-agent system.

An analytical model of active inference in the Iterated Prisoner's Dilemma