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Strategies for sustaining cooperation and preventing exploitation by selfishagents in repeated games have mostly been restricted to Markovian strategieswhere the response of an agent depends on the actions in the previous round.Such strategies are characterized by lack of learning. However, learning fromaccumulated evidence over time and using the evidence to dynamically update ourresponse is a key feature of living organisms. Bayesian inference provides aframework for such evidence-based learning mechanisms. It is thereforeimperative to understand how strategies based on Bayesian learning fare inrepeated games with Markovian strategies. Here, we consider a scenario wherethe Bayesian player uses the accumulated evidence of the opponent's actionsover several rounds to continuously update her belief about the reactiveopponent's strategy. The Bayesian player can then act on her inferred belief indifferent ways. By studying repeated Prisoner's dilemma games with suchBayesian inferential strategies, both in infinite and finite populations, weidentify the conditions under which such strategies can be evolutionarilystable. We find that a Bayesian strategy that is less altruistic than theinferred belief about the opponent's strategy can outperform a larger set ofreactive strategies, whereas one that is more generous than the inferred beliefis more successful when the benefit-to-cost ratio of mutual cooperation ishigh. Our analysis reveals how learning the opponent's strategy throughBayesian inference, as opposed to utility maximization, can be beneficial inthe long run, in preventing exploitation and eventual invasion by reactivestrategies.

Inferring to C or not to C: Evolutionary games with Bayesian inferential strategies