Recursive Markov Process for Iterated Games with Markov Strategies

2015/09/02 by Hidaka, Shohei
#60J20 #91A15 #91A60 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1509.00535

Abstract

The dynamics in games involving multiple players, who adaptively learn from their past experience, is not yet well understood. We analyzed a class of stochastic games with Markov strategies in which players choose their actions probabilistically. This class is formulated as a k^th order Markov process, in which the probability of choice is a function of k past states. With a reasonably large k or with the limit k → ∞, numerical analysis of this random process is unfeasible. This study developed a technique which gives the marginal probability of the stationary distribution of the infinite-order Markov process, which can be constructed recursively. We applied this technique to analyze an iterated prisoner's dilemma game with two players who learn using infinite memory.

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