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Markovian Analysis of a Small Population Evolutionary Prisoner’s Dilemma Game

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  • Athanasios Kehagias

    (Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, University Campus, 54124 Thessaloniki, Greece)

Abstract

In this work we consider an evolutionary game in which a small population repeatedly plays the Iterated Prisoner’s Dilemma (IPD) game using the pairwise proportional imitation (PPI) revision protocol. Since we are dealing with a small population, we can explicitly formulate a Markov chain (MC) model of the evolutionary game and study its properties. In particular, we identify the absorbing states and their basins of attraction . In addition, we briefly study the replicator dynamics of the same game for the case of a large population. We find that, as the size of the population increases, the Markovian dynamics approximate the replicator dynamics.

Suggested Citation

  • Athanasios Kehagias, 2026. "Markovian Analysis of a Small Population Evolutionary Prisoner’s Dilemma Game," Games, MDPI, vol. 17(4), pages 1-22, June.
    • Handle: RePEc:gam:jgames:v:17:y:2026:i:4:p:34-:d:1975910
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