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Equilibrium payoffs in repeated two-player zero-sum games of finite automata

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  • O. V. Baskov

    (Saint Petersburg State University
    Higher School of Economics
    Saint Petersburg State Electrotechnical University)

Abstract

Repeated two-player zero-sum games of finite automata are studied. The players are charged a penalty proportional to the size of their automata to limit the complexity of strategies they can use. The notion of bounded computational capacity equilibrium payoff is thus transferred to the case of zero-sum games. It is proved that the set of bounded computational capacity equilibrium payoffs contains exactly one value, namely the value of the one-shot game, or, equivalently, that the value of the game with penalty approaches the value of the one-shot game as the penalty goes to zero. An estimate of the rate of convergence is also provided.

Suggested Citation

  • O. V. Baskov, 2019. "Equilibrium payoffs in repeated two-player zero-sum games of finite automata," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 423-431, June.
    • Handle: RePEc:spr:jogath:v:48:y:2019:i:2:d:10.1007_s00182-018-0634-x
    DOI: 10.1007/s00182-018-0634-x
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    References listed on IDEAS

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    5. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-1281, November.
    6. Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, vol. 39(1), pages 83-96, June.
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