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Finite Automata in Undiscounted Repeated Games with Private Monitoring

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  • Julian Romero

Abstract

I study two-player undiscounted repeated games with imperfect private monitoring. When strategies are restricted to those implementable by nite automata, fewer equilibrium outcomes are possible. When only two-state automata are allowed, a simple strategy, "Win-Stay, Lose-Shift," leads to cooperation. WSLS has the nice property that it is able to endogenously recoordinate back to cooperation after an incorrect signal. I show that WSLS is essentially the only equilibrium that leads to cooperation in the in nitely repeated Prisoner's Dilemma game. In addition, it is also an equilibrium for a wide range of 2 x 2 games. I also give necessary and su cient conditions on the structure of equilibrium strategies when players can use strategies implementable by fnite automata.

Suggested Citation

  • Julian Romero, 2011. "Finite Automata in Undiscounted Repeated Games with Private Monitoring," Purdue University Economics Working Papers 1260, Purdue University, Department of Economics.
    • Handle: RePEc:pur:prukra:1260
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    References listed on IDEAS

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    Cited by:

    1. Daniel Monte & Maher Said, 2014. "The value of (bounded) memory in a changing world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 59-82, May.

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    More about this item

    Keywords

    Bounded Rationality; Finite Automata; Prisoner's Dilemma; Private Monitoring; Tit-For-Tat; Win-Stay Lose-Shift;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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