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A Note on the Consistency of Game Theory

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  • Itzhak Gilboa

Abstract

It has been claimed in the literature that classical game theory is inconsistent, since it (implicitly) assumes that all players are rational and that this is common knowledge among them, while these two assumptions seem to be contradictory. The purpose of this note is to suggest a framework which allows the formalization of these implicit axioms in a consistent way. The main idea is to distinguish between conceivable and possible states of the world, while both exist as formal objects in the theory. Thus we may require that the players would make rational choices only at possible states of the world, and that this fact be common knowledge at all (conceivable) states, where the impossible ones are present in the model for the sole purpose of formally presenting the players' reasoning. It seems that the new concept of possible states of the world is an analytical tool which may have further (theoretical) applications.
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  • Itzhak Gilboa, 1989. "A Note on the Consistency of Game Theory," Discussion Papers 847, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:847
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    References listed on IDEAS

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    1. Kreps, David M. & Milgrom, Paul & Roberts, John & Wilson, Robert, 1982. "Rational cooperation in the finitely repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 27(2), pages 245-252, August.
    2. Ehud Kalai & Eitan Zemel, 1988. "On The Order of Eliminating Dominated Strategies," Discussion Papers 789, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, vol. 1(1), pages 5-39, March.
    4. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    5. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    6. Werlang, Sérgio Ribeiro da Costa, 1988. "Common knowledge," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 118, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    7. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August.
    8. Gilboa, Itzhak & Schmeidler, David, 1988. "Information dependent games : Can common sense be common knowledge?," Economics Letters, Elsevier, vol. 27(3), pages 215-221.
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    1. Itzhak Gilboa, 1991. "Rationality and Ascriptive Science," Discussion Papers 943, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

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