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Rationality and correctness in n-player games

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  • Lorenzo Bastianello
  • Mehmet S. Ismail

Abstract

There are two well-known sufficient conditions for Nash equilibrium in two-player games: mutual knowledge of rationality (MKR) and mutual knowledge of conjectures. MKR assumes that the concept of rationality is mutually known. In contrast, mutual knowledge of conjectures assumes that a given profile of conjectures is mutually known, which has long been recognized as a strong assumption. In this note, we introduce a notion of "mutual assumption of rationality and correctness" (MARC), which conceptually aligns more closely with the MKR assumption. We present two main results. Our first result establishes that MARC holds in every two-person zero-sum game. In our second theorem, we show that MARC does not in general hold in n-player games.

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  • Lorenzo Bastianello & Mehmet S. Ismail, 2022. "Rationality and correctness in n-player games," Papers 2209.09847, arXiv.org, revised Dec 2023.
    • Handle: RePEc:arx:papers:2209.09847
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    1. Battigalli, Pierpaolo & Bonanno, Giacomo, 1999. "Recent results on belief, knowledge and the epistemic foundations of game theory," Research in Economics, Elsevier, vol. 53(2), pages 149-225, June.
    2. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    3. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136, World Scientific Publishing Co. Pte. Ltd..
    4. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    5. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107401396.
    6. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    7. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    8. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107008915.
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    Cited by:

    1. Mehmet S. Ismail, 2022. "Exploring the Constraints on Artificial General Intelligence: A Game-Theoretic No-Go Theorem," Papers 2209.12346, arXiv.org, revised Nov 2023.

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