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Ontological foundation of Nash Equilibrium

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  • Pelosse, Yohan

Abstract

In the classical definition of a game, the players' hierarchies of beliefs are not part of the description. So, how can a player determine a rational choice if beliefs are initially nonexistent in his mind? We address this question in a three-valued Kripke semantics wherein statements about whether a strategy or a belief of a player is rational are initially indeterminate i.e. neither true, nor false. This ``rationalistic'' Kripke structure permits to study the ``mental states'' of players when they consider the perspectives or decision problems of the others, in order to form their own beliefs. In our main Theorem we provide necessary and sufficient conditions for Nash equilibrium in an n-person game. This proves that the initial indeterminism of the game model, together with the free will of rational players are at the origin of this concept. This equivalence result has several implications. First, this demonstrates that a Nash equilibrium is not an interactive solution concept but an intrinsic principle of decision making used by each player to shape his/her own beliefs. Second, this shows that a rational choice must be viewed in statu nascendi i.e. conceived as a genuine ``act of creation'' ex nihilo, rather than as a pre-determined decision, arising from an underlying history of the game.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 39934.

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Date of creation: Feb 2011
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Handle: RePEc:pra:mprapa:39934

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Related research

Keywords: Free will; Indeterminism; Lukasiewicz's three-valued logic; Player's perspective; Rationalistic frames; Relational truth-values; Three-valued Kripke semantics;

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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. Robert J. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Working Paper Archive 661465000000000377, David K. Levine.
  3. Sugden, Robert, 1995. "A Theory of Focal Points," Economic Journal, Royal Economic Society, vol. 105(430), pages 533-50, May.
  4. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
  5. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September.
  6. Rustichini, Aldo, 2005. "Neuroeconomics: Present and future," Games and Economic Behavior, Elsevier, vol. 52(2), pages 201-212, August.
  7. Brandenburger, Adam & Friedenberg, Amanda, 2008. "Intrinsic correlation in games," Journal of Economic Theory, Elsevier, vol. 141(1), pages 28-67, July.
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