Ontological foundation of Nash Equilibrium
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.
|Date of creation:||Feb 2011|
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- Aumann, Robert & Brandenburger, Adam, 1995.
"Epistemic Conditions for Nash Equilibrium,"
Econometric Society, vol. 63(5), pages 1161-80, September.
- Rustichini, Aldo, 2005. "Neuroeconomics: Present and future," Games and Economic Behavior, Elsevier, vol. 52(2), pages 201-212, August.
- Brandenburger, Adam & Friedenberg, Amanda, 2008.
"Intrinsic correlation in games,"
Journal of Economic Theory,
Elsevier, vol. 141(1), pages 28-67, July.
- Adam Brandenburger & Eddie Dekel, 2014.
"Hierarchies of Beliefs and Common Knowledge,"
World Scientific Book Chapters,
in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41
World Scientific Publishing Co. Pte. Ltd..
- 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.
- Pierpaolo Battigali & Giacomo Bonanno, . "Recent Results On Belief, Knowledge And The Epistemic Foundations Of Game Theory," Department of Economics 98-14, California Davis - Department of Economics.
- Giacomo Bonanno & Pierpaolo Battigalli, 2003. "Recent Results On Belief, Knowledge And The Epistemic Foundations Of Game Theory," Working Papers 9814, University of California, Davis, Department of Economics.
- Robert J. Aumann, 2010.
"Correlated Equilibrium as an expression of Bayesian Rationality,"
Levine's Working Paper Archive
661465000000000377, David K. Levine.
- Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
- R. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Bibliography 513, UCLA Department of Economics.
- Sugden, Robert, 1995. "A Theory of Focal Points," Economic Journal, Royal Economic Society, vol. 105(430), pages 533-50, May.
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