Pelosse, Yohan (2011): Ontological foundation of Nash Equilibrium.

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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 threevalued 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 nperson 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 predetermined decision, arising from an underlying history of the game.
Item Type:  MPRA Paper 

Original Title:  Ontological foundation of Nash Equilibrium 
Language:  English 
Keywords:  Free will; Indeterminism; Lukasiewicz's threevalued logic; Player's perspective; Rationalistic frames; Relational truthvalues; Threevalued Kripke semantics 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games 
Item ID:  39934 
Depositing User:  Yohan Pelosse 
Date Deposited:  09. Jul 2012 03:11 
Last Modified:  13. Feb 2013 02:01 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/39934 