A One-Person Doxastic Characterization of Nash Strategies

A One-Person Doxastic Characterization of Nash Strategies

Within a formal epistemic model for simultaneous-move games, we present the following conditions: (1) belief in the opponents' rationality (BOR), stating that a player believes that every opponent chooses an optimal strategy, (2) self-referential beliefs (SRB), stating that a player believes th...

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Veröffentlicht in:Synthese. - Springer Science + Business Media. - 158(2007), 2, Seite 251-271
1. Verfasser: Perea, Andrés (VerfasserIn)
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2007
Zugriff auf das übergeordnete Werk:Synthese
Schlagworte:Nash equilibrium Epistemic game theory Mathematics Philosophy Economics Behavioral sciences
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520 |a Within a formal epistemic model for simultaneous-move games, we present the following conditions: (1) belief in the opponents' rationality (BOR), stating that a player believes that every opponent chooses an optimal strategy, (2) self-referential beliefs (SRB), stating that a player believes that his opponents hold correct beliefs about his own beliefs, (3) projective beliefs (PB), stating that i believes that j's belief about k's choice is the same as i's belief about k's choice, and (4) conditionally independent beliefs (CIB), stating that a player believes that opponents' types choose their strategies independently. We show that, if a player satisfies BOR, SRB and CIB, and believes that every opponent satisfies BOR, SRB, PB and CIB, then he will choose a Nash strategy (that is, a strategy that is optimal in some Nash equilibrium). We thus provide a sufficient collection of one-person conditions for Nash strategy choice. We also show that none of these seven conditions can be dropped. 
540 |a Copyright 2007 Springer 
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952 |d 158  |j 2007  |e 2  |h 251-271