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- Title
A one-person doxastic characterization of Nash strategies.
- Authors
Andrés Perea
- Abstract
Abstract  Within a formal epistemic model for simultaneous-move games, we present the following conditions: (1) belief in the opponentsâ 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 jâs belief about kâs choice is the same as iâs belief about kâs choice, and (4) conditionally independent beliefs (CIB), stating that a player believes that opponentsâ 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.
- Subjects
BOARD games; GAMES; GAMEBOARDS; BACKGAMMON
- Publication
Synthese, 2007, Vol 158, Issue 2, p251
- ISSN
0039-7857
- Publication type
Article
- DOI
10.1007/s11229-007-9217-2