David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Logic, Language and Information 4 (2):145-167 (1995)
We present an axiomatic approach for a class of finite, extensive form games of perfect information that makes use of notions like “rationality at a node” and “knowledge at a node.” We distinguish between the game theorist's and the players' own “theory of the game.” The latter is a theory that is sufficient for each player to infer a certain sequence of moves, whereas the former is intended as a justification of such a sequence of moves. While in general the game theorist's theory of the game is not and need not be axiomatized, the players' theory must be an axiomatic one, since we model players as analogous to automatic theorem provers that play the game by inferring (or computing) a sequence of moves. We provide the players with an axiomatic theory sufficient to infer a solution for the game (in our case, the backwards induction equilibrium), and prove its consistency. We then inquire what happens when the theory of the game is augmented with information that a move outside the inferred solution has occurred. We show that a theory that is sufficient for the players to infer a solution and still remains consistent in the face of deviations must be modular. By this we mean that players have distributed knowledge of it. Finally, we show that whenever the theory of the game is group-knowledge (or common knowledge) among the players (i.e., it is the same at each node), a deviation from the solution gives rise to inconsistencies and therefore forces a revision of the theory at later nodes. On the contrary, whenever a theory of the game is modular, a deviation from equilibrium play does not induce a revision of the theory
|Keywords||Game theory backwards induction common knowledge theory revision|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Cristina Bicchieri & Gian Aldo Antonelli (1995). Game-Theoretic Axioms for Local Rationality and Bounded Knowledge. Journal of Logic, Language and Information 4 (2):145-167.
Reinhard Selten (1998). Multistage Game Models and Delay Supergames. Theory and Decision 44 (1):1-36.
Boudewijn de Bruin (2008). Common Knowledge of Rationality in Extensive Games. Notre Dame Journal of Formal Logic 49 (3):261-280.
Cristina Bicchieri (1988). Backward Induction Without Common Knowledge. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:329 - 343.
Martin Dufwenberg & Johan Lindén (1996). Inconsistencies in Extensive Games. Erkenntnis 45 (1):103 - 114.
Cristina Bicchieri, Richard C. Jeffrey & Brian Skyrms (eds.) (1999). The Logic of Strategy. Oxford University Press.
Philip J. Reny (1988). Common Knowledge and Games with Perfect Information. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:363 - 369.
Cristina Bicchieri, Dalla Chiara & Maria Luisa (eds.) (1992). Knowledge, Belief, and Strategic Interaction. Cambridge University Press.
Robert C. Robinson (2006). Bounded Epistemology. Ssrn Elibrary.
Yanis Varoufakis (1993). Modern and Postmodern Challenges to Game Theory. Erkenntnis 38 (3):371 - 404.
Cristina Bicchieri (1993). Counterfactuals, Belief Changes, and Equilibrium Refinements. Philosophical Topics 21 (1):21-52.
Till Grüne‐Yanoff & Paul Schweinzer (2008). The Roles of Stories in Applying Game Theory. Journal of Economic Methodology 15 (2):131-146.
Eduardo Zambrano, Counterfactual Reasoning and Common Knowledge of Rationality in Normal Form Games.
Boudewijn de Bruin (2009). Overmathematisation in Game Theory: Pitting the Nash Equilibrium Refinement Programme Against the Epistemic Programme. Studies in History and Philosophy of Science Part A 40 (3):290-300.
Jelle de Boer (2013). A Stag Hunt with Signalling and Mutual Beliefs. Biology and Philosophy 28 (4):559-576.
Added to index2010-12-22
Total downloads13 ( #125,691 of 1,099,958 )
Recent downloads (6 months)5 ( #67,010 of 1,099,958 )
How can I increase my downloads?