Proper Rationalizability and Belief Revision in Dynamic Games
Abstract
In this paper we develop an epistemic model for dynamic games in which players may revise their beliefs about the opponents'' preferences (including the opponents'' utility functions) as the game proceeds. Within this framework, we propose a rationalizability concept that is based upon the following three principles: (1) at every instance of the game, a player should believe that his opponents are carrying out optimal strategies, (2) a player should only revise his belief about an opponent''s relative ranking of two strategies if he is certain that the opponent has decided not to choose one of these strategies, and (3) the players'' initial beliefs about the opponents'' utility functions should agree on a given profile u of utility functions. Common belief about these events leads to the concept of persistent rationalizability for the profile u of utility functions. It is shown that for a given profile u of utility functions, every properly rationalizable strategy for ``types with non-increasing type supports'''' is a persistently rationalizable strategy for u. This result implies that persistently rationalizable strategies always exist for all game trees and all profiles of utility functions.Download Info
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Paper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 048.Length:
Date of creation: 2003
Date of revision:
Handle: RePEc:dgr:umamet:2003048
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Web page: http://www.maastrichtuniversity.nl/web/UMPublications.htm
Related research
Keywords: mathematical economics;This paper has been announced in the following NEP Reports:
- NEP-ALL-2003-09-08 (All new papers)
- NEP-GTH-2003-09-08 (Game Theory)
- NEP-IND-2003-09-08 (Industrial Organization)
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Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- Perea, Andrés, 2008.
"Minimal belief revision leads to backward induction,"
Mathematical Social Sciences,
Elsevier, vol. 56(1), pages 1-26, July.
- Perea,Andrés, 2004. "Minimal Belief Revision leads to Backward Induction," Research Memoranda 032, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
- Perea,Andrés, 2003. "Rationalizability and Minimal Complexity in Dynamic Games," Research Memoranda 047, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
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