Nash Equilibrium as an Expression of Self-Referential Reasoning
AbstractWithin a formal epistemic model for simultaneous-move games, we present the following conditions: (1) belief in the opponents'' rationality (BOR), stating that a player should believe 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 equilibrium strategy (that is, a strategy that is optimal in some Nash equilibrium). We thus provide a set of sufficient conditions for Nash equilibrium strategy choice. We also show that none of these seven conditions can be dropped.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 035.
Date of creation: 2006
Date of revision:
Contact details of provider:
Web page: http://www.maastrichtuniversity.nl/web/UMPublications.htm
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-09-16 (All new papers)
- NEP-CBA-2006-09-16 (Central Banking)
- NEP-HPE-2006-09-16 (History & Philosophy of Economics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Balkenborg, Dieter & Winter, Eyal, 1997.
"A necessary and sufficient epistemic condition for playing backward induction,"
Journal of Mathematical Economics,
Elsevier, vol. 27(3), pages 325-345, April.
- Balkenborg, Dieter & Eyal Winter, 1995. "A Necessary and Sufficient Epistemic Condition for Playing Backward Induction," Discussion Paper Serie B 331, University of Bonn, Germany.
- Samet, Dov, 1996.
"Hypothetical Knowledge and Games with Perfect Information,"
Games and Economic Behavior,
Elsevier, vol. 17(2), pages 230-251, December.
- Dov Samet, 1994. "Hypothetical Knowledge and Games with Perfect Information," Game Theory and Information 9408001, EconWPA, revised 17 Aug 1994.
- Clausing, Thorsten, 2004. "Belief Revision In Games Of Perfect Information," Economics and Philosophy, Cambridge University Press, vol. 20(01), pages 89-115, April.
- Asheim, Geir B. & Perea, Andres, 2005. "Sequential and quasi-perfect rationalizability in extensive games," Games and Economic Behavior, Elsevier, vol. 53(1), pages 15-42, October.
- Asheim,G.B., 1999.
"On the epistemic foundation for backward induction,"
30/1999, Oslo University, Department of Economics.
- Asheim, Geir B., 2002. "On the epistemic foundation for backward induction," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 121-144, November.
- Aumann, Robert J., 1998. "On the Centipede Game," Games and Economic Behavior, Elsevier, vol. 23(1), pages 97-105, April.
- Reny Philip J., 1993.
"Common Belief and the Theory of Games with Perfect Information,"
Journal of Economic Theory,
Elsevier, vol. 59(2), pages 257-274, April.
- P. Reny, 2010. "Common Belief and the Theory of Games with Perfect Information," Levine's Working Paper Archive 386, David K. Levine.
- Stalnaker, Robert, 1998. "Belief revision in games: forward and backward induction1," Mathematical Social Sciences, Elsevier, vol. 36(1), pages 31-56, July.
- Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
- Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
- Bonanno, G., 1991. "Rational Beliefs in Extensive Games," Papers 383, California Davis - Institute of Governmental Affairs.
- Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
- 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.
- Rubinstein, Ariel, 1991. "Comments on the Interpretation of Game Theory," Econometrica, Econometric Society, vol. 59(4), pages 909-24, July.
- Antonio Quesada, 2002. "Belief system foundations of backward induction," Theory and Decision, Springer, vol. 53(4), pages 393-403, December.
- Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
- Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August.
- Philip J. Reny, 1992. "Rationality in Extensive-Form Games," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 103-118, Fall.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Charles Bollen).
If references are entirely missing, you can add them using this form.