Iterated Admissibility as Solution Concept in Game Theory

This file is part of IDEAS, which uses RePEc data

Iterated Admissibility as Solution Concept in Game Theory

Author Info

Mario Gilli () (Department of Economics, University of Milan-Bicocca)

Additional information is available for the following registered author(s):

Mario Gilli

Abstract

Admissibility, i.e. the deletion of weakly dominated strategies, is a highly controversia1 solution concept for non cooperative games. This paper proposes a complete theory of weak dominance and, contrary to almost al1 the literature on this topic, it provides positive results on foundations of iterated admissibility. The main contribution of this work is to show that (iterated) admissibility can be justified once payoffs' ties are seriously taken into considerations and players optimise taking into consideration the information provided by these ties, i.e. using strategic independent sets (Mailath at al. 1993) and conditional dominance (Shimoji and Watson 1998). In particular we prove that (iterated) maximal simultaneous deletion of weakly dominated strategies endogenously emerges as axiomatic characterization of iterated admissibility. As a consequence of this result, the paper provides axiomatic and Bayesian foundations of iterated admissibility, proves the logical consistency of (iterated) admissibility as solution concept in game theory, and that common knowledge of admissibility leads to iterated admissibility, showing why previous attempts using cautious behaviour were ineffective.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. In case of further problems read the IDEAS help file. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

Publisher Info
Paper provided by University of Milano-Bicocca, Department of Economics in its series Working Papers with number 47.

Download reference. The following formats are available: HTML, plain text, BibTeX, RIS (EndNote), ReDIF
Length: 28 pages
Date of creation: Mar 2002
Date of revision: Mar 2002
Handle: RePEc:mib:wpaper:47

Contact details of provider:
Postal: Edificio U6 (III Piano) - Piazza dell'Ateneo Nuovo, 1 - 20126 Milano
Phone: 02/6448-6581/89
Fax: 02/6448-6585
Email:
Web page: http://dipeco.economia.unimib.it
More information through EDIRC

For technical questions regarding this item, or to correct its listing, contact: (Roberto Reale).

Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

References listed on IDEAS
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.:

Moulin, Herve, 1979. "Dominance Solvable Voting Schemes," Econometrica, Econometric Society, vol. 47(6), pages 1137-51, November. [Downloadable!] (restricted)
Tan, Tommy Chin-Chiu & da Costa Werlang, Sergio Ribeiro, 1988. "The Bayesian foundations of solution concepts of games," Journal of Economic Theory, Elsevier, vol. 45(2), pages 370-391, August. [Downloadable!] (restricted)
Vincent J. Vannetelbosch & P. Jean-Jacques Herings, 1999. "Refinements of rationalizability for normal-form games," International Journal of Game Theory, Springer, vol. 28(1), pages 53-68. [Downloadable!] (restricted)
Other versions:
- Herings, P.J.J. & Vannetelbosch, V.J., 1997. "Refinements of rationalizability for normal-form games," Discussion Paper 3, Tilburg University, Center for Economic Research. [Downloadable!]
Battigalli, Pierpaolo & Siniscalchi, Marciano, 1999. "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 88(1), pages 188-230, September. [Downloadable!] (restricted)
Other versions:
- Pierpaolo Battigalli, . "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Working Papers 111, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University. [Downloadable!]
Milgrom, Paul & Roberts, John, 1991. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 82-100, February. [Downloadable!] (restricted)
Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April. [Downloadable!] (restricted)
Bernheim, B Douglas, 1986. " Axiomatic Characterizations of Rational Choice in Strategic Environme nts," Scandinavian Journal of Economics, Blackwell Publishing, vol. 88(3), pages 473-88.
Hillas, John, 1990. "On the Definition of the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 58(6), pages 1365-90, November. [Downloadable!] (restricted)
Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-28, July. [Downloadable!] (restricted)
Mailath, George J & Samuelson, Larry & Swinkels, Jeroen M, 1993. "Extensive Form Reasoning in Normal Form Games," Econometrica, Econometric Society, vol. 61(2), pages 273-302, March. [Downloadable!] (restricted)
Other versions:
- Mailath, G.J. & Samuelson, L. & Swinkels, J., 1991. "extensive Form Reasoning in Normal Form Games," Papers 9130, Tilburg - Center for Economic Research.
- Mailath, G.J. & Samuelson, L. & Swinkels, J., 1990. "Extensive Form Reasoning In Normal Form Games," Papers 1-90-1, Pennsylvania State - Department of Economics.
- Mailath, G.J. & Samuelson, L. & Swinkels, J., 1990. "Extensive Form Reasoning In Normal Form Games," Working papers 90-13, Wisconsin Madison - Social Systems.
Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October. [Downloadable!] (restricted)
Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July. [Downloadable!] (restricted)
Jackson Matthew O. & Palfrey Thomas R. & Srivastava Sanjay, 1994. "Undominated Nash Implementation in Bounded Mechanisms," Games and Economic Behavior, Elsevier, vol. 6(3), pages 474-501, May. [Downloadable!] (restricted)
Other versions:
- Matthew, Jackson O. & Palfrey, Thomas R. & Srivastava, Sanjay., 1990. "Undominated Nash Implementation in Bounded Mechanism," Working Papers 754, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
- Matthew O. Jackson, 1990. "Undominated Nash Implementation in Bounded Mechanisms," Discussion Papers 966, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
Marx, Leslie M., 1999. "Adaptive Learning and Iterated Weak Dominance," Games and Economic Behavior, Elsevier, vol. 26(2), pages 253-278, January. [Downloadable!] (restricted)
Dufwenberg, Martin & Stegeman, Mark, 1999. "When Order matters for Iterated Strict Dominance," Research Papers in Economics 1999:2, Stockholm University, Department of Economics. [Downloadable!]
Van Damme, E., 1991. "Refinements of Nash Equilibrium," Papers 9107, Tilburg - Center for Economic Research.
Borgers, Tilman & Samuelson, Larry, 1992. ""Cautious" Utility Maximization and Iterated Weak Dominance," International Journal of Game Theory, Springer, vol. 21(1), pages 13-25.
Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September. [Downloadable!] (restricted)
Stahl, Dale O., 1995. "Lexicographic rationalizability and iterated admissibility," Economics Letters, Elsevier, vol. 47(2), pages 155-159, February. [Downloadable!] (restricted)
Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August. [Downloadable!] (restricted)
Abreu, Dilip & Pearce, David G., 1984. "On the inconsistency of certain axioms on solution concepts for non-cooperative games," Journal of Economic Theory, Elsevier, vol. 34(1), pages 169-174, October. [Downloadable!] (restricted)
Shimoji, Makoto & Watson, Joel, 1998. "Conditional Dominance, Rationalizability, and Game Forms," Journal of Economic Theory, Elsevier, vol. 83(2), pages 161-195, December. [Downloadable!] (restricted)
Other versions:
- Makoto Shimoji & Joel Watson, 1997. "Conditional Dominance, Rationalizability, and Game Forms," University of California at San Diego, Economics Working Paper Series 97-16, Department of Economics, UC San Diego. [Downloadable!]
Marx, Leslie M. & Swinkels, Jeroen M., 1997. "Order Independence for Iterated Weak Dominance," Games and Economic Behavior, Elsevier, vol. 18(2), pages 219-245, February. [Downloadable!] (restricted)
Other versions:
- Leslie McFarland-Marx & Jeroen M. Swinkels, 1993. "Order Independence for Iterated Weak Dominance," Discussion Papers 1040, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
- Marx, Leslie M. & Swinkels, Jeroen M., 2000. "Order Independence for Iterated Weak Dominance," Games and Economic Behavior, Elsevier, vol. 31(2), pages 324-329, May. [Downloadable!] (restricted)

Full references

Statistics
Access and download statistics

Did you know? Data contributors to RePEc receive monthly emails with details about downloads and abstract views of their works.

This page was last updated on 2008-11-5.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.