How Proper is Sequential Equilibrium

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How Proper is Sequential Equilibrium

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George J. Mailath
Larry Samuelson
Jeroen M. Swinkels

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Abstract

We show, that Strategy profile of a normal form game is proper if and only if it is quasiperfect in every extensive form (with that normal form). Thus, properness requires optimality along a sequence of suppol ting trembles, while sequentiality only requires optimality in the limit. A decision-theoretic implementation of sequential rationality, strategic independence respecting equilibrium (SIRE), is then defined and compared to proper equilibrium, using lexicographic probability systems. SIRE and proper equilibrium difler in which indifference over strategies are appealed to higher level beliefs in a player's lexicographic sequence. Finally, we give tremble based characterizations of the rankings of strategies that underlie proper equilibrium and SIRE that do not involve structural futures of the game.

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Paper provided by ESRC Centre on Economics Learning and Social Evolution in its series ELSE working papers with number 045.

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Handle: RePEc:els:esrcls:045

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Article
- Mailath, George J. & Samuelson, Larry & Swinkels, Jeroen M., 1997. "How Proper Is Sequential Equilibrium?," Games and Economic Behavior, Elsevier, vol. 18(2), pages 193-218, February. [Downloadable!] (restricted)
Paper
- George J. Mailath, 1996. "How Proper is Sequential Equilibrium?," Discussion Papers 1161, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]

Find related papers by JEL classification:
C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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repec:att:wimass:19925 is not listed on IDEAS
Roger B. Myerson, 1977. "Refinements of the Nash Equilibrium Concept," Discussion Papers 295, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
Mailath George J. & Samuelson Larry & Swinkels Jeroen M., 1994. "Normal Form Structures in Extensive Form Games," Journal of Economic Theory, Elsevier, vol. 64(2), pages 325-371, December. [Downloadable!] (restricted)
Other versions:
- George J. Mailath, 1993. "Normal Form Structures in Extensive Form Games," Discussion Papers 1041, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]

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Antoni Calvó-Armengol & Rahmi Ilkiliç, 2005. "Pairwise-Stability and Nash Equilibria in Network Formation," Working Papers 2005.34, Fondazione Eni Enrico Mattei. [Downloadable!]
Other versions:
- Antoni Calvó-Armengol & Rahmi İlkılıç, 2009. "Pairwise-stability and Nash equilibria in network formation," International Journal of Game Theory, Springer, vol. 38(1), pages 51-79, March. [Downloadable!] (restricted)
Srihari Govindan & Robert Wilson, 2007. "'On Forward Induction," Levine's Working Paper Archive 321307000000000825, David K. Levine. [Downloadable!]
Other versions:
- Srihari Govindan & Robert Wilson, 2008. "On Forward Induction," Levine's Working Paper Archive 122247000000001859, David K. Levine. [Downloadable!]
- Wilson, Robert B. & Govindan, Srihari, 2007. "On Forward Induction," Research Papers 1955, Stanford University, Graduate School of Business. [Downloadable!]
- Srihari Govindan & Robert Wilson, 2007. "On Forward Induction," Levine's Bibliography 321307000000000788, UCLA Department of Economics. [Downloadable!]
- Srihari Govindan & Robert Wilson, 2006. "On Forward Induction," Levine's Working Paper Archive 321307000000000618, David K. Levine. [Downloadable!]
- Srihari Govindan & Robert Wilson, 2009. "On Forward Induction," Econometrica, Econometric Society, vol. 77(1), pages 1-28, 01. [Downloadable!] (restricted)
John Hillas, 1996. "On the Relation Between Perfect Equilibria in Extensive Form Games and Proper Equilibria in Normal Form Games," Game Theory and Information 9605002, EconWPA, revised 14 May 1996. [Downloadable!]

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