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How Proper is Sequential Equilibrium

  • George J. Mailath
  • Larry Samuelson
  • Jeroen M. Swinkels

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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  1. Mailath, G.J. & Samuelson, L. & Swinkels, J., 1991. "extensive Form Reasoning in Normal Form Games," Papers 9130, Tilburg - Center for Economic Research.
  2. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
  3. 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.
  4. Roger B. Myerson, 1977. "Refinements of the Nash Equilibrium Concept," Discussion Papers 295, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, David K. Levine.
  6. Roger B. Myerson, 1984. "Multistage Games with Communication," Discussion Papers 590, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. 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.
  8. van Damme, E.E.C., 1984. "A relation between perfect equilibria in extensive form games and proper equilibria in normal form games," Other publications TiSEM 3734d89e-fd5c-4c80-a230-5, Tilburg University, School of Economics and Management.
  9. Lawrence Blume & Adam Brandenburger & Eddie Dekel, 2014. "Lexicographic Probabilities and Choice Under Uncertainty," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 6, pages 137-160 World Scientific Publishing Co. Pte. Ltd..
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