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Normal Form Structures in Extensive Form Games

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

Abstract

Mailaith, Samuelson, and Swinkels (1992) introduce the normal form information set. Normal form information sets capture situations in which players can make certain decisions as if they knew their opponents' had chosen from a particular subset of their strategies. In this paper, we say that an extensive form game represents a normal form game if, for each situation, the corresponding choice in the extnesive form is made with the player knowing that the opponents have chosen from the relevant subset. We show that normal form games exist that cannot be represented. We develop an algorithm that generates a representation whenever one exists and present a necessary and sufficient condition for a normal form game to be representable. Keywords: representation, extensive form game, normal form game, information set, extensive form--normal form equivalence. JEL Classification Numbers: C70, C72.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 64 (1994)
Issue (Month): 2 (December)
Pages: 325-371

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Handle: RePEc:eee:jetheo:v:64:y:1994:i:2:p:325-371

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Web page: http://www.elsevier.com/locate/inca/622869

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References

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  1. David M Kreps & Robert Wilson, 2003. "Sequential Equilibria," Levine's Working Paper Archive 618897000000000813, David K. Levine.
  2. Mailath, G. & Samuelson, L. & Swinkels, J., 1991. "Extensive form reasoning in normal form games," Discussion Paper 1991-30, Tilburg University, Center for Economic Research.
  3. Kreps, David M & Ramey, Garey, 1987. "Structural Consistency, Consistency, and Sequential Rationality," Econometrica, Econometric Society, vol. 55(6), pages 1331-48, November.
  4. Elmes Susan & Reny Philip J., 1994. "On the Strategic Equivalence of Extensive Form Games," Journal of Economic Theory, Elsevier, vol. 62(1), pages 1-23, February.
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Cited by:
  1. Shimoji, Makoto & Watson, Joel, 1998. "Conditional Dominance, Rationalizability, and Game Forms," Journal of Economic Theory, Elsevier, vol. 83(2), pages 161-195, December.
  2. Man, Priscilla T.Y., 2012. "Forward induction equilibrium," Games and Economic Behavior, Elsevier, vol. 75(1), pages 265-276.
  3. 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.

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