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Normal Form Structures in Extensive Form Games

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George J. Mailath

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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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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1041.

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Date of creation: Apr 1993
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Handle: RePEc:nwu:cmsems:1041

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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.:
  1. Kreps, David M & Ramey, Garey, 1987. "Structural Consistency, Consistency, and Sequential Rationality," Econometrica, Econometric Society, vol. 55(6), pages 1331-48, November. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. 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)
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  4. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-94, July. [Downloadable!] (restricted)
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(explanations, 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.)

  1. Brams, Steven J. & Jones, Christopher B., 1997. "Catch-22 and King-of-the-Mountain Games : Cycling, Frustration, and Power," Working Papers 97-23, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
  2. Brams, S.J., 1998. "To Mobilize of Not to Mobilize: Catch 22s in International Crises," Working Papers 98-11, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
  3. George J. Mailath & Larry Samuelson & Jeroen M. Swinkels, . "How Proper is Sequential Equilibrium," ELSE working papers 045, ESRC Centre on Economics Learning and Social Evolution. [Downloadable!]
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