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Normal Form Structures in Extensive Form Games

Author

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  • George J. Mailath

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.

Suggested Citation

  • 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.
    • Handle: RePEc:nwu:cmsems:1041
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Kreps, David M & Ramey, Garey, 1987. "Structural Consistency, Consistency, and Sequential Rationality," Econometrica, Econometric Society, vol. 55(6), pages 1331-1348, November.
    4. 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.
    5. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
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    2. Shimoji, Makoto, 2004. "On the equivalence of weak dominance and sequential best response," Games and Economic Behavior, Elsevier, vol. 48(2), pages 385-402, August.
    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.
    4. Steven J. Brams & Christopher B. Jones, 1999. "Catch-22 And King-Of-The-Mountain Games," Rationality and Society, , vol. 11(2), pages 139-167, May.
    5. Shimoji, Makoto & Watson, Joel, 1998. "Conditional Dominance, Rationalizability, and Game Forms," Journal of Economic Theory, Elsevier, vol. 83(2), pages 161-195, December.
    6. 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.
    7. Man, Priscilla T.Y., 2012. "Forward induction equilibrium," Games and Economic Behavior, Elsevier, vol. 75(1), pages 265-276.

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    More about this item

    Keywords

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    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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