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Normal Form Structures in Extensive Form Games

Author

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  • Mailath, G.J.
  • Samuelson, L.
  • Swinkels, J.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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Suggested Citation

  • Mailath, G.J. & Samuelson, L. & Swinkels, J.M., 1992. "Normal Form Structures in Extensive Form Games," Working papers 9205, Wisconsin Madison - Social Systems.
    • Handle: RePEc:att:wimass:9205
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    References listed on IDEAS

    as
    1. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    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.
    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.
    4. 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.
    5. Kreps, David M & Ramey, Garey, 1987. "Structural Consistency, Consistency, and Sequential Rationality," Econometrica, Econometric Society, vol. 55(6), pages 1331-1348, November.
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    Cited by:

    1. 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.
    2. 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.
    3. Shimoji, Makoto & Watson, Joel, 1998. "Conditional Dominance, Rationalizability, and Game Forms," Journal of Economic Theory, Elsevier, vol. 83(2), pages 161-195, December.
    4. 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.
    5. Man, Priscilla T.Y., 2012. "Forward induction equilibrium," Games and Economic Behavior, Elsevier, vol. 75(1), pages 265-276.
    6. 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.

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    More about this item

    Keywords

    game theory ; information ; economic models;
    All these keywords.

    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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