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Player splitting in extensive form games


  • Dries Vermeulen

    (Department of Economics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands)

  • Mathijs Jansen

    (Department of Quantitative Economics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands)

  • Andrés Perea y Monsuwé

    () (Department of Economics, Universidad Carlos III de Madrid, Calle Madrid 126, 28903 Getafe-Madrid, Spain)


By a player splitting we mean a mechanism that distributes the information sets of a player among so-called agents. A player splitting is called independent if each path in the game tree contains at most one agent of every player. Following Mertens (1989), a solution is said to have the player splitting property if, roughly speaking, the solution of an extensive form game does not change by applying independent player splittings. We show that Nash equilibria, perfect equilibria, Kohlberg-Mertens stable sets and Mertens stable sets have the player splitting property. An example is given to show that the proper equilibrium concept does not satisfy the player splitting property. Next, we give a definition of invariance under (general) player splittings which is an extension of the player splitting property to the situation where we also allow for dependent player splittings. We come to the conclusion that, for any given dependent player splitting, each of the above solutions is not invariant under this player splitting. The results are used to give several characterizations of the class of independent player splittings and the class of single appearance structures by means of invariance of solution concepts under player splittings.

Suggested Citation

  • Dries Vermeulen & Mathijs Jansen & Andrés Perea y Monsuwé, 2000. "Player splitting in extensive form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(3), pages 433-450.
  • Handle: RePEc:spr:jogath:v:29:y:2000:i:3:p:433-450
    Note: Received: December 1996/Revised Version: January 2000

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    References listed on IDEAS

    1. In-Koo Cho & David M. Kreps, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, Oxford University Press, vol. 102(2), pages 179-221.
    2. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    3. Jean-François Mertens, 2004. "Ordinality in non cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(3), pages 387-430, June.
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    More about this item


    Extensive form games; equilibrium refinements; player splitting.;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games


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