Player splitting in extensive form games
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.
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Volume (Year): 29 (2000)
Issue (Month): 3 ()
|Note:||Received: December 1996/Revised Version: January 2000|
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References listed on IDEAS
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- Jean-François Mertens, 2004.
"Ordinality in non cooperative games,"
International Journal of Game Theory,
Springer;Game Theory Society, vol. 32(3), pages 387-430, 06.
- MERTENS, Jean-François, "undated". "Ordinality in non cooperative games," CORE Discussion Papers RP 1738, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Mertens, J.-F., 1987. "Ordinality in non cooperative games," CORE Discussion Papers 1987028, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
- In-Koo Cho & David M. Kreps, 1997. "Signaling Games and Stable Equilibria," Levine's Working Paper Archive 896, David K. Levine.
- Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
- KOHLBERG, Elon & MERTENS, Jean-François, "undated". "On the strategic stability of equilibria," CORE Discussion Papers RP 716, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, David K. Levine.
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