Player splitting in extensive form games |
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Authors: | Andrés Perea y Monsuwé Mathijs Jansen Dries Vermeulen |
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Institution: | (1) Department of Economics, Universidad Carlos III de Madrid, Calle Madrid 126, 28903 Getafe–Madrid, Spain (e-mail: perea@eco.uc3m.es), ES;(2) Department of Quantitative Economics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands, NL;(3) Department of Economics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands, NL |
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Abstract: | 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.
Received: December 1996/Revised Version: January 2000 |
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Keywords: | JEL classification: C72 |
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