Player splitting in extensive form games

Player splitting in extensive form games

0.00 Avg rating0 Votes
Article ID: iaor20013514
Country: Germany
Volume: 29
Issue: 3
Start Page Number: 433
End Page Number: 450
Publication Date: Jan 2000
Journal: International Journal of Game Theory
Authors: , ,
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, 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.

Reviews

Required fields are marked *. Your email address will not be published.