For two person games, stable sets in the sense of Kohlberg and Mertens and quasi-stable sets in the sense of Hillas are finite. In this paper we present an example to show that these sets are not necessarily finite in games with more than two players.

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...

Hillas (1990) introduced a definition of strategic stability based on perturbations of the best reply correspondence that satisfies all of the requirements given by Kohlberg and Mertens (1986). Hillas et al. (2001) point out though that the proofs of the iterated dominance and forward induction...