Economics Letters 76 (2002) 393–396 www.elsevier.com / locate / econbase On non-existence of pure strategy Markov perfect equilibrium * Igor Livshits Department of Economics, Social Science Center, University of Western Ontario, London, Ont., Canada N6A 5C2 Received 29 August 2000; received in revised form 5 March 2002; accepted 12 March 2002 Abstract This paper provides a simple counterexample to existence of pure strategy (stationary) Markov perfect equilibrium for a class of infinite-horizon games with complete information, finitely many actions, and finitely many ordered states. For the given example, the proof of non-existence is provided.  2002 Elsevier Science B.V. All rights reserved. Keywords: Markov perfect equilibrium; Coalition formation JEL classification: C7 1. Introduction Non-existence of pure strategy Markov perfect equilibrium (PS MPE) for infinite-horizon games with complete information has been established by Gurvich (1986). However, the game proposed by him is cyclical by design, and economic interpretation of it is not clear. I consider a class of economically interesting games with irreversible actions. A particularly interesting part of this class are games of coalition formation. The class of games I analyze here are infinite-horizon games of complete information with finitely many states, finitely many actions, and discounting. The crucial property is that states are ordered, and states can only go one step down in the ordering or stay the same. If there are finitely many states, and the states have to move down the ordering (or the game terminates if that does not happen), then the game is essentially finite, and Kuhn’s (1953) theorem guarantees existence of pure strategy Markov perfect equilibrium. However, once we allow the state to stay unchanged (status quo), the game loses its finiteness, and existence of pure strategy Markov perfect equilibrium can no longer be guaranteed. *Tel.: 11-519-661-2111x85539; fax: 11-519-661-3666. E-mail address: livshits@uwo.ca (I. Livshits). 0165-1765 / 02 / $ – see front matter  2002 Elsevier Science B.V. All rights reserved. PII: S0165-1765(02)00080-0