Math. Meth. Oper. Res. (2007) 66: 531–544 DOI 10.1007/s00186-006-0143-8 ORIGINAL ARTICLE El˙ zbieta Z. Ferenstein Randomized stopping games and Markov market games Received: 17 December 2004 / Revised: 31 October 2006 / Published online: 12 January 2007 © Springer-Verlag 2007 Abstract We study nonzero-sum stopping games with randomized stopping strategies. The existence of Nash equilibrium and ε-equilibrium strategies are dis- cussed under various assumptions on players random payoffs and utility functions dependent on the observed discrete time Markov process. Then we will present a model of a market game in which randomized stopping times are involved. The model is a mixture of a stochastic game and stopping game. Keywords Stopping games · Stochastic games · Nash equilibrium · Markov chain 1 Introduction and preliminaries The paper is concerned with two types of games: m-person nonzero-sum nonco- operative sequential games in which randomized stopping times are players strat- egies and some specific stochastic games interpreted as market games (or some econometric models). In the former, players payoffs are their utility functions (in particular case) dependent on a state of the observed sequentially discrete—time Markov process at the random moment of stopping. These games are generaliza- tions of the stopping game formulated by Dynkin (1969) as an example of optimal stopping of random sequences. In the latter, players control transition probability law of a Markov chain so as to stop it at a random moment with the aim to max- imize their expected utilities dependent on the current state of the process and on the collection of players who have decided to stop it. Research supported by grant PBZ-KBN-016/P03/99. E. Z. Ferenstein Faculty of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warsaw, Poland E-mail: efer@mini.pw.edu.pl