Research supported in part by Israel Science Foundation Grant 1596/10. I am grateful to Abraham Neyman for going over the drafts of this paper and providing countless corrections and suggestions. I thank Eilon Solan for pointing out the work Simon (2003) of Bob Simon, with its inspirational techniques, to me. I also thank Bob Simon, Ilan Nehama, and Ziv Hellman for many helpful conversations, and the anonymous referees who performed extremely diligent proofreadings.
Discounted Stochastic Games With No Stationary Nash Equilibrium: Two Examples
Article first published online: 18 SEP 2013
© 2013 The Econometric Society
Volume 81, Issue 5, pages 1973–2007, September 2013
How to Cite
Levy, Y. (2013), Discounted Stochastic Games With No Stationary Nash Equilibrium: Two Examples. Econometrica, 81: 1973–2007. doi: 10.3982/ECTA10530
- Issue published online: 18 SEP 2013
- Article first published online: 18 SEP 2013
- Manuscript received January, 2012; final revision received December, 2012.
- Stochastic game;
- stationary equilibrium
We present two examples of discounted stochastic games, each with a continuum of states, finitely many players, and actions, that possess no stationary equilibria. The first example has deterministic transitions—an assumption undertaken in most of the early applications of dynamics games in economics—and perfect information, and does not possess even stationary approximate equilibria or Markovian equilibria. The second example satisfies, in addition to stronger regularity assumptions, that all transitions are absolutely continuous with respect to a fixed measure—an assumption that has been widely used in more recent economic applications. This assumption has been undertaken in several positive results on the existence of stationary equilibria in special cases, and in particular, guarantees the existence of stationary approximate equilibria.