Continuous-Time Stochastic Games of Fixed Duration
We study non-zero-sum continuous-time stochastic games, also known as continuous-time Markov games, of fixed duration. We concentrate on Markovian strategies. We show by way of example that equilibria need not exist in Markovian strategies, but they always exist in Markovian public-signal correlated strategies. To do so, we develop criteria for a strategy profile to be an equilibrium via differential inclusions, both directly and also by modeling continuous-time stochastic as differential games and using the Hamilton-Jacobi-Bellman equations. We also give an interpretation of equilibria in mixed strategies in continuous-time, and show that approximate equilibria always exist.
|Date of creation:||Aug 2012|
|Contact details of provider:|| Postal: Feldman Building - Givat Ram - 91904 Jerusalem|
Web page: http://www.ratio.huji.ac.il/
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- Yehuda (John) Levy, 2012. "A Discounted Stochastic Game with No Stationary Nash Equilibrium," Discussion Paper Series dp596r, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem, revised May 2012.
- Eric Maskin & Jean Tirole, 1997.
"Markov Perfect Equilibrium, I: Observable Actions,"
Harvard Institute of Economic Research Working Papers
1799, Harvard - Institute of Economic Research.
- John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, September.
- KOHLBERG, Elon & MERTENS, Jean-François, "undated".
"On the strategic stability of equilibria,"
CORE Discussion Papers RP
716, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Abraham Neyman, 2012. "Continuous-time Stochastic Games," Discussion Paper Series dp616, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
- Judd, Kenneth L., 1985. "The law of large numbers with a continuum of IID random variables," Journal of Economic Theory, Elsevier, vol. 35(1), pages 19-25, February.
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