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Continuous-Time Stochastic Games of Fixed Duration

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  • Yehuda (John) Levy

Abstract

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.

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Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp617.

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Length: 45 pages
Date of creation: Aug 2012
Date of revision:
Handle: RePEc:huj:dispap:dp617

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  1. Abraham Neyman, 2012. "Continuous-time Stochastic Games," Discussion Paper Series dp616, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  2. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
  3. 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.
  4. 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, December.
  5. E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, David K. Levine.
  6. Yehuda (John) Levy, 2012. "A Discounted Stochastic Game with No Stationary Nash Equilibrium," Discussion Paper Series dp596r, The Center for the Study of Rationality, Hebrew University, Jerusalem, revised May 2012.
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Cited by:
  1. Abraham Neyman, 2012. "Continuous-time Stochastic Games," Discussion Paper Series dp616, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  2. Abraham Neyman, 2013. "Stochastic games with short-stage duration," Discussion Paper Series dp636, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  3. Abraham Neyman, 2013. "Stochastic Games with Short-Stage Duration," Dynamic Games and Applications, Springer, vol. 3(2), pages 236-278, June.

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