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ON ASYMPTOTIC VALUE FUNCTION FOR DYNAMIC GAMES WITH LONG- TIME-AVERAGE PAYOFF

Annotation

The work is devoted to value functions of dynamic zero-sum games. The asymptotics of value functions is considered when each payoff averages over time by a given probability density (in particular for long- time-average payoff and discounted average payoff). For dynamics and families of probability densities, we found the conditions guaranteeing that the asymptotics, if present, is independent of the chosen family of probability densities.

Keywords

dynamic games; Abel mean; Cesaro mean; infinite horizon; dynamic programming principle; probability density; asymptotic value function

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UDC

517.977

Pages

1503-1507

References

1. Oliu-Barton M., Vigeral G. A uniform Tauberian theorem in optimal control // in: Advances in Dynamic Games. Boston: Birkh¨auser, 2013. P. 199-215. 2. Khlopin D.V. Tauberova teorema dlya differentsial'nykh igr // MTIP. 2015. 7. № 1. C. 93-120. 3. Khlopin D.V. On uniform Tauberian theorems for dynamic games // arXiv preprint arXiv:1412.7331 (2014). 4. Ziliotto B. A Tauberian theorem for nonexpansive operators and applications to zero-sum stochastic games // arXiv preprint arXiv:1501.06525 (2015). 5. Mertens J.F., Neyman A. Stochastic Games // Int. J. of Game Theory. 1981. 10. P. 53-66. 6. Monderer D., Sorin S. Asymptotic properties in Dynamic Programming // Int. J. of Game Theory. 1993. 22. P. 1-11. 7. Khlopin D.V. Ob asimptotike tsen v differentsial'nykh igrakh pri usrednenii platezhey po bol'shim promezhutkam // Trudy Mezhdunarodnoy konferentsii Mezhdunarodnoy konferentsii «Dinamika sistem i protsessy upravleniya» (SDCP-2014), posvyashchennoy 90-letiyu so dnya rozhdeniya akademika N.N.Krasovskogo, Izd-vo UMTs UPI, Ekaterinburg, 2015. C. 341-348. 8. Khlopin D.V. On asymptotic value for dynamic games with saddle point // arXiv preprint arXiv:1501.06933 (2015).

Received

2015-05-05

Section of issue

Scientific articles

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