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Regular version of the site
Of all publications in the section: 5
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Article
Gurvich V., Boros E., Elbassioni K. et al. Dynamic Games and Applications. 2018. Vol. 8. No. 1. P. 22-41.

We suggest a new algorithm for two-person zero-sum undiscounted stochastic games focusing on stationary strategies. Given a positive real εε, let us call a stochastic game εε-ergodic, if its values from any two initial positions differ by at most εε. The proposed new algorithm outputs for every ε>0ε>0 in finite time either a pair of stationary strategies for the two players guaranteeing that the values from any initial positions are within an εε-range, or identifies two initial positions u and v and corresponding stationary strategies for the players proving that the game values starting from u and v are at least ε/24ε/24 apart. In particular, the above result shows that if a stochastic game is εε-ergodic, then there are stationary strategies for the players proving 24ε24ε-ergodicity. This result strengthens and provides a constructive version of an existential result by Vrieze (Stochastic games with finite state and action spaces. PhD thesis, Centrum voor Wiskunde en Informatica, Amsterdam, 1980) claiming that if a stochastic game is 0-ergodic, then there are εε-optimal stationary strategies for every ε>0ε>0. The suggested algorithm is based on a potential transformation technique that changes the range of local values at all positions without changing the normal form of the game.

Added: Oct 10, 2018
Article
Averboukh Y. Dynamic Games and Applications. 2019. Vol. 9. No. 3. P. 573-593.

A mean field type differential game is a mathematical model of a large system of identical agents under mean field interaction controlled by two players with opposite purposes. We study the case when the dynamics of each agent is given by ODE and the players can observe the distribution of the agents. We construct suboptimal strategies and prove the existence of the value function.

Added: Apr 17, 2020
Article
Sandomirskiy F. Dynamic Games and Applications. 2018. Vol. 8. No. 1. P. 180-198.

We consider repeated zero-sum games with incomplete information on the side of Player 2 with the total payoff given by the non-normalized sum of stage gains. In the classical examples the value of such an N-stage game is of the order of N or of square root of N, as N tends to infinity. Our aim is to find what is causing another type of asymptotic behavior of the value observed for the discrete version of the financial market model introduced by De Meyer and Saley. For this game Domansky and independently De Meyer with Marino found that the value remains bounded, as N tends to infinity, and converges to the limit value. This game is almost-fair, i.e., if Player 1 forgets his private information the value becomes zero. We describe a class of almost-fair games having bounded values in terms of an easy-checkable property of the auxiliary non-revealing game. We call this property the piecewise property, and it says that there exists an optimal strategy of Player 2 that is piecewise-constant as a function of a prior distribution. Discrete market models have the piecewise property. We show that for non-piecewise almost-fair games with an additional non-degeneracy condition the value is of the order of square root of N.

Added: Mar 13, 2017
Article
Averboukh Y., Baklanov A. Dynamic Games and Applications. 2014. Vol. 4. No. 1. P. 1-9.

The reverse Stackelberg solution of a two-person nonzero-sum differential game is considered. We assume that the leader plays in the class of nonanticipative strategies. The main result is the description of the Stackelberg solutions via an auxiliary zero-sum differential game. The case when the leader’s strategies depend on the actual control of the follower is compared with the case when the leader uses nonanticipative strategies.

Added: Apr 22, 2020
Article
Averboukh Y., Baklanov A. Dynamic Games and Applications. 2014. Vol. 4. No. 1. P. 1-9.

The reverse Stackelberg solution of a two-person nonzero-sum differential game is considered. We assume that the leader plays in the class of nonanticipative strategies. The main result is the description of the Stackelberg solutions via an auxiliary zero-sum differential game. The case when the leader’s strategies depend on the actual control of the follower is compared with the case when the leader uses nonanticipative strategies.

Added: Jan 23, 2019