Research seminar on March, 21: Elena Parilina (AM&CP SPbSU)

Time: 16.50 - 18.10
Place: 3A Kantemirovskaya st., room: 354

Speaker: Elena Parilina (AM&CP SPbSU)

Title: Optimal solutions of cooperative stochastic games

Abstract: The cooperativeversion of a stochastic game is constructed. Three types of stochastic gamesare considered: (i) stochastic games with finite duration, (ii) discountedstochastic games with infinite duration, (iii) stochastic games played overevent trees with a given state dynamics. For the first type of stochastic gamesthe methods of construction of subgame-consistent and stronglysubgame-consistent cooperative solutions are proposed. To construct thesesolutions the method of determining transfer payments (imputation distributionprocedure) is proposed. In case of discounted stochastic games with infiniteduration, three principles of stable cooperation in dynamics including subgameconsistency, a strategic support principle and irrational behaviour proof areconsidered. The sufficient conditions for these principles are obtained.Moreover, an extension of strategic support principle, namely, an existence ofa strong transferable equilibrium is proved if the game satisfies someconditions. In case of stochastic games played over event trees, the method ofconstruction of a node-consistent core is proposed as well as conditions of theexistence of a subgame perfect epsilon-equilibria with cooperative payoffs ininitially given or regularized games are obtained. Moreover, the specific classof stochastic games played over binary event trees is examined. The cooperativeand non-cooperative versions of the game in pollution control are constructed,the explicit forms of optimal strategies as well as the price of anarchy arefound. We also consider applications of stochastic games to the modeling ofdata transmission in wireless networks. The model of finding stable coalitionstructures as the solutions of a specially constructed stochastic gameincluding a case of restricted coalitions is proposed. We also consider a modelof a stochastic Prisoners' Dilemma game with two states with incompleteinformation, for which the Bayesian approach is applied and Partially MarkovPerfect Bayesian Equilibrium is obtained.