Dr. Anna Rettieva
Institute of Applied Mathematical Research
Russian Academy of Science
Tuesday 13.4 13-14 at Spektri, 3rd floor
"Dynamic games and cooperation maintenance"
The presentation consists of two parts. In the first one the main constructions and definitions in the field of dynamic games are presented. Namely, we give the notion of control system and types of the player’s payoff function. We consider main solution concepts in non-cooperative and cooperative dynamic games. It’s presented that the characteristic function for the cooperative game can be constructed in unusual form. We consider main dynamic optimization techniques, the Bellman principle and the Pontryagin maximal principle, for discrete-time and continuous-time problems.
In the second part we apply the main techniques to resource management problems and consider the problem of cooperation maintenance. Namely, we consider two schemes to maintain the cooperation: incentive equilibrium and time-consistent imputation distribution procedure.
We present two models related with a bioresource management problem: continuous-time model and discrete-time model with migration.
In the first model: for finite horizon the Pontryagin's maximal principle is applied to determine the Nash and the cooperative equilibria. The incentive equilibria are constructed in the case when the players punish each other for a deviation from the cooperative equilibrium, and in the case when the center punishes them for a deviation.
In the second model: for infinite horizon the Bellman principle is applied to determine the equilibria. Also we consider the case when the center is a player and forms coalition with the players (countries). We find Shapley value and time-consistent imputation distribution procedure for this model. We introduce new condition which offers an incentive to
players to cooperate and compare it with well-known Yeung condition.
Last updated on 9 Apr 2010 by Visa Noronen - Page created on 14 Apr 2010 by Visa Noronen