Groupe d’études et de recherche en analyse des décisions

Game-theoretic dynamic problems with random duration

Ekaterina Gromova Saint Petersburg State University, Russie

In this talk, I will present novel game-theoretic dynamic models with random duration as well as new results for (deterministic) cooperative dynamic games that can also be applied to the reported models. In particular, new problem statements will be considered both in the framework of discrete and differential games. Typically, a differential (resp. discrete) game is considered over a fixed interval \([t_0,T]\), where \(T\) can be equal to infinity. We consider the following modifications: random start \(t_0\), random terminal time \(T\), random terminal time \(T\) for asymmetric players. The latter can be extended in the following ways: the game may stop when one of the players leaves the game or the game may continue with a subset of players. Another generalization consists in considering the probability distribution function \(F(t)\) which changes with time (state). For instance, in pollution control games the probability of the termination of the game (leading to a revision of the game regulations) changes depending on the current state of pollution. Apart from the above, we will consider new results for (deterministic) cooperative games related to (strong) time-consistency. These results are formulated for all classes of problems formulated above.

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