We consider a general class of nonzero-sum N-player stochastic games with impulse controls, where players control the underlying dynamics discrete interventions. adopt veri?cation approach and provide su?cient conditions for Nash equilibria (NEs) game. then limiting situation when N goes to in?nity, that is, suitable mean-?eld game (MFG) controls. show under appropriate technical conditions, th...

The multi-level programming problem is defined as an n-person nonzero-sum game with perfect information in which the players move sequentially. The bi-level linear case is addressed in detail. Solutions are obtained by recasting this problem as a standard mathematical probram and appealing to its implicitly separable structure. The reformulated optimization problem is linear save for a ~ompleme...

This paper presents a robust optimization model for n-person finite state/action stochastic games with incomplete information. We consider nonzero sum discounted stochastic games in which none of the players knows the true data of a game, and each player adopts a robust optimization approach to address the uncertainty. We call these games discounted robust stochastic games. Such games allow us ...

The computational complexity of finding a Nash equilibrium in a nonzero sum bimatrix game is an important open question. We put forward the notion of (0, 1)-bimatrix games, and show that some associated computational problems are as hard as in the general case.

Mertens [In Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986) (1987) 1528–1577 Amer. Math. Soc.] proposed two general conjectures about repeated games: the first one is that, in any two-person zero-sum repeated game, the asymptotic value exists, and the second one is that, when Player 1 is more informed than Player 2, in the long run Player 1 is able to guaran...