Dynamic Set Values for Nonzero-Sum Games with Multiple Equilibriums

Nonzero - Sum Stochastic Games

This paper extends the basic work that has been done on tero-sum stochastic games to those that are nonzerosum. Appropriately defined equilibrium points are shown to exist for both the case where the players seek to maximize the total value of their discounted period rewards and the case where they wish to maximize their average reward per period. For the latter case, conditions required on the...

Approximating Nash Equilibria in nonzero-Sum Games

This paper deals with the approximation of Nash-equilibria in m-player games. We present conditions under which an approximating sequence of games admits near-equilibria that approximate near equilibria in the limit game. We apply the results to two classes of games: (i) a duopoly game approximated by a sequence of matrix games; (ii) a stochastic game played under the S-adapted information stru...

Two-player Nonzero-sum !-regular Games

We study in nite stochastic games played by two-players on a nite graph with goals speci ed by sets of in nite traces. The games are concurrent (each player simultaneously and independently chooses an action at each round), stochastic (the next state is determined by a probability distribution depending on the current state and the chosen actions), in nite (the game continues for an in nite num...

Numerical Approximations for Nonzero-Sum Stochastic Differential Games

The Markov chain approximation method is a widely used, and efficient family of methods for the numerical solution a large part of stochastic control problems in continuous time for reflected-jump-diffusion-type models. It converges under broad conditions, and there are good algorithms for solving the numerical approximations if the dimension is not too high. It has been extended to zero-sum st...

Necessary optimality conditions for N-player nonzero-sum multistage games