Nonzero-sum semi-Markov games with countable state spaces

Nonzero-sum Risk-sensitive Stochastic Games on a Countable State Space

The infinite horizon risk-sensitive discounted-cost and ergodic-cost nonzero-sum stochastic games for controlled Markov chains with countably many states are analyzed. For the discounted-cost game, we prove the existence of Nash equilibrium strategies in the class of Markov strategies under fairly general conditions. Under an additional geometric ergodicity condition and a small cost criterion,...

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...

Nonzero-Sum Games of Optimal Stopping for Markov Processes

On Continuous Time Markov Games with Countable State Space

This paper is a continuation of our papers [61 and [71 and is concerned with a continuous time Markov game in which the state space is countable and the action spaces of player I and player n are compact metric spaces. In the game, the players continuously observe the state of the system and then choose actions. As a result, the reward is paid to player I from player n and the system moves to a...

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...