Stochastic nonzero-sum games: a new connection between singular control and optimal stopping

Stochastic nonzero-sum games: a new connection between singular control and optimal stopping

In this paper we establish a new connection between a class of 2-player nonzerosum games of optimal stopping and certain 2-player nonzero-sum games of singular control. We show that whenever a Nash equilibrium in the game of stopping is attained by hitting times at two separate boundaries, then such boundaries also trigger a Nash equilibrium in the game of singular control. Moreover a different...

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

Nash Equilibrium in Nonzero-Sum Games of Optimal Stopping for Brownian Motion

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...