NUMERICAL-SOLUTION OF QUASI-VARIATIONAL INEQUALITIES ARISING IN STOCHASTIC GAME-THEORY

We study the finite-difference approximation for the quasi-variational inequalities for a stochastic game involving discrete actions of the players and continuous and discrete payoff. We prove convergence of it erative schemes for the solution of the discretized quasi-variational inequalities, with estimates of the rate of convergence (via contracti on mappings) in two particular cases. Further, we prove stability of t he finite-difference schemes, and convergence of the solution of the d iscrete problems to the solution of the continuous problem as the disc retization mesh goes to zero. We provide a direct interpretation of th e discrete problems in terms of finite-state, continuous-time Markov p rocesses.