Numerical Methods for Non-Zero-Sum Stochastic Differential Games: Convergence of the Markov Chain Approximation Method
The Markov chain approximation method is an efficient and popular collection of methods for the numerical solution of stochastic control problems in continuous time, for reflected-jump-diffusion-type models and the convergence proofs have been extended to zero-sum stochastic differential games. We apply it to a class of non-zero-sum stochastic differential games with a diffusion system model where the controls for the two players are separated, It is shown that equilibrium values for the approximating chain converge to equilibrium values for the original process and that any equilibrium value for the original process can be approximated by an ε-equilibrium for the chain for arbitrarily small ε > 0. The actual numerical algorithm is that for a stochastic game for a finite-state Markov chain.
KeywordsWiener Process Differential Game Convergence Proof Game Problem Stochastic Control Problem
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