Policy Iteration Algorithms for Zero-Sum Stochastic Differential Games with Long-Run Average Payoff Criteria

Abstract

This paper studies the policy iteration algorithm (PIA) for zero-sum stochastic differential games with the basic long-run average criterion, as well as with its more selective version, the so-called bias criterion. The system is assumed to be a nondegenerate diffusion. We use Lyapunov-like stability conditions that ensure the existence and boundedness of the solution to certain Poisson equation. We also ensure the convergence of a sequence of such solutions, of the corresponding sequence of policies, and, ultimately, of the PIA.

From Chutes and Ladders to No Te Enojes: Simulation of two (moral) random paths

“…These are precisely the reasons for which a board game like No Te Enojes is significantly more difficult to implement. Pages 81-90 of Reference [7]-in Spanish language-and the references cited there discuss this issue for several board games in a discrete context, while Reference [8] delves into the differential case.…”