Strategy Synthesis for Stochastic Games with Multiple Long-Run Objectives

Abstract

We consider turn-based stochastic games whose winning conditions are conjunctions of satisfaction objectives for long-run average rewards, and address the problem of finding a strategy that almost surely maintains the averages above a given multi-dimensional threshold vector. We show that strategies constructed from Pareto set approximations of expected energy objectives are e-optimal for the corresponding average rewards. We further apply our methods to compositional strategy synthesis for multi-component stochastic games that leverages composition rules for probabilistic automata, which we extend for long-run ratio rewards with fairness. We implement the techniques and illustrate our methods on a case study of automated compositional synthesis of controllers for aircraft primary electric power distribution networks that ensure a given level of reliability.