Rational Verification for Probabilistic Systems

TL;DR

This paper extends rational verification to probabilistic systems, specifically concurrent stochastic games, analyzing how agents' strategic behaviors affect the satisfaction of temporal logic properties under uncertainty.

Contribution

It develops the theory and algorithms for rational verification in probabilistic multi-agent systems, focusing on both non-cooperative and cooperative game settings.

Findings

Rational verification in probabilistic systems is 2EXPTIME-complete.

The problem is comparable in complexity to LTL model checking of MDPs.

Framework applies to both Nash equilibria and core solutions.

Abstract

Rational verification is the problem of determining which temporal logic properties will hold in a multi-agent system, under the assumption that agents in the system act rationally, by choosing strategies that collectively form a game-theoretic equilibrium. Previous work in this area has largely focussed on deterministic systems. In this paper, we develop the theory and algorithms for rational verification in probabilistic systems. We focus on concurrent stochastic games (CSGs), which can be used to model uncertainty and randomness in complex multi-agent environments. We study the rational verification problem for both non-cooperative games and cooperative games in the qualitative probabilistic setting. In the former case, we consider LTL properties satisfied by the Nash equilibria of the game and in the latter case LTL properties satisfied by the core. In both cases, we show that the problem is 2EXPTIME-complete, thus not harder than the much simpler verification problem of model checking LTL properties of systems modelled as Markov decision processes (MDPs).