Rational Verification for Probabilistic Systems
This work addresses verification challenges for uncertain multi-agent environments, providing foundational complexity results for both non-cooperative and cooperative settings.
The paper tackles rational verification in probabilistic multi-agent systems, showing that verifying temporal logic properties under game-theoretic equilibria in concurrent stochastic games is 2EXPTIME-complete, matching the complexity of simpler model checking in Markov decision processes.
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).