# Rational Verification for Probabilistic Systems

arXiv: https://arxiv.org/abs/2107.09119 · HTML: https://mlsanity.com/paper/2107.09119/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 32 references that are in the map.
- First posted on arXiv 19 Jul 2021.

## Builds on (most cited first, 7 of 7)

- [Equilibria-based Probabilistic Model Checking for Concurrent Stochastic Games](https://mlsanity.com/paper/1811.07145/) (2018)
- [Pure Nash Equilibria in Concurrent Deterministic Games](https://mlsanity.com/paper/1503.06826/) (2015)
- [Multi-player Equilibria Verification for Concurrent Stochastic Games](https://mlsanity.com/paper/2007.03365/) (2020)
- [Liveness of Randomised Parameterised Systems under Arbitrary Schedulers (Technical Report)](https://mlsanity.com/paper/1606.01451/) (2016)
- [Automated Temporal Equilibrium Analysis: Verification and Synthesis of Multi-Player Games](https://mlsanity.com/paper/2008.05638/) (2020)
- [Fair Termination for Parameterized Probabilistic Concurrent Systems (Technical Report)](https://mlsanity.com/paper/1710.10756/) (2017)
- [Mixing Probabilistic and non-Probabilistic Objectives in Markov Decision Processes](https://mlsanity.com/paper/2004.13789/) (2020)

## Built on by (most cited first, 1 of 1)

- [(Ir)rationality in AI: State of the Art, Research Challenges and Open Questions](https://mlsanity.com/paper/2311.17165/) (2023)

## Abstract (arXiv)

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).