PRISM-games 3.0: Stochastic Game Verification with Concurrency, Equilibria and Time

Abstract

We present a major new release of the PRISM-games model checker, featuring multiple significant advances in its support for verification and strategy synthesis of stochastic games. Firstly, concurrent stochastic games bring more realistic modelling of agents interacting in a concurrent fashion. Secondly, equilibria-based properties provide a means to analyse games in which competing or collaborating players are driven by distinct objectives. Thirdly, a real-time extension of (turn-based) stochastic games facilitates verification and strategy synthesis for systems where timing is a crucial aspect. This paper describes the advances made in the tool's modelling language, property specification language and model checking engines in order to implement this new functionality. We also summarise the performance and scalability of the tool, and describe a selection of case studies, ranging from security protocols to robot coordination, which highlight the benefits of the new features.

Automated Verification of Concurrent Stochastic Games

“…We consider a variant of the public good game presented in Example 2, in which the parameter f is fixed, where each player receives an initial amount of capital (e init ) and, in each of k months, can invest none, half or all of their current capital. A 2-player version of the game was modelled in [26]. when player 1 acts in isolation and players 2 and 3 form a coalition (indicated by ), which would be required if the two-coalitional variant of rPATL [25] was used.…”

“…Related work. As summarised above, there are various algorithms to solve CSGs, e.g., [2,3,10], and model checking techniques have been developed for both zero-sum [23] and equilibria-based [25] versions of rPATL on CSGs, implemented in PRISM-games [26]. However, all of this work assumes or reduces to the 2-player case.…”

Comparison of Algorithms for Simple Stochastic Games

“…Implementation: We implemented all our algorithms as an extension of PRISM-games 3.0 [34]. They are available via github https://github.com/ga67vib/Algorithms-For-Stochastic-Games.…”

“…Value Iteration (VI), see e.g. [36], is the most common algorithm for solving MDPs and SGs, and the only method implemented in PRISM-games [34]. Originally, VI only computed a convergent sequence of under-approximations; however, as it was unclear how to stop, results returned by model checkers could be off by arbitrary amounts [22].…”

“…For MDPs (games with a single player), we refer to [23] for an overview of existing tools. Most importantly, PRISMgames 3.0 [34] is a recent tool that offers algorithms for several classes of games. However, for SGs with a reachability objective, it offers only variants of value iteration, none of which give a guarantee, so the result might be arbitrarily far off.…”