A Tool for the Automated Verification of Nash Equilibria in Concurrent Games

Abstract

Reactive Modules is a high-level specification language for concurrent and multi-agent systems, used in a number of practical model checking tools. Reactive Modules Games is a game-theoretic extension of Reactive Modules, in which concurrent agents in the system are assumed to act strategically in an attempt to satisfy a temporal logic formula representing their individual goal. The basic analytical concept for Reactive Modules Games is Nash equilibrium. In this paper, we describe a tool through which we can automatically verify Nash equilibrium strategies for Reactive Modules Games. Our tool takes as input a system, specified in the Reactive Modules language, a representation of players' goals (expressed as CTL formulae), and a representation of players strategies; it then checks whether these strategies form a Nash equilibrium of the Reactive Modules Game passed as input. The tool makes extensive use of conventional temporal logic satisfiability and model checking techniques. We first give an overview of the theory underpinning the tool, briefly describe its structure and implementation, and conclude by presenting a worked example analysed using the tool.

Natural strategic ability

“…The above decision problems come very close to the recent work on equilibrium checking by Wooldridge, Gutierrez and colleagues [116,128,63]. The difference is that they look at arbitrary combinatorial strategies with perfect recall, whereas we consider natural strategies under bound k (both perfect recall and memoryless).…”

“…Finally, rational verification (also known as equilibrium checking) is an extension of model checking to verify behavior of agents limited to rational choices. Typically, this kind of verification is based on Nash equilibrium, and applied to concurrent games with players' objectives defined by formulas of linear time logic [116,128,63]. Preliminary approaches to similar analysis based on other solution concepts were presented in [65,41,100,99].…”

“…Besides redefining strategy-based requirements, natural strategies provide a new, different view of concurrent multi-player games. In concurrent games, the overall behavior of the system emerges from interaction of individual behaviors driven by individual goals of agents [116,128,63]. In the new view, the emergence results from simple individual play.…”

PRISM-games: verification and strategy synthesis for stochastic multi-player games with multiple objectives

“…Analysis of Nash equilibria can be performed with EAGLE [41] or PRALINE [9], but only for non-stochastic games. Lastly, Uppaal Stratego [19] performs strategy synthesis against quantitative properties, but with a focus on real-time systems.…”

Quantitative Evaluation of Systems

“…GAVS+ [10] is a general-purpose tool for algorithmic game solving, supporting TSGs and (non-stochastic) concurrent games, but not CSGs. Two further tools, PRALINE [5] and EAGLE [25], allow the computation of Nash equilibria [20] for the restricted class of (non-stochastic) concurrent games.…”