Verification of Strong Nash-equilibrium for Probabilistic BAR Systems

Verifying whether rational participants in a BAR system (a distributed system including Byzantine, Altruistic and Rational participants) would deviate from the specified behaviour is important but challenging. Existing works consider this as Nash-equilibrium verification in a multi-player game. If the game is probabilistic and non-terminating, verifying whether a coalition of rational players would deviate becomes even more challenging. There is no automatic verification algorithm to address it. In this article, we propose a formalization to capture that coalitions of rational players do not deviate, following the concept of Strong Nash-equilibrium (SNE) in game-theory, and propose a model checking algorithm to automatically verify SNE of non-terminating probabilistic BAR systems. We implemented a prototype and evaluated the algorithm in three case studies.