Cooperative concurrent games ?

In rational verification, the aim is to verify which temporal logic properties will obtain in a multi-agent system, under the assumption that agents (players) in the system choose strategies for acting that form a game theoretic equilibrium. Preferences are typically defined by assuming that agents act in pursuit of individual goals, specified as temporal logic formulae. To date, rational verification has been studied using noncooperative solution concepts-Nash equilibrium and refinements thereof. Such noncooperative solution concepts assume that there is no possibility of agents forming binding agreements to cooperate, and as such they are restricted in their applicability. In this article, we extend rational verification to cooperative solution concepts, as studied in the field of cooperative game theory. We focus on the core, as this is the most fundamental (and most widely studied) cooperative solution concept. We begin by presenting a variant of the core that seems well-suited to the concurrent game setting, and we show that this version of the core can be characterised using ATL*. We then study the computational complexity of key decision problems associated with the core, which range from problems in PSpACE to problems in 3ExpTImE. We also investigate conditions that are sufficient to ensure that the core is non-empty, and explore when it is invariant under bisimilarity. We then introduce and study a number of variants of the main definition of the core, leading to the issue of credible deviations, and to stronger notions of collective stable behaviour. Finally, we study cooperative rational verification using an alternative model of preferences, in which players seek to maximise the mean-payoff they obtain over an infinite play in games where quantitative information is allowed. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This article extends rational verification to cooperative solution concepts and investigates the computational complexity, non-emptiness conditions, and invariance of the core. It also introduces variants of the core and explores the application of cooperative rational verification in an alternative preferences model.