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Thomas Steeples

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6 papers

2 author rows

CSL Conference 2024 Conference Paper

Characterising and Verifying the Core in Concurrent Multi-Player Mean-Payoff Games

Julian Gutierrez 0001
Anthony W. Lin
Muhammad Najib
Thomas Steeples
Michael J. Wooldridge

Concurrent multi-player mean-payoff games are important models for systems of agents with individual, non-dichotomous preferences. Whilst these games have been extensively studied in terms of their equilibria in non-cooperative settings, this paper explores an alternative solution concept: the core from cooperative game theory. This concept is particularly relevant for cooperative AI systems, as it enables the modelling of cooperation among agents, even when their goals are not fully aligned. Our contribution is twofold. First, we provide a characterisation of the core using discrete geometry techniques and establish a necessary and sufficient condition for its non-emptiness. We then use the characterisation to prove the existence of polynomial witnesses in the core. Second, we use the existence of such witnesses to solve key decision problems in rational verification and provide tight complexity bounds for the problem of checking whether some/every equilibrium in a game satisfies a given LTL or GR(1) specification. Our approach is general and can be adapted to handle other specifications expressed in various fragments of LTL without incurring additional computational costs.

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AIJ Journal 2023 Journal Article

Cooperative concurrent games

Julian Gutierrez
Szymon Kowara
Sarit Kraus
Thomas Steeples
Michael Wooldridge

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 non-cooperative solution concepts—Nash equilibrium and refinements thereof. Such non-cooperative 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.

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Highlights Conference 2021 Conference Abstract

Mean-Payoff Games with omega-Regular Specifications

Thomas Steeples

Multi-player mean-payoff games are a natural formalism for modelling the behaviour of concurrent and multi-agent systems with self-interested players. Players in such a game traverse a graph, while trying to maximise a mean-payoff function that depends on the plays so generated. As with all games, the equilibria that could arise may have undesirable properties. However, as system designers, we typically wish to ensure that equilibria in such systems correspond to desirable system behaviours, for example, satisfying certain safety or liveness properties. One natural way to do this would be to specify such desirable properties using temporal logic. Unfortunately, the use of temporal logic specifications causes game theoretic verification problems to have very high computational complexity. To this end, we consider -regular specifications, which offer a concise and intuitive way of specifying desirable behaviours of a system. The main result of our work has been the characterisation and complexity bounds for the problem of determining if there are equilibria that satisfy a given -regular specification in a multi-player mean-payoff game in a number of computationally relevant game-theoretic settings.

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LAMAS&SR Workshop 2021 Workshop Paper

Mean-Payoff Games with Omega-Regular Specifications

Thomas Steeples
Julian Gutierrez
Michael Wooldridge

Multi-player mean-payoff games are a natural formalism for modelling the behaviour of concurrent and multi-agent systems with self-interested players. Players in such a game traverse a graph, while trying to maximise a mean-payoff function that depends on the plays so generated. As with all games, the equilibria that could arise may have undesirable properties. However, as system designers, we typically wish to ensure that equilibria in such systems correspond to desirable system behaviours, for example, satisfying certain safety or liveness properties. One natural way to do this would be to specify such desirable properties using temporal logic. Unfortunately, the use of temporal logic specifications causes game theoretic verification problems to have very high computational complexity. To this end, we consider 𝜔-regular specifications, which offer a concise and intuitive way of specifying desirable behaviours of a system. The main results of this work are characterisation and complexity bounds for the problem of determining if there are equilibria that satisfy a given 𝜔-regular specification in a multiplayer mean-payoff game in a number of computationally relevant game-theoretic settings.

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AAMAS Conference 2021 Conference Paper

Mean-Payoff Games with ω-Regular Specifications

Thomas Steeples
Julian Gutierrez
Michael Wooldridge

Multi-player mean-payoff games are a natural formalism to model concurrent and multi-agent systems with self-interested players. Players in such a game traverse a graph, while trying to maximise a mean-payoff function that depends on the plays so generated. As with all games, the equilibria that could arise may have undesirable properties. However, as system designers, we typically wish to ensure that equilibria in such systems correspond to desirable system behaviours, for example, satisfying certain safety or liveness properties. One natural way to do this would be to specify such desirable properties using temporal logic. Unfortunately, the use of temporal logic specifications causes game theoretic verification problems to have very high computational complexity. To this end, we consider ω-regular specifications, which offer a concise and intuitive way of specifying desirable behaviours of a system. The main results of this work are characterisation and complexity bounds for the problem of determining if there are equilibria that satisfy a given ω-regular specification in a multi-player mean-payoff game in a number of computationally relevant game-theoretic settings.

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AAMAS Conference 2018 Conference Paper

Local Equilibria in Logic-Based Multi-Player Games

Julian Gutierrez
Paul Harrenstein
Thomas Steeples
Michael Wooldridge

Game theory provides a well-established framework for the analysis and verification of concurrent and multi-agent systems. Typically, the analysis of a multi-agent system involves computing the set of equilibria in the associated multi-player game representing the behaviour of the system. As systems grow larger, it becomes increasingly harder to find equilibria in the game – which represent the rationally stable behaviours of the multi-agent system (the solutions of the game). To address this issue, in this paper, we study the concept of local equilibria, which are defined with respect to (maximal) stable coalitions of agents for which an equilibrium can de found. We focus on the solutions given by the Nash equilibria of Boolean games and iterated Boolean games, two logic-based models for multi-agent systems, in which the players’ goals are given by formulae of propositional logic and LTL, respectively.

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