Equilibria for Games with Combined Qualitative and Quantitative Objectives

• URL: http://arxiv.org/abs/2008.05643v1
• Date: Thu, 13 Aug 2020 01:56:24 GMT
• Title: Equilibria for Games with Combined Qualitative and Quantitative Objectives
• Authors: Julian Gutierrez and Aniello Murano and Giuseppe Perelli and Sasha Rubin and Thomas Steeples and Michael Wooldridge
• Abstract summary: We study concurrent games in which each player is a process that is assumed to act independently and strategically. Our main result is that deciding the existence of a strict epsilon Nash equilibrium in such games is 2ExpTime-complete.
• Score: 15.590197778287616
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The overall aim of our research is to develop techniques to reason about the equilibrium properties of multi-agent systems. We model multi-agent systems as concurrent games, in which each player is a process that is assumed to act independently and strategically in pursuit of personal preferences. In this article, we study these games in the context of finite-memory strategies, and we assume players' preferences are defined by a qualitative and a quantitative objective, which are related by a lexicographic order: a player first prefers to satisfy its qualitative objective (given as a formula of Linear Temporal Logic) and then prefers to minimise costs (given by a mean-payoff function). Our main result is that deciding the existence of a strict epsilon Nash equilibrium in such games is 2ExpTime-complete (and hence decidable), even if players' deviations are implemented as infinite-memory strategies.

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