Equilibria for Games with Combined Qualitative and Quantitative Objectives

TL;DR

This paper investigates the existence of equilibria in multi-agent concurrent games where players have combined qualitative (LTL) and quantitative (mean-payoff) objectives, establishing the problem's 2ExpTime-completeness.

Contribution

It introduces a framework for analyzing equilibria in games with combined LTL and mean-payoff objectives and proves the complexity of deciding strict epsilon Nash equilibria.

Findings

Deciding strict epsilon Nash equilibrium existence is 2ExpTime-complete.

The problem remains decidable even with infinite-memory deviations.

Provides a formal model for multi-objective strategic reasoning.

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.