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The overall aim of our research is to develop techniques to reason about theequilibrium properties of multi-agent systems. We model multi-agent systems asconcurrent games, in which each player is a process that is assumed to actindependently and strategically in pursuit of personal preferences. In thisarticle, we study these games in the context of finite-memory strategies, andwe assume players' preferences are defined by a qualitative and a quantitativeobjective, which are related by a lexicographic order: a player first prefersto satisfy its qualitative objective (given as a formula of Linear TemporalLogic) and then prefers to minimise costs (given by a mean-payoff function).Our main result is that deciding the existence of a strict epsilon Nashequilibrium in such games is 2ExpTime-complete (and hence decidable), even ifplayers' deviations are implemented as infinite-memory strategies.

Equilibria for Games with Combined Qualitative and Quantitative Objectives