  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.
