** Nash Equilibria in Concurrent Games with Lexicographic Preferences **

**Abstract**
We study concurrent games with finite-memory
strategies where players are given a Buchi and
a mean-payoff objective, which are related by
a lexicographic order: a player first prefers to
satisfy its Buchi objective, and then prefers to
minimise costs, which are given by a mean-payoff
function. In particular, we show that deciding
the existence of a strict Nash equilibrium in such
games is decidable, even if players' deviations are
implemented as infinite memory strategies.

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