Equilibrium in two-player stochastic games with shift-invariant payoffs.

We show that every two-player stochastic game with finite state and action sets, and bounded, Borel-measurable, and shift-invariant payoffs, admits an ε -equilibrium for all ε > 0. • We study two-player stochastic games with shift-invariant payoffs. • We show that such games admit an ε -equilibrium for all ε > 0. • This result extends earlier work of Vieille (2000) on stochastic games with the long-term average payoff. • This result extends Chatterjee (2005) who studied stochastic games with ω -regular objectives expressed as parity objectives. [ABSTRACT FROM AUTHOR]