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Pareto-Optimal Nash Equilibrium in Win-Lose Games

Determine whether the existence of a Pareto-optimal Nash equilibrium remains ER-complete for win-lose games.

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Background

Pareto-optimal Nash equilibria are those not strictly dominated by any other equilibrium in all players’ payoffs.

The survey proves ER-completeness in certain settings, but explicitly notes that the win-lose payoff regime is still unresolved.

References

It is open whether the result also holds for win-lose games.

— The Existential Theory of the Reals as a Complexity Class: A Compendium (2407.18006 - Schaefer et al., 25 Jul 2024) in ProblemGT “Pareto Optimal Nash Equilibrium” entry