Existence of Pareto-optimal Nash equilibria in win-lose games

Determine whether the existence of a Pareto-optimal Nash equilibrium in 3-player win-lose games is ER-complete.

Background

For general and zero-sum 3-player games, Pareto-optimal Nash existence has been shown ER-complete. The symmetry and payoff restriction to win-lose games might alter complexity.

The authors point out that whether win-lose constraints preserve ER-completeness is explicitly 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 Compendium — Problem 'Pareto Optimal Nash Equilibrium'