Existence of strong Nash equilibria in win-lose games

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

Background

Strong Nash equilibria forbid beneficial coalitional deviations; for general and zero-sum games, ER-completeness is established. Win-lose payoff restrictions may change complexity behavior.

The authors highlight this as open.

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 'Strong Nash Equilibrium'