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Strong Nash Equilibrium in Win-Lose Games

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

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Background

Strong Nash equilibria are resilient to deviations by coalitions; their existence problem has been shown ER-complete in zero-sum settings.

The survey explicitly states that the win-lose setting is an open case.

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 “Strong Nash Equilibrium” entry