Arrival in the patient limit under myopic sharing

Determine whether arrival at a grand coalition can fail as the discount factor tends to one under the static-surplus sharing rule of Assumption , particularly with unilateral termination.

Background

The paper constructs cycling equilibria under myopic sharing for moderate discount factors, including an explicit four-player example for discount factors up to 3/4. The same example reaches grand states for discount factors at least 0.8, and no counterexample is known in the patient limit.

This is the paper's principal unresolved question: a positive answer would show that patience ensures arrival under myopic sharing, whereas a negative answer would require constructing cycling equilibria for discount factors approaching one. The corresponding question is partly resolved under far-sighted sharing, but that rule eliminates the persistent relative-share term responsible for the myopic difficulty.

References

Whether arrival can fail as $\delta \to 1$ therefore remains open, and it is the case that matters most, for the reasons given in Section~\ref{sec:delta}.

— Does the grand coalition form? Persistence, arrival, and the role of the sharing rule in a dynamic process of nested binding agreements  (2608.17766 - Heitzig, 18 Aug 2026) in Section 'Open problems', item (2); see also Remark (What is still open)