Arrival under bounded transfers

Establish whether imposing a tight cap on side payments favors arrival at the grand coalition, as conjectured, by determining which of the grand-coalition merger and the blocking deviations requires the larger transfer.

Background

The baseline model assumes unbounded transferable utility. The paper explains that bounded transfers can eliminate both the Pareto improvement from the merge-all move and the transfer-intensive deviations that sustain cycling, so their net effect on arrival is unresolved.

The authors formulate a concrete conjecture: tight transfer caps may favor arrival because blocking coalitions rely more heavily on large redistributions than the grand coalition does. Testing this requires a raw-payoff and feasible-transfer model, since the partition function alone does not record the required transfer magnitudes.

References

The natural conjecture---that a tight cap favours arrival, because blocking coalitions rely on large redistributions more than the grand coalition does---is plausible, and the counterexample is the place to test it: the grand state $[ABCD]$ pays $(4,4,116,132)$ against raw payoffs summing to $256$, while ${A,B}$ forming alone pays $(120,120,0,0)$ against a partition worth $240$ to that pair alone.

— 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 (Bounded transfers), paragraph beginning 'What it buys'