Generalize structural characterizations beyond the existing-equilibrium class

Establish that the structural characterizations of equilibrium sequences for Bayesian multiple-concurrent-proposer transaction fee mechanisms remain valid when exact symmetric Bayesian Nash equilibria with atomless finite visible-bid distributions do not exist.

Background

The paper studies exact symmetric Bayesian Nash equilibria of finite multiple-concurrent-proposer transaction fee mechanism games, imposing an equilibrium class with atomless finite visible-bid distributions. The principal asymptotic results characterize limits of such equilibria as the number of users tends to infinity while the number of proposers and relative congestion remain fixed.

The authors explicitly conjecture that these structural characterizations should extend beyond the assumed equilibrium class, including cases in which existence of equilibria of the specified type cannot be established. The conjecture is unresolved because the paper conditions its formal characterizations on the existence of equilibria satisfying those assumptions.

References

We conjecture that our structural characterizations can be generalized even when this existence of the particular equilibrium class above is violated, but---in a similar way to \citet{matt_itcs}---our formal characterizations are conditioned to existing equilibria of the type we describe.

— Bayesian Analysis of Inclusion Transaction Fee Mechanisms with Multiple Concurrent Proposers  (2610.26570 - Milionis et al., 19 Oct 2026) in Section 2, paragraph “Equilibria and limits” (immediately before Section 3, “Outcomes”)