Pure-equilibrium existence with value maximizers on both sides

Establish the existence of pure Nash equilibria satisfying the no-dominated-bids convention for repeated Trade Reduction when both buyers and sellers are value-maximizing agents.

Background

The paper establishes pure-equilibrium existence for Trade Reduction in the one-sided cases: hybrid buyers with utility-maximizing sellers, and utility-maximizing buyers with value-maximizing sellers. These constructions rely on processing the strategic side sequentially while the quasi-linear side reports truthfully.

The corresponding existence question remains unresolved when both buyers and sellers are value maximizers. In that setting, changes in bids on either side can alter the posted prices or revenues faced by agents on the other side, so the monotone one-pass invariant used in the existence proofs may fail. The paper therefore states its welfare upper bounds only for pure equilibria that exist, while explicitly providing lower-bound equilibria in the relevant constructions.