Decentralized markets without a central exchange rely on bilateral contracts. Agents trade with their neighbors in a network. The question is whether such markets can reach equilibrium, and whether that equilibrium is fair.
Bulazel and colleagues (arXiv:2602.20868) show that decentralized trading networks converge to Nash equilibria that are also competitive equilibria — the decentralized process reaches the same outcomes as a centralized market. But the fairness result is sharp: inessential agents always receive zero utility in any core outcome. Not low utility. Zero.
An agent is inessential if the market can clear without them — if all transactions can be rerouted through other paths in the network. The core of the cooperative game, which represents the set of stable outcomes, assigns such agents nothing. This is not a deficiency of the mechanism or a consequence of a particular trading protocol. It is a property of the solution concept itself. Any stable outcome — any outcome that no coalition can improve upon — gives inessential agents exactly zero.
Worse: even essential agents — those whose removal would disrupt some transactions — may receive zero utility across all core outcomes in certain network configurations. Essentiality is necessary but not sufficient for positive utility. The network topology determines not just who trades but who benefits.
The result connects stability and exploitation. The core is the standard solution concept for cooperative games — outcomes where no group has incentive to deviate. But stability-optimal outcomes can be maximally unfair to agents with weak network positions. The most stable market is the one that extracts the most from the least connected.
The general observation: in network-structured markets, an agent's bargaining power is entirely determined by their structural position — whether they are on a bottleneck path or a redundant one. The market doesn't exploit agents through mechanism design or information asymmetry. It exploits them through topology. If you can be routed around, you get nothing.