When the Price Is Shared, So Is the Skill: Competition and Common Value in Shared-Clearing Markets (Abstract)

Paper is submitted to AAMAS 2027 for review.

abstract

A scalar rating, such as an Elo score or a leaderboard rank, presumes that performance is one-dimensional. In certain markets that clear at a shared price this presumption fails, and it fails by construction. When both competitors sell into the same downward-sloping demand, each payoff carries a large common-value component that is shared with the opponent. Only a small competitive residual decides who wins. We establish this on a corpus from Kaggriculture, a two-player production-and-trading competition. About 90% of payoff variance is common, against 50% for two payoffs that move independently. A supply sink both agents face accounts for about a quarter of that excess. The earnings-optimal direction is nearly orthogonal to winning. A scalar earning-skill index predicts the winner at chance, while the relative behavior of the two agents predicts it well. Two causal interventions on the same game explain the split. A lever that acts through the shared price, whether cooperative or predatory, moves the common pool much more than the margin between the agents. Suppressing an agent's production moves that margin by four to five orders of magnitude more. A structural sibling of the game reproduces the split and shows that the competitive band widens as clearing becomes more private. We test the private end on an independently built market, PyMarketSim, whose continuous double auction clears privately. There the common share falls back to independence, and the same earning-skill index recovers the winner. Shared clearing is therefore what splits performance into two axes, and no scalar rating carries both. This failure is distinct from intransitivity, and the remedy is to report the common component alongside the competitive edge.