Concave Pro-rata Games
Nicholas A. G Johnson, Theo Diamandis, Alex Evans, Henry de Valence,, Guillermo Angeris

TL;DR
This paper introduces concave pro-rata games, analyzing their equilibrium properties, efficiency bounds, and convergence behavior, with applications to decentralized exchanges and practical scenarios.
Contribution
It defines a new class of games, proves the uniqueness of symmetric pure equilibria, and analyzes their efficiency and convergence properties.
Findings
Unique symmetric pure equilibrium exists and is the only equilibrium.
Price of anarchy is at least proportional to the number of players.
Players tend to quickly converge to equilibrium in iterative play.
Abstract
In this paper, we introduce a family of games called concave pro-rata games. In such a game, players place their assets into a pool, and the pool pays out some concave function of all assets placed into it. Each player then receives a pro-rata share of the payout; i.e., each player receives an amount proportional to how much they placed in the pool. Such games appear in a number of practical scenarios, including as a simplified version of batched decentralized exchanges, such as those proposed by Penumbra. We show that this game has a number of interesting properties, including a symmetric pure equilibrium that is the unique equilibrium of this game, and we prove that its price of anarchy is in the number of players. We also show some numerical results in the iterated setting which suggest that players quickly converge to an equilibrium in iterated play.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsEconomic theories and models · Game Theory and Applications · Economic Theory and Institutions
