Concave Pro-rata Games: The concave pro-rata game

Written by @prorata | Published on 2025/1/14

TL;DR —

This paper explores concave pro-rata games, showing equilibrium properties, price of anarchy, and quick convergence in iterative play for decentralized exchange.

Authors:

(1) Nicholas A. G. Johnson (nagj@mit.edu);

(2) Theo Diamandis (tdiamand@mit.edu);

(3) Alex Evans (aevans@baincapital.com);

(4) Henry de Valence (hdevalence@penumbra.zone);

(5) Guillermo Angeris (gangeris@baincapital.com).

Table of Links

Abstract and Introduction

1 The concave pro-rata game

1.1 Symmetric pure strict equilibrium

1.2 Uniqueness of equilibrium

1.3 Equilibrium payoff

2 Batched decentralized exchanges

2.1 Arbitrage

3 Conclusion and References

A Numerics

B Additional Numerics

C Relaxing strict concavity

D Rosen condition

1 The concave pro-rata game

This paper is available on arxiv under CC BY 4.0 DEED license.

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@prorata

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