Arctic Auctions, Linear Fisher Markets, and Rational Convex Programs

TL;DR

This paper unifies Arctic Auctions and linear Fisher markets, showing their equilibrium can be characterized by a Rational Convex Program and providing a polynomial-time algorithm for computing these equilibria.

Contribution

It introduces a novel connection between Arctic Auctions and Rational Convex Programs, and presents the first combinatorial polynomial-time algorithm for Arctic Auction equilibria.

Findings

Equilibrium of Arctic Auctions is captured by Rational Convex Programs

First polynomial-time combinatorial algorithm for Arctic Auction equilibria

Unified framework for complex market allocations

Abstract

This paper unifies two foundational constructs from economics and algorithmic game theory, the Arctic Auction and the linear Fisher market, to address the efficient allocation of differentiated goods in complex markets. Our main contributions are showing that an equilibrium for the Arctic Auction is captured by a Rational Convex Program, and deriving the first combinatorial polynomial-time algorithm for computing Arctic Auction equilibria.