Markets Beyond Nash Welfare for Leontief Utilities
Ashish Goel, Reyna Hulett, Benjamin Plaut

TL;DR
This paper explores how flexible price curves can support a wider range of allocations beyond Nash welfare in markets with Leontief utilities, providing characterizations and polynomial algorithms.
Contribution
It characterizes when an allocation can be supported by increasing price curves and provides polynomial-time algorithms to find such curves or determine their non-existence.
Findings
Price curve equilibria extend beyond Nash welfare allocations.
Polynomial algorithms support or refute the existence of supporting price curves.
Any CES welfare maximizing allocation can be supported by price curves in bandwidth settings.
Abstract
We study the allocation of divisible goods to competing agents via a market mechanism, focusing on agents with Leontief utilities. The majority of the economics and mechanism design literature has focused on \emph{linear} prices, meaning that the cost of a good is proportional to the quantity purchased. Equilibria for linear prices are known to be exactly the maximum Nash welfare allocations. \emph{Price curves} allow the cost of a good to be any (increasing) function of the quantity purchased. We show that price curve equilibria are not limited to maximum Nash welfare allocations with two main results. First, we show that an allocation can be supported by strictly increasing price curves if and only if it is \emph{group-domination-free}. A similarly characterization holds for weakly increasing price curves. We use this to show that given any allocation, we can compute strictly (or…
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Taxonomy
TopicsEconomic theories and models · Game Theory and Applications · Auction Theory and Applications
