Non-Price Equilibria in Markets of Discrete Goods
Abstract: We study markets of indivisible items in which price-based
(Walrasian) equilibria often do not exist due to the discrete non-convex setting.
Instead we consider Nash equilibria of the market viewed as a game, where players bid
for items, and where the highest bidder on an item wins it and pays his bid. We first
observe that pure Nash-equilibria of this game excatly correspond to price-based
equilibiria (and thus need not exist), but that mixed-Nash equilibria always do exist,
and we analyze their structure in several simple cases where no price-based equilibrium
exists. We also undertake an analysis of the welfare properties of these equilibria
showing that while pure equilibria are always perfectly efficient (“first welfare
theorem”), mixed equilibria need not be, and we provide upper and lower bounds on their
amount of inefficiency.