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.
(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.
Research Areas
