Non-price equilibria in markets of discrete goods

• DOI: 10.1145/1993574.1993619
• Publication Date: 2011-06-06T11:53:52Z
• Authors: Avinatan Hassidim; Haim Kaplan; Yishay Mansour; Noam Nisan
• Keywords: FOS: Computer and information sciences; Computer Science - Computer Science and Game Theory; 0102 computer and information sciences; 01 natural sciences; Computer Science and Game Theory (cs.GT)

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.<br/>ACM EC 2011<br/>