Competitive Equilibria in Two Sided Matching Markets with Non-transferable Utilities

We consider two sided matching markets consisting of agents with non-transferable utilities; agents from the opposite sides form matching pairs (e.g., buyers-sellers) and negotiate the terms of their math which may include a monetary transfer. Competitive equilibria are the elements of the core of this game. We present the first combinatorial characterization of competitive equilibria that relates the utility of each agent at equilibrium to the equilibrium utilities of other agents in a strictly smaller market excluding that agent; thus automatically providing a constructive proof of existence of competitive equilibria in such markets. Our characterization also yields a group strategyproof mechanism for allocating indivisible goods to unit demand buyers with non-quasilinear utilities that highly resembles the Vickrey–Clarke-Groves (VCG) mechanism. As a direct application of this, we present a group strategyproof welfare maximizing mechanism for Ad-Auctions without requiring the usual assumption that search engine and advertisers have consistent estimates of the clickthrough rates. ∗Id: ce.tex 312 2012-11-13 21:32:38Z saeed †Dept. of Computer Science, Cornell University, Ithaca, NY 14850. [email protected]. Part of this work was done when the author was visiting Microsoft Research, Redmond. This work was partially supported by the NSF grant CCF-0728839 ‡eBay Research, 2065 Hamilton Ave, San Jose, 95125 [email protected]. §Laboratory of Information and Decision Systems, MIT, Cambridge, MA 02142. [email protected].