Competitive equilibrium in two sided matching markets with general utility functions

Abstract

Two sided matching markets are among the most studied models in market design. There is a vast literature on the structure of competitive equilibria in these markets, yet most of it is focused on quasilinear settings. General (non-quasilinear) utilities can, for instance, model smooth budget constraints as a special case. Due to the difficulty of dealing with arbitrary non-quasilinear utilities, most of the existing work on non-quasilinear utilities is limited to the special case of hard budget constraints in which the utility of each agent is quasilinear as long as her payment is within her budget limit and is negative infinity otherwise. Most of the work on competitive equilibria with hard budget constraints rely on some form of ascending auction. For general non-quasilinear utilities, such ascending auctions may not even converge in finite time. As such, almost all of the existing work on general non-quasilinear utilities have resorted to non-constructive proofs based on fixed point theorems or discretization. We present the first direct characterization of competitive equilibria in such markets. Our approach is constructive and solely based on induction. Our characterization reveals striking similarities between the payments at the lowest competitive equilibrium for general utilities and VCG payments for quasilinear utilities. We also show that lowest competitive equilibrium is group strategyproof for the agents on one side of the market (e.g., for buyers).