Computation and Incentives of Competitive Equilibria in a Matching Market

Matching market and its many variants have been an intensively studied problem in Economics and Computer Science. In many applications centralized prices are used to determine allocations of indivisible items under the principles of individual optimization and market clearance, based on public knowledge of individual preferences. Alternatively, auction mechanisms have been used with a different set of principles for the determination of prices, based on individuals’ incentives to report their preferences. This talk considers matching markets run by a single seller with an objective of maximizing revenue of the seller, who employs a market equilibrium pricing for allocation. We will give a polynomial time algorithm to compute such an equilibrium given budget constraints, and show that the maximum revenue market equilibrium mechanism converges, under an optimal dynamic re-bidding sequence of the buyers, to a solution equivalent to the minimum revenue equilibrium under the true preferences of buyers, which in turn is revenue equivalent to a VCG solution. We will also discuss other related issues as well as open problems.