Reallocation Mechanisms

We consider reallocation problems in settings where the initial endowment of each agent consists of a subset of the resources. The private information of the players is their value for every possible subset of the resources. The goal is to redistribute resources among agents to maximize efficiency. Monetary transfers are allowed, but participation is voluntary. We develop incentive-compatible, individually-rational and budget balanced mechanisms for several classic settings, including bilateral trade, partnership dissolving, Arrow-Debreu markets, and combinatorial exchanges. All our mechanisms (except one) provide a constant approximation to the optimal efficiency in these settings, even in ones where the preferences of the agents are complex multi-parameter functions

The performance of deferred-acceptance auctions

Deferred-acceptance auctions are mechanisms whose allocation rule can be implemented using an adaptive reverse greedy algorithm. Milgrom and Segal recently introduced these auctions and proved that they satisfy remarkable incentive guarantees: in addition to being dominant strategy and incentive compatible, they are weakly group-strategyproof and can be implemented by ascending-clock auctions. Neither forward greedy mechanisms nor the VCG mechanism generally possess any of these additional incentive properties. The goal of this paper is to initiate the study of deferred-acceptance auctions from an approximation standpoint. We study what fraction of the optimal social welfare can be guaranteed by these auctions in two canonical problems, knapsack auctions and combinatorial auctions with single-minded bidders. For knapsack auctions, we prove a separation between deferred-acceptance auctions and arbitrary dominant-strategy incentive-compatible mechanisms. For combinatorial auctions with single-minded bidders, we design novel polynomial-time mechanisms that achieve the best of both worlds: the incentive guarantees of a deferred-acceptance auction, and approximation guarantees close to the best possible

Bribeproof mechanisms for two-values domains

Schummer (Journal of Economic Theory 2000) introduced the concept of bribeproof mechanism which, in a context where monetary transfer between agents is possible, requires that manipulations through bribes are ruled out. Unfortunately, in many domains, the only bribeproof mechanisms are the trivial ones which return a fixed outcome. This work presents one of the few constructions of non-trivial bribeproof mechanisms for these quasi-linear environments. Though the suggested construction applies to rather restricted domains, the results obtained are tight: For several natural problems, the method yields the only possible bribeproof mechanism and no such mechanism is possible on more general domains.Comment: Extended abstract accepted to SAGT 2016. This ArXiv version corrects typos in the proofs of Theorem 7 and Claims 28-29 of prior ArXiv versio

Modularity and greed in double auctions

Designing double auctions is a complex problem, especially when there are restrictions on the sets of buyers and sellers that may trade with one another. The goal of this paper is to develop a modular approach to the design of double auctions, by relating it to the exhaustively-studied problem of designing one-sided mechanisms with a single seller (or, alternatively, a single buyer). We consider several desirable properties of a double auction: feasibility, dominant-strategy incentive compatibility, the still stronger incentive constraints offered by a deferred-acceptance implementation, exact and approximate welfare maximization, and budget balance. For each of these properties, we identify sufficient conditions on two one-sided algorithms—one for ranking the buyers, one for ranking the sellers—and on a method for their composition into trading pairs, which guarantee the desired property of the double auction. Our framework also offers new insights into classic double auction designs, such as the VCG and McAfee auctions with unit-demand buyers and unit-supply sellers

Complexity of finding Pareto-efficient allocations of highest welfare

We allocate objects to agents as exemplified primarily by school choice. Welfare judgments of the objectallocating agency are encoded as edge weights in the acceptability graph. The welfare of an allocation is the sum of its edge weights. We introduce the constrained welfare-maximizing solution, which is the allocation of highest welfare among the Pareto-efficient allocations. We identify conditions under which this solution is easily determined from a computational point of view. For the unrestricted case, we formulate an integer program and find this to be viable in practice as it quickly solves a real-world instance of kindergarten allocation and large-scale simulated instances. Incentives to report preferences truthfully are discussed briefly

Complexity Theory, Game Theory, and Economics: The Barbados Lectures

This document collects the lecture notes from my mini-course "Complexity Theory, Game Theory, and Economics," taught at the Bellairs Research Institute of McGill University, Holetown, Barbados, February 19--23, 2017, as the 29th McGill Invitational Workshop on Computational Complexity. The goal of this mini-course is twofold: (i) to explain how complexity theory has helped illuminate several barriers in economics and game theory; and (ii) to illustrate how game-theoretic questions have led to new and interesting complexity theory, including recent several breakthroughs. It consists of two five-lecture sequences: the Solar Lectures, focusing on the communication and computational complexity of computing equilibria; and the Lunar Lectures, focusing on applications of complexity theory in game theory and economics. No background in game theory is assumed.Comment: Revised v2 from December 2019 corrects some errors in and adds some recent citations to v1 Revised v3 corrects a few typos in v

Ex-Post Optimal Knapsack Procurement

We consider a budget-constrained mechanism designer who selects an optimal set of projects to maximize her utility. Projects may differ in their value for the designer, and their cost is private information. In this allocation problem, the quantity of procured projects is endogenously determined by the mechanism. The designer faces ex-post constraints: The participation and budget constraints must hold for each possible outcome, while the mechanism must be strategyproof. We identify settings in which the class of optimal mechanisms has a deferred acceptance auction representation which allows an implementation with a descending-clock auction. Only in the case of symmetric projects do price clocks descend synchronously such that the cheapest projects are implemented. The case in which values or costs are asymmetrically distributed features a novel tradeoff between quantity and quality. The reason is that guaranteeing allocation to the most favorable projects under strategyproofness comes at the cost of a diminished expected number of conducted projects