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

Networks of Complements

We consider a network of sellers, each selling a single product, where the graph structure represents pair-wise complementarities between products. We study how the network structure affects revenue and social welfare of equilibria of the pricing game between the sellers. We prove positive and negative results, both of "Price of Anarchy" and of "Price of Stability" type, for special families of graphs (paths, cycles) as well as more general ones (trees, graphs). We describe best-reply dynamics that converge to non-trivial equilibrium in several families of graphs, and we use these dynamics to prove the existence of approximately-efficient equilibria.Comment: An extended abstract will appear in ICALP 201

Selling Complementary Goods: Dynamics, Efficiency and Revenue

We consider a price competition between two sellers of perfect-complement goods. Each seller posts a price for the good it sells, but the demand is determined according to the sum of prices. This is a classic model by Cournot (1838), who showed that in this setting a monopoly that sells both goods is better for the society than two competing sellers. We show that non-trivial pure Nash equilibria always exist in this game. We also quantify Cournot\u27s observation with respect to both the optimal welfare and the monopoly revenue. We then prove a series of mostly negative results regarding the convergence of best response dynamics to equilibria in such games

Implementation with a bounded action space

While traditional mechanism design typically assumes isomorphism between the agents’ type- and action spaces, in many situations the agents face strict restrictions on their action space due to, e.g., technical, behavioral or regulatory reasons. We devise a general framework for the study of mechanism design in single-parameter environments with restricted action spaces. Our contribution is threefold. First, we characterize sufficient conditions under which the information-theoretically optimal social-choice rule can be implemented in dominant strategies, and prove that any multilinear social-choice rule is dominant-strategy implementable with no additional cost. Second, we identify necessary conditions for the optimality of actionbounded mechanisms, and fully characterize the optimal mechanisms and strategies in games with two players and two alternatives. Finally, we prove that for any multilinear social-choice rule, the optimal mechanism with k actions incurs an expected loss of O ( 1 k2) compared to the optimal mechanisms with unrestricted action spaces. Our results apply to various economic and computational settings, and we demonstrate their applicability to signaling games, public-good models and routing in networks.

Welfare maximization in congestion games

Congestion games are non-cooperative games where the utility of a player from using a certain resource depends on the total number of players that are using the same resource. While most work so far took a distributed game-theoretic approach to this problem, this paper studies centralized solutions for congestion games. The first part of the paper analyzes the problem from a computational perspective. We analyze the computational complexity of the welfare-maximization problem, for which we provide both approximation algorithms and lower bounds. We study this optimization problem under different kinds of congestion effects (externalities) among the players: positive, negative, and unrestricted. Our main algorithmic result is a constant approximation algorithm for congestion games with unrestricted externalities. In the second part of the paper, we also take the strategic behavior of the players into account, and present centralized truthful mechanisms for congestion-game environments. Our main result in this part is an incentive-compatible mechanism for m-resource n-player congestion games that achieves an O ( √ m log n) approximation to the optimal welfare. We also describe an important and useful connection between congestion games and combinatorial auctions. This connection allows us to use insights and methods from the combinatorial-auction literature for solving congestion-game problems