Mechanisms for discrete optimization with rational agents

Abstract

We study “discrete optimization with a blindfold.” We are given an optimization problem such as finding the shortest path in a graph or balancing load on machines, but some of the relevant data, such as edge costs or machine speeds, is missing. There are various selfish economic agents who each know part of the data, and who are affected by the decisions we make. We can ask them to report the data, but they might lie if it is in their self-interest to do so. We aim to design truthful mechanisms: algorithms for solving our optimization problems that, with the help of monetary incentives, induce the agents to report the true data. We identify and address four major problems with the Vickrey-Clarke-Groves (VCG) mechanism, the most famous general technique for designing truthful mechanisms. First, the VCG mechanism can be used only if we want to maximize the overall social welfare, e.g., minimize the cost to the agents. We develop other techniques for optimizing other types of objective functions. Second, even if our goal is to maximize the overall social welfare, the VCG mechanism may be computationally intractable because the underlying optimization problem is NP-hard. We investigate how to develop approximation algorithms that preserve the truth-inducing properties of the VCG mechanism. Third, even though the VCG mechanism can be used to minimize the total cost incurred by the agents, the amount the mechanism must pay to the agents can be significantly higher. We prove that in some natural cases, this is an inherent difficulty with truthful mechanisms, and is not peculiar to the VCG mechanism. Fourth, even though it is never in an agent's individual selfish interest to lie to the VCG mechanism, coalitions of agents can sometimes benefit by lying in a coordinated way. We study what types of coordination must occur for this type of cheating to be successful.

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