Automated Design of Multistage Mechanisms

Tuomas Sandholm
Computer Science Department
Carnegie Mellon University
Pittsburgh, PA, 15213
email: sandholm@cs.cmu.edu

Vincent Conitzer
Computer Science Department
Carnegie Mellon University
Pittsburgh, PA, 15213
email: conitzer@cs.cmu.edu

Craig Boutilier
Department of Computer Science
University of Toronto
Toronto, ON M5S 3H5
email: cebly@cs.toronto.edu

Abstract
Mechanism design is the study of preference aggregation protocols that work well in the face of self-interested agents. We present the first general-purpose techniques for automatically designing multistage mechanisms. These can reduce elicitation burden by only querying agents for information that is relevant given their answers to previous queries. We first show how to turn a given (e.g., automatically designed using constrained optimization techniques) single-stage mechanism into the most efficient corresponding multistage mechanism given a specified elicitation tree. We then present greedy and dynamic programming (DP) algorithms that will determine the elicitation tree (optimal in the DP case). Next, we show how the query savings inherent in the multistage model can be used to design the underlying single-stage mechanism to maximally take advantage of this approach. We illustrate all of these techniques on an optimal auction example. Finally, we present negative results on the design of multistage mechanisms that do not correspond to dominant-strategy single-stage mechanisms: an optimal multistage mechanism in general has to randomize over queries to hide information from the agents.

First International Workshop on Incentive Based Computing, at the IEEE/WIC/ACM International Conference on Web Intelligence (WI), Compiegne, France.

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