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Adaptive Mechanism Design using Multi-Agent Revealed Preferences

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  • Luke Snow
  • Vikram Krishnamurthy

Abstract

This paper constructs an algorithmic framework for adaptively achieving the mechanism design objective, finding a mechanism inducing socially optimal Nash equilibria, without knowledge of the utility functions of the agents. We consider a probing scheme where the designer can iteratively enact mechanisms and observe Nash equilibria responses. We first derive necessary and sufficient conditions, taking the form of linear program feasibility, for the existence of utility functions under which the empirical Nash equilibria responses are socially optimal. Then, we utilize this to construct a loss function with respect to the mechanism, and show that its global minimization occurs at mechanisms under which Nash equilibria system responses are also socially optimal. We develop a simulated annealing-based gradient algorithm, and prove that it converges in probability to this set of global minima, thus achieving adaptive mechanism design.

Suggested Citation

  • Luke Snow & Vikram Krishnamurthy, 2024. "Adaptive Mechanism Design using Multi-Agent Revealed Preferences," Papers 2404.15391, arXiv.org.
    • Handle: RePEc:arx:papers:2404.15391
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    References listed on IDEAS

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    1. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, vol. 144(1), pages 135-145, January.
    2. Krawczyk, Jacek & Zuccollo, James, 2006. "NIRA-3: An improved MATLAB package for finding Nash equilibria in infinite games," MPRA Paper 1119, University Library of Munich, Germany.
    3. repec:dau:papers:123456789/4099 is not listed on IDEAS
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