Reducing Inefficiency in Carbon Auctions with Imperfect Competition

Authors Kira Goldner , Nicole Immorlica, Brendan Lucier

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Author Details

Kira Goldner
  • Department of Computer Science, Columbia University, New York, NY, USA
Nicole Immorlica
  • Microsoft Research, New York, NY, USA
Brendan Lucier
  • Microsoft Research, Cambridge, MA, USA

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Kira Goldner, Nicole Immorlica, and Brendan Lucier. Reducing Inefficiency in Carbon Auctions with Imperfect Competition. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 15:1-15:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We study auctions for carbon licenses, a policy tool used to control the social cost of pollution. Each identical license grants the right to produce a unit of pollution. Each buyer (i.e., firm that pollutes during the manufacturing process) enjoys a decreasing marginal value for licenses, but society suffers an increasing marginal cost for each license distributed. The seller (i.e., the government) can choose a number of licenses to put up for auction, and wishes to maximize the societal welfare: the total economic value of the buyers minus the social cost. Motivated by emission license markets deployed in practice, we focus on uniform price auctions with a price floor and/or price ceiling. The seller has distributional information about the market, and their goal is to tune the auction parameters to maximize expected welfare. The target benchmark is the maximum expected welfare achievable by any such auction under truth-telling behavior. Unfortunately, the uniform price auction is not truthful, and strategic behavior can significantly reduce (even below zero) the welfare of a given auction configuration. We describe a subclass of "safe-price" auctions for which the welfare at any Bayes-Nash equilibrium will approximate the welfare under truth-telling behavior. We then show that the better of a safe-price auction, or a truthful auction that allocates licenses to only a single buyer, will approximate the target benchmark. In particular, we show how to choose a number of licenses and a price floor so that the worst-case welfare, at any equilibrium, is a constant approximation to the best achievable welfare under truth-telling after excluding the welfare contribution of a single buyer.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory and mechanism design
  • Theory of computation → Computational pricing and auctions
  • welfare
  • price of anarchy
  • mechanism design
  • equilibrium
  • costs


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