  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.
