Reducing Inefficiency in Carbon Auctions with Imperfect Competition

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

Simple and Approximately Optimal Pricing for Proportional Complementarities

We study a new model of complementary valuations, which we call "proportional complementarities." In contrast to common models, such as hypergraphic valuations, in our model, we do not assume that the extra value derived from owning a set of items is independent of the buyer's base valuations for the items. Instead, we model the complementarities as proportional to the buyer's base valuations, and these proportionalities are known market parameters. Our goal is to design a simple pricing scheme that, for a single buyer with proportional complementarities, yields approximately optimal revenue. We define a new class of mechanisms where some number of items are given away for free, and the remaining items are sold separately at inflated prices. We find that the better of such a mechanism and selling the grand bundle earns a 12-approximation to the optimal revenue for pairwise proportional complementarities. This confirms the intuition that items should not be sold completely separately in the presence of complementarities. In the more general case, a buyer has a maximum of proportional positive hypergraphic valuations, where a hyperedge in a given hypergraph describes the boost to the buyer's value for item $i$ given by owning any set of items $T$ in addition. The maximum-out-degree of such a hypergraph is $d$, and $k$ is the positive rank of the hypergraph. For valuations given by these parameters, our simple pricing scheme is an $O(\min\{d,k\})$-approximation.Comment: Appeared in the 2019 ACM Conference on Economics and Computation (ACM EC '19

Optimal Mechanism Design for Single-Minded Agents

We consider revenue-optimal mechanism design in the interdimensional setting, where one dimension is the 'value' of the buyer, and one is a 'type' that captures some auxiliary information. One setting is the FedEx Problem, for which FGKK [2016] characterize the optimal mechanism for a single agent. We ask: how far can such characterizations go? In particular, we consider single-minded agents. A seller has heterogenous items. A buyer has a value v for a specific subset of items S, and obtains value v iff he gets (at least) all the items in S. We show: 1. Deterministic mechanisms are optimal for distributions that satisfy the "declining marginal revenue" (DMR) property; we give an explicit construction of the optimal mechanism. 2. Without DMR, the result depends on the structure of the directed acyclic graph (DAG) representing the partial order among types. When the DAG has out-degree at most 1, we characterize the optimal mechanism a la FedEx. 3. Without DMR, when the DAG has some node with out-degree at least 2, we show that in this case the menu complexity is unbounded: for any M, there exist distributions over (v,S) pairs such that the menu complexity of the optimal mechanism is at least M. 4. For the case of 3 types, we show that for all distributions there exists an optimal mechanism of finite menu complexity. This is in contrast to 2 additive heterogenous items or which the menu complexity could be uncountable [MV07; DDT15]. In addition, we prove that optimal mechanisms for Multi-Unit Pricing (without DMR) can have unbounded menu complexity. We also propose an extension where the menu complexity of optimal mechanisms can be countable but not uncountable. Together these results establish that optimal mechanisms in interdimensional settings are both much richer than single-dimensional settings, yet also vastly more structured than multi-dimensional settings

Mechanism Design for a Complex World: Rethinking Standard Assumptions

Thesis (Ph.D.)--University of Washington, 2019The data used as input for many algorithms today comes from real human beings who have a stake in the outcome. In order to design algorithms that are robust to potential strategic manipulation, the field of algorithmic mechanism design formally models the strategic interests of the individuals and engineers their actions using game theory. The primary research directions in this area concern designing mechanisms to maximize either revenue or social welfare when selling to agents of various valuation types. This thesis addresses barriers to progress in three fundamental directions in auction theory by rethinking standard models and assumptions and provides positive results in all three cases. First, we design revenue-optimal mechanisms in ``interdimensional'' settings---highly structured correlated settings that sit in between the assumed dichotomy of single-dimensional and multi-dimensional settings. Second, we propose a new model of proportional complementarities and construct an intuitive, simple mechanism that guarantees near-optimal revenue. Third, we study welfare maximization in the interdependent values setting without the single-crossing condition, and guarantee strong approximations for the most general setting of combinatorial auctions