Reallocation Mechanisms

We consider reallocation problems in settings where the initial endowment of each agent consists of a subset of the resources. The private information of the players is their value for every possible subset of the resources. The goal is to redistribute resources among agents to maximize efficiency. Monetary transfers are allowed, but participation is voluntary. We develop incentive-compatible, individually-rational and budget balanced mechanisms for several classic settings, including bilateral trade, partnership dissolving, Arrow-Debreu markets, and combinatorial exchanges. All our mechanisms (except one) provide a constant approximation to the optimal efficiency in these settings, even in ones where the preferences of the agents are complex multi-parameter functions

Proving soundness of combinatorial Vickrey auctions and generating verified executable code

Using mechanised reasoning we prove that combinatorial Vickrey auctions are soundly specified in that they associate a unique outcome (allocation and transfers) to any valid input (bids). Having done so, we auto-generate verified executable code from the formally defined auction. This removes a source of error in implementing the auction design. We intend to use formal methods to verify new auction designs. Here, our contribution is to introduce and demonstrate the use of formal methods for auction verification in the familiar setting of a well-known auction

Online Auctions

The economic literature on online auctions is rapidly growing because of the enormous amount of freely available field data. Moreover, numerous innovations in auction-design features on platforms such as eBay have created excellent research opportunities. In this article, we survey the theoretical, empirical, and experimental research on bidder strategies (including the timing of bids and winner's-curse effects) and seller strategies (including reserve-price policies and the use of buy-now options) in online auctions, as well as some of the literature dealing with online-auction design (including stopping rules and multi-object pricing rules).

License auctions with exit (and entry) options: Alternative remedies for the exposure problem

Inspired by some spectrum auctions, we consider a stylized license auction with incumbents and one entrant. Whereas the entrant values only the bundle of several units (synergy), incumbents are subject to non-increasing demand. The seller proactively encourages entry and restricts incumbent bidders. In this framework, an English clock auction gives rise to an exposure problem that distorts efficiency and impairs revenue. We consider three remedies: a (constrained) Vickrey package auction, an English clock auction with exit option that allows the entrant to annul his bid, and an English clock auction with exit and entry option that lifts the bidding restriction if entry failed

Efficient Combinatorial Exchanges

We investigate combinatorial exchanges as a generalization of combinatorial auctions and bilateral trades, where the multiple commodities to be traded are possessed by participants and a central planner as endowments. Private values, risk neutrality, and independent types are assumed. Efficiency, Bayesian Incentive Compatibility, and Interim Individual Rationality are required. We characterize the least upper bound of the central plannerfs expected revenue. We introduce a stability notion, namely, the marginal core, to the assumption that the central plannerfs endowment is unprotected. We show that the central planner has a deficit in expectation if and only if the marginal core is non-empty.