Optimal Shill Bidding in the VCG Mechanism

This paper studies shill bidding in the VCG mechanism applied to combinatorial auctions. Shill bidding is a strategy whereby a single decision-maker enters the auction under the guise of multiple identities (Sakurai, Yokoo, and Matsubara 1999). I formulate the problem of optimal shill bidding for a bidder who knows the aggregate bid of her opponents. A key to the analysis is a subproblem--the cost minimization problem (CMP)--which searches for the cheapest way to win a given package using shills. An analysis of the CMP leads to several fundamental results about shill bidding: (i) I provide an exact characterization of the aggregate bids b such that some bidder would have an incentive to shill bid against b in terms of a new property, Submodularity at the Top; (ii) the problem of optimally sponsoring shills is equivalent to the winner determination problem (for single minded bidders)--the problem of finding an efficient allocation in a combinatorial auction; (iii) shill bidding can occur in equilibrium; and (iv) the problem of shill bidding has an inverse, namely the collusive problem that a coalition of bidders may have an incentive to merge (even after competition among coalition members has been suppressed). I show that only when valuations are additive can the incentives to shill and merge simultaneously disappear.VCG mechanism, combinatorial auctions, winner determination problem, collusion.

Price Discrimination Through Communication

We study a seller's optimal mechanism for maximizing revenue when the buyer may present evidence relevant to the buyer's value, or when different types of buyer have a differential ability to communicate. We introduce a dynamic bargaining protocol in which the buyer first makes a sequence of concessions in a cheap talk phase, and then at a time determined by the seller, the buyer presents evidence to support his previous assertions, and then the seller makes a take-it-or-leave-it offer. Our main result is that the optimal mechanism can be implemented as a sequential equilibrium of our dynamic bargaining protocol. Unlike the optimal mechanism to which the seller can commit, the equilibrium of the bargaining protocol also provides incentives for the seller to behave as required. We thereby provide a natural procedure whereby the seller can optimally price discriminate on the basis of the buyer's evidence. JEL Code: C78, D82, D83.price discrimination, communication, bargaining, commitment, evidence, network flows

Price discrimination through communication

We study a seller's optimal mechanism for maximizing revenue when the buyer may present evidence relevant to the buyer's value, or when different types of buyer have a differential ability to communicate. We introduce a dynamic bargaining protocol in which the buyer first makes a sequence of concessions in a cheap talk phase, and then at a time determined by the seller, the buyer presents evidence to support his previous assertions, and then the seller makes a take-it-or-leave-it offer. Our main result is that the optimal mechanism can be implemented as a sequential equilibrium of our dynamic bargaining protocol. Unlike the optimal mechanism to which the seller can commit, the equilibrium of the bargaining protocol also provides incentives for the seller to behave as required. We thereby provide a natural procedure whereby the seller can optimally price discriminate on the basis of the buyer's evidence

Price discrimination through communication

We study a seller's optimal mechanism for maximizing revenue when a buyer may present evidence relevant to her value. We show that a condition very close to transparency of buyer segments is necessary and sufficient for the optimal mechanism to be deterministic--hence akin to classic third degree price discrimination--independently of non-evidence characteristics. We also find another sufficient condition depending on both evidence and valuations, whose content is that evidence is hierarchical. When these conditions are violated, the optimal mechanism contains a mixture of second and third degree price discrimination, where the former is implemented via sale of lotteries. We interpret such randomization in terms of the probability of negotiation breakdown in a bargaining protocol whose sequential equilibrium implements the optimal mechanism

Generalized Social Marginal Welfare Weights Imply Inconsistent Comparisons of Tax Policies

This paper concerns Saez and Stantcheva's (2016) generalized social marginal welfare weights (GSMWW), which aggregate losses and gains due to tax policies, while incorporating non-utilitarian ethical considerations. The approach evaluates local tax changes without a global social objective. I argue that local tax policy comparisons implicitly entail global comparisons. Moreover, whenever welfare weights do not have a utilitarian structure, these implied global comparisons are inconsistent. One motivation for GSMWW is that it preserves the Pareto principle. I argue that the approach's problems should spark a reconsideration of Pareto if one wants to represent broader values in formal policy analysis

Secret Contracts for Efficient Partnerships ∗

By allocating different information to team members, secret contracts can provide better incentives to perform with an intuitive organizational design. For instance, they may help to monitor monitors, and appoint secret principals. More generally, secret contracts highlight a rich duality between detection and enforcement with linear transfers. On the one hand, every disobedient deviation must be detectable to enforce an an outcome, but different behavior may be used to detect different deviations. On the other, every disobedient deviation must be attributable, i.e., some player can be identified as innocent after the deviation, to provide incentives with budget balance. JEL Classification: D21, D23, D82

Partial Identification of Heterogeneity in Preference Orderings Over Discrete Choices

We study a variant of a random utility model that takes a probability distribution over preference relations as its primitive. We do not model products using a space of observed characteristics. The distribution of preferences is only partially identified using cross-sectional data on varying budget sets. Imposing monotonicity in product characteristics does not restore full identification. Using a linear programming approach to partial identification, we show how to obtain bounds on probabilities of any ordering relation. We also do constructively point identify the proportion of consumers who prefer one budget set over one or two others. This result is useful for welfare. Panel data and special regressors are two ways to gain full point identification.