Abstract not found

The standard profit-maximizing multi-unit auction intersects the submitted de-mand curve with a preset reservation supply curve, which is determined using the distribution from which the buyers ’ valuations are drawn. However, when this dis-tribution is unknown, a preset supply curve cannot maximize monopoly profits. The optimal pricing mechanism in this situation sets a price to each buyer on the basis of the demand distribution inferred statistically from other buyers ’ bids. The resulting profit converges to the optimal monopoly profit with known demand as the num-berofbuyersgoestoinfinity, and convergence can be substantially faster than with sequential price experimentation. * Department of Economics, Stanford University, Stanford

We study auctions with severe bounds on the communication allowed: each bidder may only transmit t bits of information to the auctioneer. We consider both welfare-maximizing and revenuemaximizing auctions under this communication restriction. For both measures, we determine the optimal auction and show that the loss incurred relative to unconstrained auctions is mild. We prove non-surprising properties of these kinds of auctions, e.g. that discrete prices are informationally ecient, as well as some surprising properties, e.g. that asymmetric auctions are better than symmetric ones.

The mechanism design literature assumes too much common knowledge of the environment among the players and planner. We relax this assumption by studying implementation on richer type spaces, with more higher order uncertainty. We study the "ex post equivalence" question: when is interim implementation on all possible type spaces equivalent to requiring ex post implementation on the space of payoff types? We show that ex post equivalence holds when the social choice correspondence is a function and in simple quasi-linear environments. When ex post equivalence holds, we identify how large the type space must be to obtain the equivalence. We also show that ex post equivalence fails in general, including in quasi-linear environments with budget balance. For quasi-linear environments, we provide an exact characterization of when interim implementation is possible in rich type spaces. In this environment, the planner can fully extract players’ belief types, so the incentive constraints reduce to conditions distinguishing types with the same beliefs about others’ types but different payoff types.

We study Bayesian mechanism design in situations where agents ’ information may be multi-dimensional, concentrating on mechanisms that lead to efficient allocations. Our main result is that a generalization of the well-known Vickrey-Clarke-Groves mechanism maximizes the planner’s “revenue ” among all efficient mechanisms. This result is then used to study multiple object auctions in situations where bidders have privately known “demand curves” and extended to include situations with complementarities across objects or externalities across bidders. We also illustrate how the main result may be used to analyze the possibility of allocating both private and public goods ef-Þciently when budget balance considerations are important. The generalized VCG mechanism, therefore, serves to unify many results in mechansim design theory. 1

We characterize ex post incentive compatible public decision rules, and apply this characterization to (i) bilateral trade and (ii) public good provision. 1

A contract with multiple agents may be susceptible to collusion. We show that agents ’ collusion imposes no cost in a large class of circumstances with risk neutral agents, including both uncorrelated and correlated types. In those circumstances, any payoff the principal can attain in the absence of collusion, including the secondbest level, can be attained in the presence of collusion in a way robust to many aspects of collusion behavior. The collusion-proof implementation generalizes to a setting in which only a subset of agents may collude, provided that noncollusive agents’ incentives can be protected via an ex post incentive compatible and ex post individually rational mechanism. Our collusion-proof implementation also sheds light on the extent to which hierarchical delegation of contracts can optimally respond to collusion.

A central question in economics is understanding the difficulties that parties have in reaching mutually beneficial agreements. Informational differences provide an appealing explanation for bargaining inefficiencies. This chapter provides an overview of the theoretical and empirical literature on bargaining with incomplete information. The chapter begins with an analysis of bargaining within a mechanism design framework. A modern development is provided of the classic result that, given two parties with independent private valuations, ex post efficiency is attainable if and only if it is common knowledge that gains from trade exist. The classic problems of efficient trade with one-sided incomplete information but interdependent valuations, and of efficiently dissolving a partnership with two-sided incomplete information, are also reviewed using mechanism design. The chapter then proceeds to study bargaining where the parties sequentially exchange offers. Under one-sided incomplete information, it considers sequentia l bargaining between a seller with a known valuation and a buyer with a private valuation. When there is a "gap" between the seller's valuation and the support of buyer valuations, the seller-offer game has essentially a unique sequential equilibrium. This equilibrium exhibits the following properties: it is stationary, trade occurs in finite time, and the price is favorable to the informed party (the Coase Conjecture). The alternating-offer game exhibits similar properties, when a refinement of sequential equilibrium is applied. However, in the case of "no gap" between the seller's valuation and the support of buyer valuations, the bargaining does not conclude with probability one after any finite number of periods, and it does not follow that sequential e...

We study multi-object auctions where agents have private and additive valuations for heterogeneous objects. We focus on the revenue properties of a class of dominant strategy mechanisms where a weight is assigned to each partition of objects. The weights influence the probability with which partitions are chosen in the mechanism. This class contains efficient auctions, pure bundling auctions, mixed bundling auctions, auctions with reserve prices and auctions with prepackaged bundles. For any number of objects and bidders, both the pure bundling auction and separate, efficient auctions for the single objects are revenue-inferior to an auction that involves mixed bundling. 1

We give a brief and biased survey of the past, present, and future of research on the interface of theoretical computer science and game theory. 1