Efficient dynamic mechanisms in environments with interdependent valuations: The role of contingent transfers

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Bargaining with Incomplete Information

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 sequential 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 equilibria need be stationary. If stationarity is nevertheless assumed, then the results parallel those for the "gap" case. However, if stationarity is not assumed, then instead a folk theorem obtains, so substantial delay is possible and the uninformed party may receive substantial surplus. The chapter also briefly sketches results for sequential bargaining with two-sided incomplete information. Finally, it reviews the empirical evidence on strategic bargaining with private information by focusing on one of the most prominent examples of bargaining: union contract negotiations.Bargaining; Delay; Incomplete Information

Allocative and Informational Externalities in Auctions and Related Mechanisms

We study the effects of allocative and informational externalities in (multi-object) auctions and related mechanisms. Such externalities naturally arise in models that embed auctions in larger economic contexts. In particular, they appear when there is downstream interaction among bidders after the auction has closed. The endogeneity of valuations is the main driving force behind many new, specific phenomena with allocative externalities: even in complete information settings, traditional auction formats need not be efficient, and they may give rise to multiple equilibria and strategic non-participation. But, in the absence of informational externalities, welfare maximization can be achieved by Vickrey-Clarke- Groves mechanisms. Welfare-maximizing Bayes-Nash implementation is, however, impossible in multi-object settings with informational externalities, unless the allocation problem is separable across objects (e.g. there are no allocative externalities nor complementarities) or signals are one-dimensional. Moreover, implementation of any choice function via ex-post equilibrium is generically impossible with informational externalities and multidimensional types. A theory of information constraints with multidimensional signals is rather complex, but indispensable for our study

Multi-Unit Open Ascending Price Efficient Auction

This paper presents an open ascending price mechanism that allocates efficiently M units of the same good among N bidders with interdependent values The mechanism consists of a number of sequential English auctions with reentry and has the following attributes. In each of the individual auctions all the bidders compete simultaneously in the open ascending price format. The most distinctive feature of the mechanism is that winners are determined first, and then additional auxillary auctions are conducted to determine prices. The total number of auctions depends only on the number of goods to be allocated and not on the number of bidders.Multiple units, Interdependent values, Sequential auctions, Ascending price auction

A dominant strategy, double clock auction with estimation-based tatonnement

The price mechanism is fundamental to economics but difficult to reconcile with incentive compatibility and individual rationality. We introduce a double clock auction for a homogeneous good market with multidimensional private information and multiunit traders that is deficit‐free, ex post individually rational, constrained efficient, and makes sincere bidding a dominant strategy equilibrium. Under a weak dependence and an identifiability condition, our double clock auction is also asymptotically efficient. Asymptotic efficiency is achieved by estimating demand and supply using information from the bids of traders that have dropped out and following a tâtonnement process that adjusts the clock prices based on the estimates

Bundling Equilibrium in Combinatorial auctions

This paper analyzes individually-rational ex post equilibrium in the VC (Vickrey-Clarke) combinatorial auctions. If $\Sigma$ is a family of bundles of goods, the organizer may restrict the participants by requiring them to submit their bids only for bundles in $\Sigma$. The $\Sigma$-VC combinatorial auctions (multi-good auctions) obtained in this way are known to be individually-rational truth-telling mechanisms. In contrast, this paper deals with non-restricted VC auctions, in which the buyers restrict themselves to bids on bundles in $\Sigma$, because it is rational for them to do so. That is, it may be that when the buyers report their valuation of the bundles in $\Sigma$, they are in an equilibrium. We fully characterize those $\Sigma$ that induce individually rational equilibrium in every VC auction, and we refer to the associated equilibrium as a bundling equilibrium. The number of bundles in $\Sigma$ represents the communication complexity of the equilibrium. A special case of bundling equilibrium is partition-based equilibrium, in which $\Sigma$ is a field, that is, it is generated by a partition. We analyze the tradeoff between communication complexity and economic efficiency of bundling equilibrium, focusing in particular on partition-based equilibrium