Welfare and Revenue Guarantees for Competitive Bundling Equilibrium

We study equilibria of markets with $m$ heterogeneous indivisible goods and $n$ consumers with combinatorial preferences. It is well known that a competitive equilibrium is not guaranteed to exist when valuations are not gross substitutes. Given the widespread use of bundling in real-life markets, we study its role as a stabilizing and coordinating device by considering the notion of \emph{competitive bundling equilibrium}: a competitive equilibrium over the market induced by partitioning the goods for sale into fixed bundles. Compared to other equilibrium concepts involving bundles, this notion has the advantage of simulatneous succinctness ($O(m)$ prices) and market clearance. Our first set of results concern welfare guarantees. We show that in markets where consumers care only about the number of goods they receive (known as multi-unit or homogeneous markets), even in the presence of complementarities, there always exists a competitive bundling equilibrium that guarantees a logarithmic fraction of the optimal welfare, and this guarantee is tight. We also establish non-trivial welfare guarantees for general markets, two-consumer markets, and markets where the consumer valuations are additive up to a fixed budget (budget-additive). Our second set of results concern revenue guarantees. Motivated by the fact that the revenue extracted in a standard competitive equilibrium may be zero (even with simple unit-demand consumers), we show that for natural subclasses of gross substitutes valuations, there always exists a competitive bundling equilibrium that extracts a logarithmic fraction of the optimal welfare, and this guarantee is tight. The notion of competitive bundling equilibrium can thus be useful even in markets which possess a standard competitive equilibrium

Asymmetric first-price auctions with uniform distributions: analytic solutions to the general case

While auction research, including asymmetric auctions, has grown significantly in recent years, there is still little analytical solutions of first-price auctions outside the symmetric case. Even in the uniform case, Griesmer et al. (1967) and Plum (1992) find solutions only to the case where the lower bounds of the two distributions are the same. We present the general analytical solutions to asymmetric auctions in the uniform case for two bidders, both with and without a minimum bid. We show that our solution is consistent with the previously known solutions of auctions with uniform distributions. Several interesting examples are presented including a class where the two bid functions are linear. We hope this result improves our understanding of auctions and provides a useful tool for future research in auctions

LP-based Covering Games with Low Price of Anarchy

We present a new class of vertex cover and set cover games. The price of anarchy bounds match the best known constant factor approximation guarantees for the centralized optimization problems for linear and also for submodular costs -- in contrast to all previously studied covering games, where the price of anarchy cannot be bounded by a constant (e.g. [6, 7, 11, 5, 2]). In particular, we describe a vertex cover game with a price of anarchy of 2. The rules of the games capture the structure of the linear programming relaxations of the underlying optimization problems, and our bounds are established by analyzing these relaxations. Furthermore, for linear costs we exhibit linear time best response dynamics that converge to these almost optimal Nash equilibria. These dynamics mimic the classical greedy approximation algorithm of Bar-Yehuda and Even [3]

Characterizing Vickrey allocation rule by anonymity

We consider the problem of allocating finitely many units of an indivisible good among a group of agents when each agent receives at most one unit of the good and pays a non-negative price. For example, imagine that a government allocates a fixed number of licenses to private firms, or that it distributes equally divided lands to households. Anonymity in welfare is a condition of impartiality in the sense that it requires allocation rules to treat agents equally in welfare terms from the viewpoint of agents who are ignorant of their own valuations or identities. We show that the Vickrey allocation rule is the unique allocation rule satisfying strategy-proofness, anonymity in welfare, and individual rationality

Corruption and bicameral reforms

During the last decade unicameral proposals have been put forward in fourteen US states. In this paper we analyze the effects of the proposed constitutional reforms, in a setting where decision making is subject to ‘hard time constraints’, and lawmakers face the opposing interests of a lobby and the electorate. We show that bicameralism might lead to a decline in the lawmakers’ bargaining power vis-a-vis the lobby, thus compromising their accountability to voters. Hence, bicameralism is not a panacea against the abuse of power by elected legislators and the proposed unicameral reforms could be effective in reducing corruption among elected representatives

Incomplete Contracts with Asymmetric Information: Exclusive v. Optional Remedies

Law and economics scholars have always had a strong interest in contract remedies. Perhaps the most explored issue in contract law has been the desirability of various contract remedies, such as expectation damages, specific performance, or liquidated damages, to name the most common. Scholars have been debating for years, from various perspectives, the comparative advantage of these remedies. Yet, most scholars have assumed that each of these remedies is exclusive, and their work has compared a single remedy contract to another single remedy contract. Interestingly, an analysis that assumes these remedies are optional (or cumulative) has not yet been explored, in spite of the fact that contract law provides the non-breaching party with a variety of optional remedies to choose from in case of a breach, and in spite of the fact that parties themselves write contracts which provide such an option. In this paper we attempt to start filling in this gap by studying the relationship between these remedies. Specifically, we study the conditions at which a contract that grants the non-breaching party an option to choose from optional remedies is superior to an exclusive remedy contract. We show that under conditions of double-sided uncertainty and asymmetric information between a seller (who might breach) and a buyer (who never breaches) the interaction of the parties\u27 distributions should determine whether a contract provides for exclusive or optional remedies. Specifically, if the buyer\u27s conditional expected valuation is larger than the seller\u27s conditional expected valuation (in both cases - conditional that their expected valuation is above the buyer\u27s mean valuation), then a contract which provides the buyer an option to choose between liquidated damages or specific performance (or actual damages) is superior. Our analysis in this paper informs transactional lawyers of the relevant economic factors they should consider when deciding the optimal composition of remedies in a given context. Moreover, our analysis is relevant for courts that interpret contracts because it will help them to better understand whether rational parties would have agreed that a particular remedy would be an exclusive remedy or an optional remedy when the language of the contract is ambiguous. Lastly, our analysis provides yet another economic rationale for why courts should enforce parties\u27 liquidated damages clauses even if it seems ex-post over, or under, compensatory. We present a model which shows when parties will agree on a non-exclusive liquidated damages clause. Under such a contract the parties stipulate ex-ante that the buyer will have the option to choose upon breach whether she prefers an optional remedy, such as actual damages or specific performance, to the pre-determined liquidated damages. We focus on the ex-ante design of the contract in light of the new information that the parties anticipate they will gain after they draft the contract. Therefore, we assume that no renegotiation or investments are involved. We demonstrate the optimal way to design contract clauses which takes advantage of the information that the seller and the buyer receive between the time they enter into the contract and the time of the actual breach. We further suggest that parties indeed use such clauses and that courts honor them. After laying out the basic model we provide some extensions to it. As is well known, an exclusive liquidated damages contract is equivalent to granting the seller a call option to breach and pay, where the exercise price is equal to the amount of the agreed liquidated damages. What is perhaps less known is that a non-exclusive, or optional, contract, where the buyer can choose performance, is equivalent to giving the buyer a consecutive call option with the same exercise price. Yet, the consecutive call option to the buyer does not have to have the same exercise price but can rather have a higher one. We call this new contract a two-price contract and show that it is even more efficient than the basic contract we have explored before. Next, we introduce more rounds of sequential options and show that while the regular ex-ante contract can achieve on average about 4 Indeed, in an environment of asymmetric information renegotiation costs are high. More on this below. 90% of the first-best allocative efficiency, an n-rounds contract approaches the first best, as n goes to infinity. We show numerically that within just 4 rounds, 96% of the allocative efficiency can be achieved. Section two describes the legal background against which we have designed our model. Section three surveys the literature that evaluates contract remedies from an economic perspective. Section four presents a simple model with two-sided incomplete information and with a liquidated damages clause. In section four we compare the performance of a regime with optional remedies with a regime of exclusive remedy and then determine the conditions at which each regime should be applied. Section five discusses some interesting extensions meant to approach the first-best allocative efficiency. The appendix provides a more rigorous mathematical demonstration of the model

The consumer scam: an agency-theoretic approach

Despite the extensive body of literature that aims to explain the phenomenon of consumer scams, the structure of information in scam relationships remains relatively understudied. The purpose of this article is to develop an agency-theoretical approach to the study of information in perpetrator-victim interactions. Drawing a distinction between failures of observation and failures of judgement in the pre-contract phase, we introduce a typology and a set of propositions that explain the severity of adverse selection problems in three classes of scam relationships. Our analysis provides a novel, systematic explanation of the structure of information that facilitates scam victimisation, while also enabling critical scrutiny of a core assumption in agency theory regarding contract design. We highlight the role of scam perpetrators as agents who have access to private information and exercise considerable control over the terms and design of scam relationships. Focusing on the consumer scam context, we question a theoretical assumption, largely taken for granted in the agency literature, that contact design is necessarily in the purview of the uninformed principal

The theory of the firm and its critics: a stocktaking and assessment

Includes bibliographical references."Prepared for Jean-Michel Glachant and Eric Brousseau, eds. New Institutional Economics: A Textbook, Cambridge, Cambridge University Press.""This version: August 22, 2005."Since its emergence in the 1970s the modern economic or Coasian theory of the firm has been discussed and challenged by sociologists, heterodox economists, management scholars, and other critics. This chapter reviews and assesses these critiques, focusing on behavioral issues (bounded rationality and motivation), process (including path dependence and the selection argument), entrepreneurship, and the challenge from knowledge-based theories of the firm