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

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]

Heterogeneity and the dynamics of technology adoption

We estimate the demand for a videocalling technology in the presence of both network effects and heterogeneity. Using a unique dataset from a large multinational firm, we pose and estimate a fully dynamic model of technology adoption. We propose a novel identification strategy based on post-adoption technology usage to disentangle equilibrium beliefs concerning the evolution of the network from observed and unobserved heterogeneity in technology adoption costs and use benefits. We find that employees have significant heterogeneity in both adoption costs and network benefits, and have preferences for diverse networks. Using our estimates, we evaluate a number of counterfactual adoption policies, and find that a policy of strategically targeting the right subtype for initial adoption can lead to a faster-growing and larger network than a policy of uncoordinated or diffuse adoption

Allocation mechanisms, incentives, and endemic institutional externalities

Whether an economic agent’s decision creates an externality often depends on the institutional context in which the decision was made. Indeed, in orthodox economics, a technological or exogenous externality occurs just in case one agent’s economic welfare or production possibilities are directly affected by the market decisions of other agents. A pecuniary externality occurs just in case one consumer’s economic welfare or producer’s profit is affected indirectly by price changes caused by changes in other agents’ decisions. Similarly, an institutional or endogenous externality may arise whenever allocations are determined by a mechanism that is not strategy proof for some agent. Then even a resource balance constraint creates an institutional externality except in special cases such as when no individual agent’s action can affect market clearing prices — i.e., there are no pecuniary externalities

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

Expression of ABA signalling genes and ABI5 protein levels in imbibed Sorghum bicolor caryopses with contrasting dormancy and at different developmental stages

Background and AimsPre-harvest sprouting susceptibility in grain sorghum (Sorghum bicolor) is related to low seed dormancy and reduced embryo sensitivity to inhibition of germination by abscisic acid (ABA). Intra-specific variability for pre-harvest sprouting might involve differential regulation of ABA signalling genes.MethodsSorghum genes encoding homologues for ABA signalling components from other species (ABI5, ABI4, VP1, ABI1 and PKABA1) were studied at the transcriptional and protein level (ABI5) during grain imbibition for two sorghum lines with contrasting sprouting phenotypes and in response to hormones.Key ResultsTranscript levels of these genes and protein levels of ABI5 were higher in imbibed immature caryopses of the more dormant line. Dormancy loss was related to lower transcript levels of these genes and lower ABI5 protein levels in both genotypes. Exogenous ABA inhibited germination of isolated embryos but failed to prevent ABI5 rapid decrease supporting a role for the seed coat in regulating ABI5 levels.ConclusionsSeveral genes involved in ABA signalling are regulated differently in imbibed caryopses from two sorghum lines with contrasting pre-harvest sprouting response before - but not after - physiological maturity. A role for ABI5 in the expression of dormancy during grain development is discussed.Fil:Rodríguez, M.V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Mendiondo, G.M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Maskin, L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Gudesblat, G.E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Iusem, N.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

The Norm Implementation Problem in Normative Multi-Agent Systems

Abstract. The norm implementation problem consists in how to see to it that the agents in a system comply with the norms specified for that system by the system designer. It is part of the more general problem of how to synthesize or create norms for multi-agent systems, by, for example, highlighting the choice between regimentation and enforcement, or the punishment associated with a norm violation. In this paper we discuss how various ways to implement norms in a multi-agent system can be distinguished in a formal game-theoretic framework. In particular, we show how different types of norm implementation can all be uniformly specified and verified as types of transformations of extensive games. We introduce the notion of retarded preconditions to implement norms, and we illustrate the framework and the various ways to implement norms in the blocks world environment

Explaining Institutional Change: Why Elected Politicians Implement Direct Democracy

In existing models of direct democratic institutions, the median voter benefits, but representative politicians are harmed since their policy choices can be overridden. This is a puzzle, since representative politicians were instrumental in creating these institutions. I build a model of direct democracy that explains why a representative might benefit from tying his or her own hands in this way. The key features are (1) that voters are uncertain about their representative's preferences; (2) that direct and representative elections are complementary ways for voters to control outcomes. The model shows that some politicians benefit from the introduction of direct democracy, since they are more likely to survive representative elections: direct democracy credibly prevents politicians from realising extreme outcomes. Historical evidence from the introduction of the initiative, referendum and recall in America broadly supports the theory, which also explains two empirical results that have puzzled scholars: legislators are trusted less, but reelected more, in US states with direct democracy. I conclude by discussing the potential for incomplete information and signaling models to improve our understanding of institutional change more generally