PARETO EFFICIENCY AND WEIGHTED MAJORITY RULES

We consider the design of decision rules in an environment with two alternatives, independent private values and no monetary transfers. The utilitarian rule subject to incentive compatibility constraints is a weighted majority rule, where agents' weights correspond to expected gains given that their favorite alternative is chosen. It is shown that a rule is interim incentive efficient if and only if it is a weighted majority rule, and we characterize those weighted majority rules that are ex ante incentive efficient. We also discuss efficiency in the class of anonymous mechanisms and the stability of weighted majority rules.     

Teaching versus research: A multi-tasking approach to multi-department universities

We study the possible implications of incentive schemes as a tool to promote efficiency in the management of universities. In this paper, we show that by designing internal financial rules which create yardstick competition for research funds, a multi-department university may induce better teaching quality and research, as compared to the performance of independent departments.     

Private provision of a discrete public good: efficient equilibria in the private-information contribution game

We study the voluntary provision of a discrete public good via the contribution game. Players independently and simultaneously make nonrefundable contributions to fund a discrete public good, which is provided if and only if contributions cover the cost of production. We characterize nonconstant continuous symmetric equilibria, giving sufficient conditions for their existence. We show the common normalization by which players’ values are distributed over [0, 1] is not without loss of generality: if the distribution over this interval has continuous density f with f(0) >  0, then no (nonconstant) continuous symmetric equilibrium exists. We study in detail the case in which players’ private values are uniformly distributed, showing that, generically, when one continuous equilibrium exists, a continuum of continuous equilibria exists. For any given cost of the good, multiple continuous equilibria cannot be Pareto ranked. Nevertheless, not all continuous equilibria are interim incentive efficient. The set of interim incentive efficient equilibria is exactly determined. The authors thank Manfred Dix, George Mailath, Andrew Postlewaite, and an anonymous referee for their comments.     

Public-Good Provision with Many Participants

For a nonexcludable public good with benefit and cost functions independent of the number of participants, this paper studies second-best allocations under Bayesian interim incentive compatibility and interim individual rationality. As the number of participants becomes large, second-best provision levels converge in distribution to first-best levels if the latter are bounded. Second-best provision levels become large in absolute terms but small relative to first-best levels if benefit and cost functions are isoelastic. In contrast, for an excludable public good, the ratio of second-best to first-best levels is bounded away from zero.     

Bundling as an optimal selling mechanism for a multiple-good monopolist

Multiple objects may be sold by posting a schedule consisting of one price for each possible bundle and permitting the buyer to select the price-bundle pair of his choice. We identify conditions that must be satisfied by any price schedule that maximizes revenue within the class of all such schedules. We then provide conditions under which a price schedule maximizes expected revenue within the class of all incentive compatible and individually rational mechanisms in the n-object case. We use these results to characterize environments, mainly distributions of valuations, where bundling is the optimal mechanism in the two and three good cases.     

Efficient performance in two agent bargaining

This paper concerns ex ante incentive efficient performance in the bargaining of one buyer and one seller over a single item. For any element in a specified class of distributions of the buyer's and the seller's valuations of the item, all of the (interim) individually rational and efficient allocation rules are characterized. It is also shown that the “buyer's bid” and the “seller's price” double auctions are efficient for all distributions in the specified class. These results are obtained by studying efficiency as a linear programming problem.     

Efficient Equilibria in the Voluntary Contributions Mechanism with Private Information

We characterize generally the Bayesian Nash equilibria of a voluntary contributions public goods game for two consumers with private information.The two consumers simultaneously make voluntary contributions to the public good, and the contributions are refunded if the total falls short of the cost of the public good. Several families of equilibria (step‐function, regular and semi‐regular) are studied. Necessary and sufficient conditions for regular and semi‐regular equilibrium allocations to be interim incentive efficient are derived. In the uniform distribution case we prove (i) the existence of an open set of incentive efficient regular equilibria when the cost of production is large enough and (ii) the existence of an open set of incentive efficient semi‐regular equilibria when the cost of production is low enough. Step‐function equilibra are proved to be interim incentive inefficient.     

Starting Small and Commitment

I study a model of a long-term partnership with two-sided incomplete information. The partners jointly determine the stakes of their relationship and individually decide whether to cooperate with or betray each other over time. I characterize the extremal—interim incentive efficient—equilibria. In these equilibria, the partners generally “start small,” and the level of interaction grows over time. The types of players separate quickly. Further, cooperation between “good” types is viable regardless of how pessimistic the players are about each other initially. The quick nature of separation in an extremal equilibrium contrasts with the outcome selected by a strong renegotiation criterion (as studied in Watson (1999, J. Econ. Theory85, 52–90). Journal of Economic Literature Classification Numbers: C72, C73, D74.     

Fully sincere voting

In a general social choice framework where the requirement of strategy-proofness may not be sensible, we call a social choice rule fully sincere if it never gives any individual an incentive to vote for a less-preferred alternative over a more-preferred one and provides an incentive to vote for an alternative if and only if it is preferred to the default option that would result from abstaining. If the social choice rule can depend only on the number of votes that each alternative receives, those rules satisfying full sincerity are convex combinations of the rule that chooses each alternative with probability equal to the proportion of the vote it receives and an arbitrary rule that ignores voters' preferences. We note a sense in which the natural probabilistic analog of approval voting is the fully sincere rule that allows voters maximal flexibility in expressing their preferences and gives these preferences maximal weight.     

Behavioral Mechanism Design

This paper studies the mechanism design problem for the class of Bayesian environments where agents do care for the well‐being of others. For these environments, we fully characterize interim efficient (IE) mechanisms and examine their properties. This set of mechanisms is compelling, since IE mechanisms are the best in the sense that there is no other mechanism which generates unanimous improvement. For public good environments, we show that these mechanisms produce public goods closer to the efficient level of production as the degree of altruism in the preferences increases. For private good environments, we show that altruistic agents trade more often than selfish agents.     

Mechanism design with side payments: Individual rationality and iterative dominance

We investigate the collective decision with incomplete information and side payments. We show that a direct mechanism associated with the social choice function that satisfies budget balancing, incentive compatibility, and interim individual rationality exists for generic prior distributions. We consider the possibility that a risk-averse principal extracts full surplus in agency problems with adverse selection. With regard to generic prior distributions, we show that there exists a modified direct mechanism associated with the virtual social choice function, which satisfies budget balancing and interim individual rationality, such that truth telling is the unique three times iteratively undominated message rule profile.     

On the design of incentive schemes under moral hazard and adverse selection

This paper characterizes a class of optimal incentive schemes in a simple principal–agent model which allows for moral hazard and adverse selection. We show that incentive compatible allocation can always be (approximately) implemented through a menu of quadratic incentive schemes. It is also proved that the set of incentive compatible allocations is independent of the distribution of the additive uncertainty which affects the outcome. Informational requirements and economic interpretation of quadratic and linear schemes are discussed.     

When too little is as good as nothing at all: Rationing a disposable good among satiable people with acceptance thresholds

We study the problem of rationing a divisible good among a group of people. Each person?s preferences are characterized by an ideal amount that he would prefer to receive and a minimum quantity that he will accept: any amount less than this threshold is just as good as receiving nothing at all. Any amount beyond his ideal quantity has no effect on his welfare.We search for Pareto-efficient, strategy-proof, and envy-free rules. The definitions of these axioms carry through from the more commonly studied problem without disposability or acceptance thresholds. However, these are not compatible in the model that we study. We adapt the equal-division lower bound axiom and propose another fairness axiom called awardee-envy-freeness. Unfortunately, these are also incompatible with strategy-proofness. We characterize all of the Pareto-efficient rules that satisfy these two properties. We also characterize all Pareto-efficient, strategy-proof, and non-bossy rules.     

Threshold uncertainty in the private-information subscription game

We introduce threshold uncertainty, à la Nitzan and Romano (1990), into a private-values model of voluntary provision of a discrete public good. Players are allowed to make any level of contribution toward funding the good, which is provided if the cost threshold is reached. Otherwise, contributions are refunded. Conditions ensuring existence and uniqueness of a Bayesian equilibrium are established. Further restricting the threshold uncertainty to a uniform distribution, we show the equilibrium strategies are very simple, even allowing for any number of players with asymmetric distributions of values. Comparative statics with respect to changes in players' distributions are derived, allowing changes in both the intensity and the dispersion of values. For example, increased uncertainty, in the sense of mean-preserving spreads of players' distributions of values, increases equilibrium contributions. Finally, we show the equilibrium is interim incentive inefficient. The sharpness of our results greatly contrasts with the more qualified insights of earlier private-values models with known cost threshold, which relied on there being two symmetric players and generally exhibited multiple equilibria.     

Efficiency and incentive compatibility in differential information economies

Summary. We introduce several efficiency notions depending on what kind of expected utility is used (ex ante, interim, ex post) and on how agents share their private information, i.e., whether they redistribute their initial endowments based on their own private information, or common knowledge information, or pooled information. Moreover, we introduce several Bayesian incentive compatibility notions and identify several efficiency concepts which maintain (coalitional) Bayesian incentive compatibility. Received: March 25, 1996; revised September 5, 1996     

Mechanism design with partial state verifiability

We study implementation in environments where agents have limited ability to imitate others. Agents are randomly and privately endowed with type-dependent sets of messages. So sending a message becomes a partial proof regarding type. For environments where agents can send any combination of available messages, we develop an Extended Revelation Principle and characterize the incentive constraints which implementable allocations must satisfy. When not all message combinations are feasible, static mechanisms no longer suffice. If a ‘punishment’ allocation exists for each agent, then implementable allocations can be characterized as equilibria of a “Revelation Game,” in which agents first select from the menus of allocation rules, then the mediator requests each agent to send some verifying messages. When a punishment allocation fails to exist for some agent, dynamic games in which agents gradually reveal their evidence implement a larger set of outcomes. The latter result provides a foundation for a theory of debate.     

The (sub-)optimality of the majority rule

We consider collective choice from two alternatives. Ex-ante, each agent is uncertain about which alternative she prefers, and may be uncertain about the intensity of her preferences. An environment is given by a probability distribution over utility vectors that is symmetric across agents and neutral across alternatives. In many environments, the majority voting rule maximizes agents? ex-ante expected utilities among all anonymous and dominant-strategy implementable choice rules. But in some environments where the agents? utilities are stochastically correlated, other dominant-strategy choice rules are better for all agents. If utilities are stochastically independent across agents, majority voting is ex-ante optimal among all anonymous and incentive-compatible rules. We also compare rules from an interim-viewpoint.     

Supply and demand biases in linear interindustry models

We explore the sectoral and aggregate implications of some endogeneization rules (i.e. on value-added and final demand) which have been common in the extended demand-driven Leontief model and have been recently proposed in the supply-driven Ghosh model. Extended linear models are refinements that aim at endowing the linear models with additional general equilibrium feedbacks. We detect that these rules may give rise in these models to some allegedly pathological and biased behavior. We find that in these models sectoral or aggregate output may not follow the logical and economically expected direct relationship with some underlying endogenous variables — namely, output and value-added in the supply-driven model and output and consumption in the demand-driven model. Because of their shared mathematical structure, whatever is or seems to be pathological in the Ghosh model also has a symmetric counterpart in the Leontief model. These would not be good news for the inner consistency of these linear models and raise doubts regarding the validity of their empirical applications. To avoid such possible inconsistencies, we propose new and simple endogeneization rules that have a sound economic interpretation.     

Optimal search,learning and implementation

We characterize the incentive compatible, constrained efficient policy (“second-best”) in a dynamic matching environment, where impatient, privately informed agents arrive over time, and where the designer gradually learns about the distribution of agents? values. We also derive conditions on the learning process ensuring that the complete-information, dynamically efficient allocation of resources (“first-best”) is incentive compatible. Our analysis reveals and exploits close, formal relations between the problem of ensuring implementable allocation rules in our dynamic allocation problems with incomplete information and learning, and between the classical problem, posed by Rothschild (1974) [20], of finding optimal stopping policies for search that are characterized by a reservation price property.