Prize sharing in collective contests

The characteristics of endogenously determined sharing rules and the group-size paradox are studied in a model of group contest with the following features: (i) The prize has mixed private–public good characteristics. (ii) Groups can differ in marginal cost of effort and their membership size. (iii) In each group the members decide how much effort to put without observing the sharing rules of the other groups. It is shown that endogenous determination of group sharing rules completely eliminates the group-size paradox, i.e. a larger group always attains a higher winning probability than a smaller group, unless the prize is purely private. In addition, an interesting pattern of equilibrium group sharing rules is revealed: The group attaining the lower winning probability is the one choosing the rule giving higher incentives to the members.     

Membership in citizen groups

We analyze the coordination problem of agents deciding to join a group that uses membership revenues to provide a discrete public good and excludable benefits. The public good and the benefits are jointly produced, so that benefits are valued only if the group succeeds in providing the public good. With asymmetric information about the cost of provision, the static membership game admits a unique equilibrium and we characterize the optimal membership fee. We show that heterogeneity in valuations for the excludable benefits is always detrimental to the group. However, in a dynamic contest in which heterogeneity arises endogenously (returning members receive additional seniority benefits at the expense of junior members), we show that, in the ex-ante optimal contract, offering seniority benefits is beneficial for the group, despite the heterogeneity in valuations created.     

Lotteries vs. All‐Pay Auctions in Fair and Biased Contests

The form of contests for a single fixed prize can be determined by a designer who maximizes the contestants' efforts. This article establishes that, under common knowledge of the two asymmetric contestants' prize valuations, a fair Tullock‐type endogenously determined lottery is always superior to an all‐pay‐auction; it yields larger expected efforts (revenues) for the contest designer. If the contest can be unfair (structural discrimination is allowed), then the designer's payoff under the optimal lottery is equal to his expected payoff under the optimal all‐pay auction.     

Proposal power and majority rule in multilateral bargaining with costly recognition

This paper studies a sequential bargaining model in which agents expend efforts to be the proposer. In equilibrium, agents’ effort choices are influenced by the prize and cost effects. The (endogenous) prize is the difference between the residual surplus an agent obtains when he is the proposer and the payment he expects to receive when he is not. Main results include: (1) under the unanimity voting rule, two agents with equal marginal costs propose with equal probabilities, regardless of their time preferences; (2) under a nonunanimity rule, however, the more patient agent proposes with a greater probability; (3) while, under the unanimity rule, the social cost decreases in group heterogeneity, it can increase under a nonunanimity rule; and (4) when agents are identical, the unanimity rule is socially optimal.     

Tournaments with Prize‐setting Agents*

In some tournaments, it is the contestants themselves who determine reward allocation. Union members bargain over wage distribution, and some firms allow self‐managed teams to freely determine internal resource allocation, incentive structure, and division of labor. We analyze, and test experimentally, a tournament where heterogeneous agents determine the spread between winner prize and loser prize. We investigate the relationship between prize spread, uncertainty, heterogeneity, and effort. We find that a large prize spread is associated with a low degree of uncertainty and a high degree of heterogeneity, and that heterogeneity triggers effort. By and large, our real‐effort experiment supports the theoretical predictions.     

Overbidding and overspreading in rent-seeking experiments: Cost structure and prize allocation rules

We study experimentally the effects of cost structure and prize allocation rules on the performance of rent-seeking contests. Most previous studies use a lottery prize rule and linear cost, and find both overbidding relative to the Nash equilibrium prediction and significant variation of efforts, which we term ‘overspreading.’ We investigate the effects of allocating the prize by a lottery versus sharing it proportionally, and of convex versus linear costs of effort, while holding fixed the Nash equilibrium prediction for effort. We find the share rule results in average effort closer to the Nash prediction, and lower variation of effort. Combining the share rule with a convex cost function further enhances these results. We can explain a significant amount of non-equilibrium behavior by features of the experimental design. These results contribute towards design guidelines for contests based on behavioral principles that take into account implementation features of a contest.     

Ramsey,Pigou, Heterogeneous Agents,and Nonatmospheric Consumption Externalities

This paper analyzes the effects of nonatmospheric consumption externalities on optimal commodity taxation and on the social cost and optimal levels of public good provision. A negative consumption externality, by lowering the social cost of public good provision, may require the second‐best level of public good provision to exceed the first‐best level. If those households who are most important for building up the consumption reference level respond the least to commodity taxation, the second‐best commodity tax rate may fall short of the first‐best rate. Moreover, in this case, heterogeneity may imply an equity‐efficiency tradeoff. This tradeoff is present only if the consumption externality is of the nonatmospheric type.     

PRIVATE PROVISION OF PUBLIC GOODS AND INFORMATION DIFFUSION IN SOCIAL GROUPS

I describe a dynamic model of costly information sharing where private information affecting collective‐value actions is transmitted by social proximity. Individuals make voluntary contributions toward the provision of a pure public good, and information transmission about quality of provision is a necessary condition for collective provision to take place in a stationary equilibrium. I show that unlike in the case of private goods, better informed individuals face positive incentives to incur a cost to share information with their neighbors and that these incentives are stronger and provision of the pure public good greater the smaller are individuals' social neighborhoods.     

Symmetry and impartial lotteries

A prize is to be awarded, so each candidate designates one of his peers on a ballot. The ballots determine the lottery that selects the winner, and impartiality requires that no candidate's choice of designee impacts his own chance of winning, removing incentives for strategic ballot submission. The primary results are (1) a characterization of all impartial rules that treat agents symmetrically as voters, and (2) a characterization of all impartial rules that treat agents symmetrically as candidates. Each rule in either class may be represented as a randomization over a finite set of simple rules. These results have immediate interpretation in a second context: the division of surplus among team members. Corollaries include the constant rule impossibility of Holzman and Moulin (2013), a new dictatorship impossibility, and the first axiomatic characterization of uniform random dictatorship.     

Hospital Competition with Soft Budgets

We study the incentives for quality provision and cost efficiency for hospitals with soft budgets, where the payer can cover deficits or confiscate surpluses. While a higher bailout probability reduces cost efficiency, the effect on quality is ambiguous. Profit confiscation reduces both quality and cost efficiency. First‐best is achieved by a strict no‐bailout and no‐profit‐confiscation policy when the regulated price is optimally set. However, for suboptimal prices, a more lenient bailout policy can be welfare‐improving. When we allow for heterogeneity in costs and qualities, we also show that a softer budget can raise quality for high‐cost patients.     

The Optimal Timing of Procurement Decisions and Patent Allocations*

In a patent race, social incentives and private incentives may sometimes coincide and at other times diverge – too many researchers remain in the race. If the social planner cannot determine what stage the researchers have achieved, this informational constraint can result in a socially suboptimal outcome. We construct a mechanism in which a planner exploits the researchers' private information to determine when and to whom to allocate rights to pursue the final prize. This mechanism does not require any payments and, therefore, will not distort earlier investment incentives. It is solvable by the iterative elimination of dominated strategies.     

SHARECROPPING,LAND EXPLOITATION AND LAND‐IMPROVING INVESTMENTS*

This paper analyses the tenancy problem in a dynamic setup and addresses two long‐standing issues: inefficiency and lack of investment. It considers the problems that the tenant, with a shorter‐term interest in the farm than the landlord, might overexploit the land to maximize immediate returns even at the cost of future damages, and under‐supply long‐run productivity improving investments in land. I show that the efficient (first‐best) levels of input use and investment can be achieved (both in the steady state and in transition) by a suitable share contract which, by dampening incentives to maximize current returns, addresses the land exploitation problem, and by an appropriate cost allocation rule which can address the investment problem.     

Optimal combinatorial mechanism design

We consider an optimal mechanism design problem with several heterogenous objects and interdependent values. We characterize ex post incentives using an appropriate monotonicity condition and reformulate the problem in such a way that the choice of an allocation rule can be separated from the choice of the payment rule. Central to the analysis is the formulation of a regularity condition, which gives a recipe for the optimal mechanism. If the problem is regular, then an optimal mechanism can be obtained by solving a combinatorial allocation problem in which objects are allocated in a way to maximize the sum of virtual valuations. We identify conditions that imply regularity using the techniques of supermodular optimization.     

Optimal Monetary Policy in OLG Models with Long‐Lived Agents: A Note

This note reexamines Crettez, Michel, and Wigniolle ( 2002 ), who studied a two‐period overlapping generations model with cash‐in‐advance constraints and showed that a combination of saving tax and monetary policy involving positive nominal interest rates could achieve the first‐best allocation. The note shows that their result does not hold if agents live for three periods. The implementation of the first best requires the Friedman rule. If agents are long‐lived, saving tax cannot offset a distortion caused by the positive nominal interest rate.     

Difference-form contest success functions and effort levels in contests

We examine players' equilibrium effort levels in a contest with difference-form contest success functions in which two players compete with each other to win a prize. We show the following. At the pure-strategy Nash equilibrium of a simultaneous-move game, and in the subgame-perfect equilibrium of a sequential-move game, only one of the players expends effort or neither player expends effort. If one player's composite strength is far greater than the other player's, only the player with greater composite strength expends effort whether they move simultaneously or sequentially. If the players' valuations for the prize and their marginal probabilities of winning at (0, 0) are sufficiently small, neither player expends effort whether they move simultaneously or sequentially.     

INFORMATION,RISK SHARING,AND INCENTIVES IN AGENCY PROBLEMS

This article studies the use of information for incentives and risk sharing in agency problems. When the principal is risk neutral or the outcome is contractible, risk sharing is unnecessary or dealt with by a contract on the outcome, so information systems are used for incentives only. When the outcome is noncontractible, a risk‐averse principal relies on imperfect information for both incentives and risk sharing. Under the first‐order approach, this article relaxes Gjesdal's criterion for ranking information systems and finds conditions justifying the first‐order approach when the principal is risk averse and the outcome is noncontractible.     

Cost sharing with multiple technologies

We study cost sharing problems where gains from cooperation can come from the presence of other agents, such as when agents share their technologies. A simple model is built, where economies of scale are eliminated in order to study this effect. We use as the key axiom the property that, if an agent does not improve the technology of any coalition he joins, he should not get any part of the gain from cooperation. With properties of linearity and symmetry, this axiom characterizes a well-defined set of rules. From this set, we propose a rule derived from the familiar Shapley value. We show that it is the only rule in that set satisfying an upper-limit property on individual cost allocations or a monotonicity property when technology improves. We also derive a distinct rule using a property that ensures that no coalition has an incentive to manipulate the individual demands of its members.     

A Risk‐Dominant Allocation: Maximizing Coalition Stability

This paper presents a rule to allocate a coalition’s worth for superadditive games with positive externalities. The allocation rule awards each member their outside payoff, plus an equal share of the surplus. The resulting allocation maximizes coalition stability. Stable coalitions are Strong Nash equilibria since no subset of members has an incentive to leave. Similarly, no subset of non‐members has an incentive to join a stable coalition if the game is concave in this region. The allocation is risk‐dominant. All stable coalitions are robust to the maximum probability of 50% that players’ deviate from their individual best‐responses. The paper compares the allocation to the Shapley value and the Nash bargaining solution, and illustrates why these traditional rules result in small coalitions when applied to issues such as international environmental agreements.     

Cost sharing with multiple technologies

We study cost sharing problems where gains from cooperation can come from the presence of other agents, such as when agents share their technologies. A simple model is built, where economies of scale are eliminated in order to study this effect. We use as the key axiom the property that, if an agent does not improve the technology of any coalition he joins, he should not get any part of the gain from cooperation. With properties of linearity and symmetry, this axiom characterizes a well-defined set of rules. From this set, we propose a rule derived from the familiar Shapley value. We show that it is the only rule in that set satisfying an upper-limit property on individual cost allocations or a monotonicity property when technology improves. We also derive a distinct rule using a property that ensures that no coalition has an incentive to manipulate the individual demands of its members.     

Intragroup competition in public good games: The role of relative performance incentives and risk attitudes

We analyze a public good game (PGG) with intragroup competition in which, generally but not always, the dominant strategy is to not contribute; therefore, free riding is the unique Nash equilibrium, not achieving Pareto efficiency. We propose a PGG setup where subjects' contributions are rewarded with different individual returns following a rank‐order voluntary contribution mechanism. It is found that the resulting competition for a better return significantly increases contributions. This effect is sensitive to the salience of return differences rewarding higher contributions. Furthermore, the positive effect of return differences on contribution levels depends on an individual's return‐to‐risk sensitivity as elicited through an independent risk elicitation task.