Allocation of Prizes in Contests with Participation Constraints

We study all‐pay contests with an exogenous minimal effort constraint where a player can participate in a contest only if his effort (output) is equal to or higher than the minimal effort constraint. Contestants are privately informed about a parameter (ability) that affects their cost of effort. The designer decides about the size and number of prizes. We analyze the optimal prize allocation for the contest designer who wishes to maximize either the total effort or the highest effort. It is shown that if the minimal effort constraint is relatively high, the winner‐take‐all contest in which the contestant with the highest effort wins the entire prize sum does not maximize the expected total effort or the expected highest effort. Rather, a random contest in which the entire prize sum is equally allocated to all the participants yields a higher expected total effort as well as a higher expected highest effort.     

Strategy-proofness and population-monotonicity for house allocation problems

We study a simple model of assigning indivisible objects to agents, such as dorm rooms to students, or offices to professors, where each agent receives at most one object and monetary compensations are not possible. For these problems population-monotonicity, which requires that agents are affected by population changes in the same way, is a compelling property because tentative assignments are made in many typical situations, which may have to be revised later to take into account the changing population. We completely describe the allocation rules satisfying population-monotonicity, strategy-proofness, and efficiency. The characterized rules assign the objects by an iterative procedure in which at each step no more than two agents “trade” objects from their hierarchically specified “endowments.”     

Task assignment,incentives and technological factors

In this paper, we examine the allocation of tasks between a principal and an agent considering their incentives to provide effort, their different abilities in handling tasks, and transmission costs. We focus our attention on two tasks: the first may be handled by the principal or by the agent, whereas the second is necessarily carried out by the agent. Under a fully decentralised organisation, the agent performs both tasks, whereas, under partial delegation, the principal handles the first task and transfers the outcome to the agent who handles the second task. Assuming technological complementarities, from our analysis it emerges that, if there is imperfect observability of effort, full delegation is better at eliciting effort by the agent in the second task, whereas, in comparison with partial delegation, it lowers effort in the first task. Although with contractible effort, the choice between the two organisational forms depends only on transmission costs and on the relative ability of its members, when moral hazard problems are taken into account, the organisational choice is related to the relative importance played by the two tasks in production. If the agent's task is relatively important in production, full delegation, encouraging a higher level of effort in this task, may be optimal, even if technological factors favour partial delegation. Copyright © 2008 John Wiley & Sons, Ltd.     

Swap-flexibility in the assignment of houses

A house allocation rule should be flexible in its response to changes in agents’ preferences. We propose a specific notion of this flexibility. An agent is said to be swap-sovereign over a pair of houses at a profile of preferences if the rule assigns her one of the houses at that profile and assigns her the other house when she instead reports preferences that simply swap the positions of the two houses. A pair of agents is said to be mutually swap-sovereign over their assignments at a profile if the rule exchanges their assignments when they together report such ‘swap preferences’. An allocation rule is individually swap-flexible if any pair of houses has a swap-sovereign agent, and is mutually swap-flexible if any pair of houses has either a swap-sovereign agent or mutually swap-sovereign agents. We show for housing markets that the top-trading-cycles rule is the unique strategy-proof, individually rational and mutually swap-flexible rule. In house allocation problems, we show that queue-based priority rules are uniquely strategy-proof, individually swap-flexible and envy non-bossy. Varying the strength of non-bossiness, we characterise the important subclasses of sequential priority rules (additionally non-bossy) and serial priority rules (additionally pair-non-bossy and pair-sovereign).     

Proportional distribution schemes

An amount of income can be obtained jointly by m agents, the ith agent's share of income being θ_i. The income and the utilities of each agent are functions of the state of nature. Each agent has a probability measure over the states of nature. An efficient proportional distribution is one which is (1) Pareto optimal and for which (2) the expected proportion of income agent i recieves divided by θ_i is independent of i. It is shown that if the attitudes are strictly concave then there exists exactly one proportional distribution scheme. Furthermore, in special cases, each agent expects to recieve an income that exceeds his share.     

Fairness and implementability in allocation of indivisible objects with monetary compensations

This paper introduces a general framework for the fair allocation of indivisible objects when each agent can consume at most one (e.g., houses, jobs, queuing positions) and monetary compensations are possible. This framework enables us to deal with identical objects and monotonicity of preferences in ranking objects. We show that the no-envy solution is the only solution satisfying equal treatment of equals, Maskin monotonicity, and a mild continuity property. The same axiomatization holds if the continuity property is replaced by a neutrality property.     

Asymmetric sequential search under incomplete information

We study a multistage sequential search model with n agents who compete for one job. The agents arrive sequentially, each one in a different stage. The agents' abilities, which are private information, are derived from heterogeneous distribution functions. In each stage, the designer chooses an ability threshold. If an agent has a higher ability than the threshold in the stage in which he arrives, he gets the job and the search is over. The agent's ability is not revealed when he wins the job and the designer has only an estimation of this ability according to the threshold placed by him. We analyze the optimal ability thresholds imposed by the designer who wishes to maximize the ability estimation of the agent who gets the job net of the search cost. We also investigate the relation between the optimal ability thresholds as well as the optimal order of agents in all stages according to the agents' distributions of abilities.     

Learning and stability of the Bayesian–Walrasian equilibrium

Under the Bayesian–Walrasian Equilibrium (BWE) (see Balder and Yannelis, 2009), agents form price estimates based on their own private information, and in terms of those prices they can formulate estimated budget sets. Then, based on his/her own private information, each agent maximizes interim expected utility subject to his/her own estimated budget set. From the imprecision due to the price estimation it follows that the resulting equilibrium allocation may not clear the markets for every state of nature, i.e., exact feasibility of allocations may not occur. This paper shows that if the economy is repeated from period to period and agents refine their private information by observing the past BWE, then in the limit all agents will obtain the same information and market clearing will be reached. The converse is also true. The analysis provides a new way of looking at the asymmetric equilibrium which has a statistical foundation.     

Strategy-proof allocation when preferences are single-plateaued

Abstract. We consider private good economies with single-plateaued preferences. A solution selects for each preference profile a non-empty set of allocations. An agent strictly prefers a set of allocations to another set of allocations if and only if he strictly prefers any allocation in the first set to any in the second set according to his single-plateaued preference relation. We characterize the class of sequential-allotment solutions by essentially single-valuedness, Pareto-indifference, and coalitional stragety-proofness. These solutions are the Pareto-indifferent extensions of the solutions studied by Barberà et al. 1997. Received: 9 May 2000 / Accepted: 1 May 2001     

Team Incentives and Reference‐Dependent Preferences

We investigate a multi‐agent moral‐hazard model where agents have expectation‐based reference‐dependent preferences à la K?szegi and Rabin (2006, 2007). We show that even when each agent's probability of success in a project is independent, a principal may employ team incentives. Because the agents are loss averse, they have first‐order risk aversion to wage uncertainty. This causes the agents to work harder when their own failure is stochastically compensated through other agents' performance. In the optimal contract, agents with high performance are always rewarded, whereas agents with low performance are rewarded if and only if other agents' performance is high.     

Strategyproof multiple assignment using quotas

The allocation of heterogeneous and indivisible objects is considered where there is no medium of exchange. We characterize the set of strategyproof, nonbossy, Pareto-optimal, and neutral social choice functions when preferences are monotonic and quantity-monotonic. The characterized sets of social choice functions are sequential; agents are assigned their favorite objects among the objects not given to others before them, subject to a quota. Received: 5 January 1999 / Accepted: 14 June 1999     

On efficient trading mechanisms between one seller and n buyers

Myerson and Satterthwaite (1983) prove that if one seller and one buyer have independent private valuations for an indivisible object then no individually rational and incentive compatible trading mechanism can guarantee ex post efficiency when gains from trade are uncertain. Makowski and Mezzetti (1993) show that this is not the case when there are at least two buyers. In the latter context, if the highest possible seller's valuation is not too large, we provide an ex post efficient mechanism in which the mechanism designer and the agents are not required to know the probability distribution for the seller's valuation. Received: February 18, 1998 / Accepted: September 10, 1999     

A core equivalence theorem with an arbitrary communication structure

We formalize the concept of a communication structure by identifying it with a partition of the set of agents. Thus, a coalition can form if and only if it belongs to the given partition. Within this framework we are able to show that for every integer J≧2, if we put the uniform distribution on the space of partitions that contain exactly (or, no more than) J coalitions, the probability that such a partition will contain a blocking coalition for any Pareto optimal allocation which is bounded away from being competitive, is arbitrarily close to 1, as the number of individuals increases.     

Primetime Spin: Media Bias and Belief Confirming Information

This paper develops a model of media bias in which rational agents acquire all their news from the source that is most likely to confirm their prior beliefs. Despite only wishing to make the correct decision, agents act as if they enjoy receiving news that supports their preconceptions. By exclusively gathering information from a source biased towards his prior, there is little chance an agent will be persuaded to change his mind. Moreover, it is shown that even an unbiased agent prefers to receive biased news as it is unlikely to produce conflicting reports. The media caters to the informational demands of consumers and accordingly slants its reporting. It is shown that competition may not decrease bias, but may actually enhance it. Finally, even when it increases bias, competition may improve welfare by expanding the market for news.     

Endogenous mechanisms and Nash equilibrium in competitive contracting games

We model strategic competition in a market with asymmetric information as a noncooperative game in which each firm competes for the business of a buyer of unknown type by offering the buyer a catalog of products and prices. The timing in our model is Stackelberg: in the first stage, given the distribution of buyer types known to all firms and the deducible, type-dependent best responses of the agent, firms simultaneously and noncooperatively choose their catalog offers. In the second stage the buyer, knowing his type, chooses a single firm and product-price pair from that firm’s catalog. By backward induction, this Stackelberg game with asymmetric information reduces to a game over catalogs with payoff indeterminacies. In particular, due to ties within catalogs and/or across catalogs, corresponding to any catalog profile offered by firms there may be multiple possible expected firm payoffs, all consistent with the rational optimizing behavior of the agent for each of his types. The resolution of these indeterminacies depends on the tie-breaking mechanism which emerges in the market. Because each tie-breaking mechanism induces a particular game over catalogs, a reasonable candidate would be a tie-breaking mechanism which supports a Nash equilibrium in the corresponding catalog game. We call such a mechanism an endogenous Nash mechanism. The fundamental question we address in this paper is, does there exist an endogenous Nash mechanism—and therefore, does there exist a Nash equilibrium for the catalog game? We show under fairly mild conditions on primitives that catalog games naturally possess tie-breaking mechanisms which support Nash equilibria.     

Fair division of a measurable space

A given total product is said to be divided up fairly among N agents, if this division is Pareto optimal and equitable (i.e., every agent subjectively feels himself to be better off than any one of the others). Describing tastes of agents as measures on a measurable space, standing for total product, it is proved that fair divisions exist.     

A Mixed Contract with Alternative Performance Measures in a Multitask Agency

We compare the impact of two different mixed contracts on agent efforts when production depends on agent efforts at their own tasks as well as at helping others. The first contract combines compensation based on team output with that of a tournament where the bonus award is based on a ranking of individual output. The second contract also combines team output compensation with that of tournament except that the bonus award is based upon a relative ranking of an index constructed of alternative performance measures. We show that the latter contract can lead to higher levels of welfares than the former one. We also show that if the weights are properly constructed, the alternative contract can prompt agents into choosing first‐best levels of effort. Copyright © 2013 John Wiley & Sons, Ltd.     

Multiperiod security markets with differential information: Martingales and resolution times

We model multiperiod securities markets with differential information. A price system that admits no free lunches is related to martingales when agents have rational expectations. We introduce the concept of resolution time, and show that a better informed agent and a less informed agent must agree on the resolution times of commonly marketed events if they have rational expectations and if there are no free lunches. It then follows that if all elementary events are marketed for a less informed agent then any price system that admits no free lunches to a better informed agent must eliminate any private information asymmetry between the two. We provide an example of a dynamically fully revealing price system that is arbitrage free and yields elementarily complete markets.     

Stratification of Skewed Populations: A Comparison of Optimisation‐based versus Approximate Methods

Survey statisticians use either approximate or optimisation‐based methods to stratify finite populations. Examples of the former are the cumrootf (Dalenius & Hodges, 1957 ) and geometric (Gunning & Horgan, 2004 ) methods, while examples of the latter are Sethi ( 1963 ) and Kozak ( 2004 ) algorithms. The approximate procedures result in inflexible stratum boundaries; this lack of flexibility results in non‐optimal boundaries. On the other hand, optimisation‐based methods provide stratum boundaries that can simultaneously account for (i) a chosen allocation scheme, (ii) overall sample size or required reliability of the estimator of a studied parameter and (iii) presence or absence of a take‐all stratum. Given these additional conditions, optimisation‐based methods will result in optimal boundaries. The only disadvantage of these methods is their complexity. However, in the second decade of 21st century, this complexity does not actually pose a problem. We illustrate how these two groups of methods differ by comparing their efficiency for two artificial populations and a real population. Our final point is that statistical offices should prefer optimisation‐based over approximate stratification methods; such a decision will help them either save much public money or, if funds are already allocated to a survey, result in more precise estimates of national statistics.     

An equivalence theorem for a differential information economy

In a pure exchange economy with differential information and a finite set of traders, physical commodities and states of nature, we characterize the Walrasian expectations or Radner equilibria by using the veto power of the grand coalition. We prove that an allocation x is a Radner equilibrium allocation if and only if it is “privately non-dominated” by the grand coalition in every economy obtained by perturbing the original initial endowments in the direction of x. The first and second welfare theorems become particular cases of our main result. Since the deterministic Arrow–Debreu–McKenzie model is a special case of the differential information economy model we also provide a new characterization of the Walrasian equilibria.