Monotonicity and Implementability

Consider an environment with a finite number of alternatives, and agents with private values and quasilinear utility functions. A domain of valuation functions for an agent is a monotonicity domain if every finite‐valued monotone randomized allocation rule defined on it is implementable in dominant strategies. We fully characterize the set of all monotonicity domains.     

On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First‐Price Auctions

We establish the existence of pure strategy equilibria in monotone bidding functions in first‐price auctions with asymmetric bidders, interdependent values, and affiliated one‐dimensional signals. By extending a monotonicity result due to Milgrom and Weber (1982), we show that single crossing can fail only when ties occur at winning bids or when bids are individually irrational. We avoid these problems by considering limits of ever finer finite bid sets such that no two bidders have a common serious bid, and by recalling that single crossing is needed only at individually rational bids. Two examples suggest that our results cannot be extended to multidimensional signals or to second‐price auctions.     

PROPERTY RIGHTS AND THE EFFICIENCY OF BARGAINING

We show that efficient bargaining is impossible for a wide class of economic settings and property rights. These settings are characterized by (i) the existence of “adverse efficient opt‐out types”, whose participation does not change the efficient allocation and who, when they opt out, are the worst type other agents can face, and (ii) non‐existence of the “marginal core”, and its multivaluedness with a positive probability. We also examine the optimal allocation of property rights within a given class that satisfies (i), such as simple property rights, liability rules, and dual‐chooser rules. We characterize property rights that minimize the expected subsidy required to implement efficiency. With two agents, simple property rights that are optimal in this way maximize the expected surplus at the status quo allocation, but this no longer holds with more agents. We also study “second‐best” budget‐balanced bargaining under a liability rule. The optimal “second‐best” liability rule may differ from, but is often close to, the expectation of the victim's harm, which would be optimal if there were no bargaining. However, liability rules that are close to a simple property right result in a lower expected surplus than the simple property right they are near.     

Impartial Nominations for a Prize

A group of peers must choose one of them to receive a prize; everyone cares only about winning, not about who gets the prize if someone else. An award rule is impartial if one's message never influences whether or not one wins the prize. We explore the consequences of impartiality when each agent nominates a single (other) agent for the prize. On the positive side, we construct impartial nomination rules where both the influence of individual messages and the requirements to win the prize are not very different across agents. Partition the agents in two or more districts, each of size at least 3, and call an agent a local winner if he is nominated by a majority of members of his own district; the rule selects a local winner with the largest support from nonlocal winners, or a fixed default agent in case there is no local winner. On the negative side, impartiality implies that ballots cannot be processed anonymously as in plurality voting. Moreover, we cannot simultaneously guarantee that the winner always gets at least one nomination, and that an agent nominated by everyone else always wins.     

Quantile and Probability Curves Without Crossing

This paper proposes a method to address the longstanding problem of lack of monotonicity in estimation of conditional and structural quantile functions, also known as the quantile crossing problem (Bassett and Koenker (1982)). The method consists in sorting or monotone rearranging the original estimated non‐monotone curve into a monotone rearranged curve. We show that the rearranged curve is closer to the true quantile curve than the original curve in finite samples, establish a functional delta method for rearrangement‐related operators, and derive functional limit theory for the entire rearranged curve and its functionals. We also establish validity of the bootstrap for estimating the limit law of the entire rearranged curve and its functionals. Our limit results are generic in that they apply to every estimator of a monotone function, provided that the estimator satisfies a functional central limit theorem and the function satisfies some smoothness conditions. Consequently, our results apply to estimation of other econometric functions with monotonicity restrictions, such as demand, production, distribution, and structural distribution functions. We illustrate the results with an application to estimation of structural distribution and quantile functions using data on Vietnam veteran status and earnings.     

Priority Rules for Multi‐Task Due‐Date Scheduling under Varying Processing Costs

We study the scheduling of multiple tasks under varying processing costs and derive a priority rule for optimal scheduling policies. Each task has a due date, and a non‐completion penalty cost is incurred if the task is not completely processed before its due date. We assume that the task arrival process is stochastic and the processing rate is capacitated. Our work is motivated by both traditional and emerging application domains, such as construction industry and freelance consulting industry. We establish the optimality of Shorter Slack time and Longer remaining Processing time (SSLP) principle that determines the priority among active tasks. Based on the derived structural properties, we also propose an effective cost‐balancing heuristic policy and demonstrate the efficacy of the proposed policy through extensive numerical experiments. We believe our results provide operators/managers valuable insights on how to devise effective service scheduling policies under varying costs.     

An Evaluation of the NERJIT Priority Rule in a Kanban‐Controlled Flowshop

Significant progress in production and information technologies and innovations in management of operations during the last couple of decades have made the production of small lots and deployment of Just‐In‐Time (JIT) concepts in flowshops possible. As a result, some researchers and practitioners have been seeking to improve the performance of non‐repetitive systems using JIT concepts. In this process, the JIT concepts that were originally designed for mass production have been modified to adapt JIT to non‐repetitive systems. This article uses a priority rule that is based on real‐time demand and production information for sequencing jobs in a kanban‐controlled flowshop. The analysis of the effect of this priority rule; the number of kanbans; the length of the withdrawal cycle; First‐Come, First‐Served (FCFS); and Shortest Processing Time (SPT) on four performance measures—customer wait time, total inventory, input stock‐point inventory, and output stock‐point inventory, shows that the use of this priority rule results in a significant reduction of customer wait time and a slight decrease in inventory.     

Impartiality,Priority, and Solidarity in the Theory of Justice

The ethic of priority is a compromise between the extremely compensatory ethic of outcome equality and the needs‐blind ethic of resource equality. We propose an axiom of priority and characterize resource‐allocation rules that are impartial, prioritarian, and solidaristic. They comprise a class of rules that equalize across individuals some index of outcome and resources. Consequently, we provide an ethical rationalization for the many applications in which such indices have been used (e.g., the human development index, the index of primary goods, etc.).     

Inventory Commitment and Prioritized Backlogging Clearance with Alternative Delivery Lead Times

We propose a model where customers are classified into two groups: short lead‐time customers who require the product immediately and long lead‐time customers to whom the supplier may deliver either immediately or in the next cycle. Unmet orders are backlogged with associated costs. Specifically, the supplier faces two problems: how the on‐hand inventories should be allocated between the two classes of customers and how the backlogged orders should be cleared when replenishments arrive. We treat the former as an inventory commitment problem and handle the latter with priority rules. We characterize and compare the inventory commitment policies with three priority rules in clearing backlogs. We also explore the optimal inventory replenishment decision and evaluate the performance of each priority rule.     

MONEY PUMPS IN THE MARKET

Agents who employ non‐rational choice procedures are often vulnerable to exploitation, in the sense that a profit‐seeking trader can offer them a harmful transaction which they will nevertheless accept. We examine the vulnerability of a procedure for deciding whether to buy a lottery: observe another agent who already bought it and buy the lottery if that agent's experience was positive. We show that the exploitation of such agents can be embedded in an inter‐temporal market mechanism, in the form of speculative trade in an asset of no intrinsic value. (JEL: D84)     

Testing for Stochastic Monotonicity

We propose a test of the hypothesis of stochastic monotonicity. This hypothesis is of interest in many applications in economics. Our test is based on the supremum of a rescaled U‐statistic. We show that its asymptotic distribution is Gumbel. The proof is difficult because the approximating Gaussian stochastic process contains both a stationary and a nonstationary part, and so we have to extend existing results that only apply to either one or the other case. We also propose a refinement to the asymptotic approximation that we show works much better in finite samples. We apply our test to the study of intergenerational income mobility.     

Multiperson Bargaining and Strategic Complexity

We investigate the effect of introducing costs of complexity in the n‐person unanimity bargaining game. As is well‐known, in this game every individually rational allocation is sustainable as a Nash equilibrium (also as a subgame perfect equilibrium if players are sufficiently patient and if n & 2). Moreover, delays in agreement are also possible in such equilibria. By limiting ourselves to a plausible notion of complexity that captures length of memory, we find that the introduction of complexity costs (lexicographically with the standard payoffs) does not reduce the range of possible allocations but does limit the amount of delay that can occur in any agreement. In particular, we show that in any n‐player game, for any allocation z, an agreement on z at any period t can be sustained as a Nash equilibrium of the game with complexity costs if and only if t≤n. We use the limit on delay result to establish that, in equilibrium, the strategies implement stationary behavior. Finally, we also show that ‘noisy Nash equilibrium’ with complexity costs sustains only the unique stationary subgame perfect equilibrium allocation.     

基于优先权拍卖的产能分配机制研究

本文考虑一个供应商和两个独立零售商构成的供应链系统。当供应商的产能受到约束时，零售商可能会竞争有限的产能。本文提出将“优先分配权”作为一个有价值的标的物进行拍卖，按照出价高低确定优先分配顺序。本文证明了优先权拍卖机制属于共同价值模型，并提出了两类拍卖机制：事先拍卖和事后拍卖。本文证明两类优先权拍卖机制均会促使零售商提交真实的需求作为订单量，并且满足收益等价定理。而就供应商期望利润而言，事后优先权拍卖机制要高于事先优先权拍卖机制。     

Self‐Selective Social Choice Functions Verify Arrow and Gibbard‐Satterthwaite Theorems

This paper introduces a new notion of consistency for social choice functions, called self‐selectivity, which requires that a social choice function employed by a society to make a choice from a given alternative set it faces should choose itself from among other rival such functions when it is employed by the society to make this latter choice as well. A unanimous neutral social choice function turns out to be universally self‐selective if and only if it is Paretian and satisfies independence of irrelevant alternatives. The neutralunanimous social choice functions whose domains consist of linear order profiles on nonempty sets of any finite cardinality induce a class of social welfare functions that inherit Paretianism and independence of irrelevant alternatives in case the social choice function with which one starts is universally self‐selective. Thus, a unanimous and neutral social choice function is universally self‐selective if and only if it is dictatorial. Moreover, universal self‐selectivity for such functions is equivalent to the conjunction of strategy‐proofness and independence of irrelevant alternatives or the conjunction of monotonicity and independence of irrelevant alternatives again.     

Nonparametric Instrumental Variable Estimation Under Monotonicity

The ill‐posedness of the nonparametric instrumental variable (NPIV) model leads to estimators that may suffer from poor statistical performance. In this paper, we explore the possibility of imposing shape restrictions to improve the performance of the NPIV estimators. We assume that the function to be estimated is monotone and consider a sieve estimator that enforces this monotonicity constraint. We define a constrained measure of ill‐posedness that is relevant for the constrained estimator and show that, under a monotone IV assumption and certain other mild regularity conditions, this measure is bounded uniformly over the dimension of the sieve space. This finding is in stark contrast to the well‐known result that the unconstrained sieve measure of ill‐posedness that is relevant for the unconstrained estimator grows to infinity with the dimension of the sieve space. Based on this result, we derive a novel non‐asymptotic error bound for the constrained estimator. The bound gives a set of data‐generating processes for which the monotonicity constraint has a particularly strong regularization effect and considerably improves the performance of the estimator. The form of the bound implies that the regularization effect can be strong even in large samples and even if the function to be estimated is steep, particularly so if the NPIV model is severely ill‐posed. Our simulation study confirms these findings and reveals the potential for large performance gains from imposing the monotonicity constraint.     

Strategyproof Assignment by Hierarchical Exchange

We give a characterization of the set of group‐strategyproof, Pareto‐optimal, and reallocation‐proof allocation rules for the assignment problem, where individuals are assigned at most one indivisible object, without any medium of exchange. Although there are no property rights in the model, the rules satisfying the above criteria imitate a trading procedure with individual endowments, in which individuals exchange objects from their hierarchically determined endowment sets in an iterative manner. In particular, these assignment rules generalize Gale's top trading cycle procedure, the classical rule for the model in which each individual owns an indivisible good.     

Expedient and Monotone Learning Rules

This paper considers learning rules for environments in which little prior and feedback information is available to the decision maker. Two properties of such learning rules are studied: absolute expediency and monotonicity. Both require that some aspect of the decision maker's performance improves from the current period to the next. The paper provides some necessary, and some sufficient conditions for these properties. It turns out that there is a large variety of learning rules that have the properties. However, all learning rules that have these properties are related to the replicator dynamics of evolutionary game theory. For the case in which there are only two actions, it is shown that one of the absolutely expedient learning rules dominates all others.     

The Mirrlees Approach to Mechanism Design with Renegotiation (with Applications to Hold‐up and Risk Sharing)

The paper studies the implementation problem, first analyzed by Maskin and Moore (1999), in which two agents observe an unverifiable state of nature and may renegotiate inefficient outcomes following play of the mechanism. We develop a first‐order approach to characterizing the set of implementable utility mappings in this problem, paralleling Mirrlees's (1971) first‐order analysis of standard mechanism design problems. We use this characterization to study optimal contracting in hold‐up and risk‐sharing models. In particular, we examine when the contracting parties can optimally restrict attention to simple contracts, such as noncontingent contracts and option contracts (where only one agent sends a message).     

A Cooperative Savings Game Approach to a Time Sensitive Capacity Allocation and Scheduling Problem

We consider a competitive scheduling setting with arbitrary number of agents each having the option to utilize two parallel resources to satisfy its demand: (i) an in‐house resource dedicated to process only the tasks of each specific agent, and (ii) a flexible resource capable of processing all agents' workloads. In a noncooperative setting, each agent would determine how much of its demand it will subcontract to the flexible resource with the objective to deliver its entire demand as quickly as possible subject to the priority rules set by the owner of the flexible resource (i.e., third‐party). In this study, we also allow for agents to coalesce with other agents and update their initial subcontracting decisions to attain rescheduling savings. Evidently, a grand coalition of all agents can coordinate to achieve the maximum savings possible, but the resulting schedule may yield individual losses for a subset of agents (which we refer to as “losers”), thus necessitating a transfer payment scheme to distribute the rescheduling savings among the agents in an equitable way. We model the rescheduling interactions among the agents as a cooperative savings game, and propose savings distribution schemes that invoke the core allocation concept.     

DEMOCRATIC MECHANISMS

We introduce democratic mechanisms as a set of rules that must obey liberal democracy's fundamental principles of equal voting and agenda rights. We show that an appropriate combination of three rules may yield efficient provision of public projects: first, flexible and double majority rules, where the size of the majority depends on the proposal, and taxed and non‐taxed individuals need to support the proposal; second, flexible agenda costs, where the agenda‐setter has to pay a certain amount of money if his proposal does not generate enough supporting votes; third, a ban on subsidies. We highlight that universal equal treatment with regard to taxation is undesirable. Finally, we illustrate how simple constitutions involving fixed super majority rules yield socially desirable outcomes if the agenda‐setter is benevolent. (JEL: D62, D72, H40)