On the existence of a strictly strong Nash equilibrium under the student-optimal deferred acceptance algorithm

This study analyzes a preference revelation game in the student-optimal deferred acceptance algorithm in a college admission problem. We assume that each college's true preferences are known publicly, and analyze the strategic behavior of students. We demonstrate the existence of a strictly strong Nash equilibrium in the preference revelation game through a simple algorithm that finds it. Specifically, (i) the equilibrium outcome from our algorithm is the same matching as in the efficiency-adjusted deferred acceptance algorithm and (ii) in a one-to-one matching market, it coincides with the student-optimal von Neumann–Morgenstern (vNM) stable matching. We also show that (i) when a strict core allocation in a housing market derived from a college admission market exists, it can be supported by a strictly strong Nash equilibrium, and (ii) there exists a strictly strong Nash equilibrium under the college-optimal deferred acceptance algorithm if and only if the student-optimal stable matching is Pareto-efficient for students.     

Incomplete information and singleton cores in matching markets

We study ordinal Bayesian Nash equilibria of stable mechanisms in centralized matching markets under incomplete information. We show that truth-telling is an ordinal Bayesian Nash equilibrium of the revelation game induced by a common belief and a stable mechanism if and only if all the profiles in the support of the common belief have singleton cores. Our result matches the observations of Roth and Peranson [The redesign of the matching market for American physicians: some engineering aspects of economic design, Amer. Econ. Rev. 89 (1999) 748-780] in the National Resident Matching Program (NRMP) in the United States: (i) the cores of the profiles submitted to the clearinghouse are small and (ii) while truth-telling is not a dominant strategy most participants in the NRMP truthfully reveal their preferences.     

Strategy-proof assignment on the full preference domain

We consider the problem of efficiently allocating several indivisible objects between agents who are to receive at most one object and whose preferences are private information. We examine this standard “assignment” problem from the perspective of mechanism design giving up the usual assumption of linear preferences and instead using a full preference domain (with indifferences permitted). We characterize two classes of mechanisms: (i) Bi-polar Serially Dictatorial Rules by Essential Single-Valuedness, Pareto Indifference, Strategy-Proofness and Non-Bossiness; and (ii) all selections from Bi-polar Serially Dictatorial Rules by Single-Valuedness, Efficiency, Strategy-Proofness and Weak Non-Bossiness. We compare the outcomes from the (Bi-polar) Serially Dictatorial Rules with the outcomes obtained using a market based approach, namely the “core” of the market. We show that all strongly efficient outcomes in the core can be generated using Serially Dictatorial Rules. Moreover, we argue that Serially Dictatorial Rules have an advantage over the market based approach in that they yield strongly efficient solutions for all preference profiles, making it possible to use randomization to restore equity. When preferences are private information, this type of ex ante equity cannot be implemented using the market based approach.     

Income redistribution going awry: The reversal power of the concern for relative deprivation

We demonstrate that a rank-preserving transfer from a richer individual to a poorer individual can exacerbate income inequality (when inequality is measured by the Gini coefficient). This happens when individuals’ preferences depend negatively not only on work time (effort) but also on low relative income. It is rigorously shown that the set of preference profiles that gives rise to this perverse effect of a transfer on inequality is a non-empty open subset of all preference profiles. A robust example illustrates this result.     

A strategy-proofness characterization of majority rule

Summary. A feasible alternative x is a strong Condorcet winner if for every other feasible alternative y there is some majority coalition that prefers x to y. Let (resp., denote the set of all profiles of linear (resp., merely asymmetric) individual preference relations for which a strong Condorcet winner exists. Majority rule is the only non-dictatorial and strategy-proof social choice rule with domain , and majority rule is the only strategy-proof rule with domain . Received: August 29, 2000; revised version: November 13, 2002 RID="*" ID="*"We are grateful to Wulf Gaertner and our two referees for insightful comments on a previous draft. Correspondence to: D. E. Campbell     

Counting combinatorial choice rules

I count the number of combinatorial choice rules that satisfy certain properties: Kelso–Crawford substitutability, and independence of irrelevant alternatives. The results are important for two-sided matching theory, where agents are modeled by combinatorial choice rules with these properties. The rules are a small, and asymptotically vanishing, fraction of all choice rules. But they are still exponentially more than the preference relations over individual agents—which has positive implications for the Gale–Shapley algorithm of matching theory.     

Indifference and incompleteness distinguished by rational trade

We use an agent's strict preferences to define indifference and incompleteness relations that identify the sequences of trades that are rational to undertake. If an agent makes sequences of trades of options labeled indifferent, the agent will never be led to an inferior outcome, but trades of options where no preference judgments obtain can lead to diminished welfare. For one-shot choices, in contrast, there can be no behavioral distinction between indifference and incompleteness. Applications include: an isomorphism for incomplete preferences that indicates when weak and strict preferences contain interchangeable information, a characterization of the (possibly incomplete) preference relations consistent with a one-shot choice function, and an equivalent definition of incompleteness that relies on the philosophical theory of incommensurability.     

The probability of violating Arrow’s conditions

Arrow’s impossibility theorem shows that all preference aggregation rules (PARs) must violate a specific set of normative conditions (transitivity, Pareto, IIA, nondictatorship) over an unrestricted domain of preference profiles. However, the theorem does not address which PARs are more likely to violate those conditions across preference profiles. We compare the probabilities that thirteen PARs (anti-plurality, Hare, Nanson, plurality, plurality runoff, Simpson–Kramer, Baldwin, Borda, Coombs, Copeland, Dowdall, pairwise majority, and ranked pairs) violate Arrow’s conditions. We prove that Baldwin, Borda, Coombs, Copeland, Dowdall, and ranked pairs are less likely to violate IIA than the first six PARs, and they are less likely to violate Arrow’s conditions jointly. In contrast, pairwise majority never violates IIA but can violate transitivity. Simulations with three alternatives reveal that among the PARs studied, pairwise majority is the most likely to satisfy Arrow’s conditions jointly. Our results suggest pairwise majority violates transitivity with a small probability, while the other PARs violate IIA with much larger probabilities.     

Analysis of the equity preference influence in customer participation incentives

In this paper, equity preference is introduced into the customer participation (CP) incentive problem and new principal–agent models are built. The proposed models are different from the Holmstrom and Milgrom's models (1987) because of the consideration of equity preference, which emphasize the material utility and equitable distribution of customers. By assuming that the incentives that firms pay to customers have the same effect on monetary incentives, the optimal incentives are discussed, in which the equilibrium solutions are explored and the respective impact of horizontal equity preference and vertical equity preference on CP incentives are compared. The proposed models are validated by numerical experiments in the product enhancement project of a large software enterprise in Guangzhou. It can be demonstrated that 1) asymmetric information induces lazy behaviors of customers concerning vertical equity preference; 2) horizontal equity preference promotes the work enthusiasm of customers in CP more than self-interest does; and 3) it is more conducive to obtain a much bigger expected income when firms employ customers with horizontal equity preference to participate in innovation process.     

Not quite the best response: truth-telling,strategy-proof matching,and the manipulation of others

Following the advice of economists, school choice programs around the world have lately been adopting strategy-proof mechanisms. However, experimental evidence presents a high variation of truth-telling rates for strategy-proof mechanisms. We crash test the connection between the strategy-proofness of the mechanism and truth-telling. We employ a within-subjects design by making subjects take two simultaneous decisions: one with no strategic uncertainty and one with some uncertainty and partial information about the strategies of other players. We find that providing information about the out-of-equilibrium strategies played by others has a negative and significant effect on truth-telling rates. That is, most participants in our within-subjects design try and fail to best-respond to changes in the environment. We also find that more sophisticated subjects are more likely to play the dominant strategy (truth-telling) across all the treatments. These results have potentially important implications for the design of markets based on strategy-proof matching mechanisms.     

On the observational equivalence of random matching

Random matching is often used in economic models as a means of introducing uncertainty in sequential decision problems. We show that random matching processes that satisfy standard proportionality laws are not unique. We give conditions on the payoffs and transition functions of sequential decision models that insure that economic models are robust to the nonuniqueness of the matching process. Under these conditions, the information contained in the proportionality laws is all that is needed to know about the matching process to formulate the model.     

On the distribution of job characteristics: an analysis of the DOT data

We analyse the information in the Dictionary of Occupational Titles to characterize the structure of labour demand. Two dimensions, an intellectual factor and a dexterity factor, capture two-thirds of the variance in job requirements; the remaining (co-)variance cannot be easily structured. Simple linear relationships go a long way in describing the matching between job activities and required worker qualities (Intellect for complex relations to Data and to People, Dexterity for complex relations to Things). There is no dichotomy between mathematical and verbal required skills. Poor working conditions are not restricted to workers in low-level jobs; we find strong support for compensating wage differentials. At more intellectual jobs, men receive less wage compensation for working conditions, while in jobs requiring greater dexterity they receive more. Such a relationship is absent for women.     

基于不同产业的产学研人员匹配关系研究

在现实经济中,由于产业类型不同,产学研合作中的企业人员和研究人员组合匹配关系也不一样。基于演化博弈的方法,以各类人员选择进入某产业作为战略和利润函数,并以这两种函数作为效用函数,展开对产学研人员匹配关系的分析。研究发现,在一个国家两个产业同时存在的条件下,均衡点成立的效用函数等式关系;根据此等式关系,找到了均衡点,并对这些均衡点展开分析说明,发现有些均衡点是稳定的,有些是不稳定的;同时在给定的参数值的基础上,计算出这些均衡点的各种数值,说明这些均衡中存在一个帕累托均衡点;通过引入稳定点的转移成本,计算出各个稳定点之间的转移成本,证明了这个帕累托均衡点是可以实现的。     

STRATEGY‐PROOF ALLOCATION OF INDIVISIBLE GOODS AMONG COUPLES

We consider the problem of allocating indivisible goods among couples. Agents in a couple share the indivisible good assigned to them. The main result is that an allocation rule is strategy‐proof, neutral and non‐bossy if and only if it is serially dictatorial. An allocation rule is serially dictatorial if there is a priority order of couples and a function that identifies who chooses in each couple, such that for all preference profiles, a good assigned to couple i is the best element according to the preference of the identified agent in couple i among the remaining goods when the couples with higher priorities have made their choice.     

Existence and stability of rational expectation-equilibria in a simple overlapping generation model

We consider a simple overlapping generation model with outside money and one consumption good. For a big class of preference relations, it is shown that globally no self-fulfilling expectation exists (except the trivial one) if the information set contains only past and present prices. Even locally, positive results can be obtained for homothetic preferences only. To get asymptotic stability this class must be restricted again: The elasticity of substitution must be very small. The implications of this are very negative: A Learning process can never reach rationality.     

Dynamic Matching and Evolving Reputations

This paper introduces a general model of matching that includes evolving public Bayesian reputations and stochastic production. Despite productive complementarity, assortative matching robustly fails for high discount factors, unlike in Becker (1973) . This failure holds around the highest (lowest) reputation agents for "high skill" ("low skill") technologies. We find that matches of likes eventually dissolve. In another life-cycle finding, young workers are paid less than their marginal product, and old workers more. Also, wages rise with tenure but need not reflect marginal products: information rents produce non-monotone and discontinuous wage profiles.     

旅游区域的城市与景区空间匹配及其实践意义

城市和景区是区域旅游网络中两个基本节点,它们之间关系紧密,包含多种空间匹配关系。数量关系上由一对一匹配、一对多匹配、多对一匹配、多对多匹配构成;等级关系上由正位匹配和倒位匹配构成;距离关系上由城区城郊型、一日游型、离散型构成;几何分布关系上由点轴匹配和面状匹配构成;管理匹配关系上由同位管理匹配和异位管理匹配构成。分析城市与景区空间匹配组合特征,对于寻找合理的景区依托城镇、采取正确的区域旅游发展战略等都具有重要的实践意义。     

Matching mechanisms and matching quality: Evidence from a top university in China

We compare competing college admission matching mechanisms that differ in preference submission timing (pre-exam, post-exam but pre-score, or post-score) and in matching procedure (Boston (BOS) and serial dictatorship (SD) matching). Pre-exam submission asks students to submit college preferences before entrance exam scores are known, whereas post-score (post-exam) submission removes (reduces) score uncertainties. Theoretical analyses show that although mechanisms with post-score submission or SD matching are ex-post fair and efficient, they are not so ex-ante. Instead, the mechanism with pre-exam submission and BOS matching can be more fair and efficient ex-ante. These hypotheses are supported by empirical test on data from a top school at a top-ranked Chinese university with identification based on temporal and provincial changes. We find that although students admitted under the pre-exam BOS mechanism have lower college entrance exam scores than students admitted through other mechanisms on average, they exhibit similar or even better college academic performance.     

On coalitional stability of anonymous interim mechanisms

Summary.   In a situation where agents have private information, we investigate the stability of mechanisms with respect to coalitional deviations. In the cooperative tradition, we first extend the notion of Core, taking into account the information a coalition may have when it forms and the conjectures of outsiders. This leads us to propose a family of Cores rather than a single one. Secondly, we study the stability of Core mechanisms to secession proposals in simple noncooperative games. The two different stability analyses, normative and strategic, tend to give support to the more natural extension of the Core, called Statistical Core, only in situations where some strong form of increasing returns to coalition is met. Without this property, arguments for a concept of Core that is non empty in a reasonably large class of problems are less compelling. Applications to taxation and insurance are given. Received: September 6, 1999; revised version: December 3, 1999     

A note on the life-cycle search and matching model with segmented labor markets

Recently, there has been renewed interest in labor search and matching models that incorporate a life-cycle structure by assuming finite horizons. Existing studies provide detailed analyses on the age dynamics of job creation and destruction, assuming that workers of all ages search for jobs in the same market. This paper examines a related environment that has drawn less attention, where the labor market is exogenously segmented by age. The paper finds sufficient conditions for the model to yield unambiguous predictions on the age profiles of key variables, and compares them with the corresponding conditions in models with a single market. The paper further examines the age profiles of these key variables in the efficient allocation. In particular, with no persistence in idiosyncratic match productivity, the efficient allocation is found to exhibit monotonic age profiles for the job finding and separation rates.