What price stability? Social welfare in matching markets

In two-sided matching markets, stability can be costly. We define social welfare functions for matching markets and use them to formulate a definition of the price of stability. We then show that it is common to find a price tag attached to stability, and that the price of stability can be substantial. Therefore, when choosing a matching mechanism, a social planner would be well advised to weigh the price of stability against the value of stability, which varies from market to market.     

Examining risk attitudes

The existence of risky choices makes the study of attitudes toward risk important. In this article we ask the following questions: Do risk‐neutral preferences maximize utility? Are there other measures of social welfare that can explain risk aversion in society? What effect does evolution have on the distribution of risk attitudes and the measures of social welfare? In a static environment risk‐neutral risk attitudes maximize utilitarian measures of social welfare, and risk‐averse attitudes maximize Rawlsian measures. In a dynamic system agents will tend toward risk, preferring greater affinity for risk when they can accumulate wealth. © 2004 Wiley Periodicals, Inc. Complexity 9: 25–30, 2004     

Optimizing reserves in school choice: A dynamic programming approach

We introduce a new model of school choice with reserves in which asocial planner is constrained by a limited supply of reserve seats and tries to find the matching that is optimal according to a social welfare function. We construct the optimal distribution of reserves via a quartic-time dynamic programming algorithm. Due to the modular nature of the algorithm, the resulting mechanism is strategy-proof for reserve-eligible students.     

信息不对称条件下竞价排名机制的信息匹配效率研究

本文聚焦消费者依赖搜索引擎平台的关键词检索实施购买商品行为的现象,尝试将消费者购买策略引入搜索平台竞价排名机制,构造内嵌搜索引擎平台、销售商、消费者三方主体的博弈模型,考察在互联网信息不对称条件下,竞价排名机制的信息匹配效率,阐释产品质量信号改善竞价排名机制信息匹配效率的理论机理。研究发现,在信息不对称及无产品质量信号机制的条件下,竞价排名均衡结果完全不能匹配消费者的购买策略,致使消费者福利因销售商逆向选择而遭受双重损失;植入产品质量信号后,搜索引擎平台能够通过识别销售商自带的产品质量信号,提高竞价排名机制的均衡结果与消费者购买策略的匹配度,进而部分地改善竞价排名机制的信息匹配效率。     

罕见灾难事件的福利减损效应研究

通过修正随机消费函数,构建了包含罕见灾难状态的理论模型,并根据中国经验消费数据测算了罕见灾难事件对国民福利的减损效应.研究发现:罕见灾难事件对国民经济福利的减损效应相当大,在合理的参数范围内,为通常意义上的经济波动福利减损效应的数十倍.罕见灾难事情的持续时间越长,福利减损效应越显著.相应的防灾减灾措施,可以有效降低灾难风险,进而提升灾难发生期的国民经济福利.因此,科学制定合理的宏观经济政策是必要的,其作用主要体现于缩短国民经济处于罕见灾难状态的时长、降低可避免的罕见灾难发生的概率以及减轻罕见灾难发生后经济衰退的幅度.     

Welfare measurement and the health environment

An important issue in environmental economics is to augment the conventional net national product measure so as to cover changes in stocks of natural resources. In this paper, we show how to treat health (capital) effects in welfare measures caused by, for example, pollution. We also show the effects the risk of doomsday caused by pollution has on these measures. A Ramsey growth model enlarged with health capital and death risks is used to derive an augmented welfare measure. A way of solving the particular technical problem one faces when the death risk depends on a state variable (health capital) is also presented. This measure is contrasted with the conventional net national product measure. We also briefly discuss the welfare properties of a market economy when individuals invest in health capital but face a strictly positive death risk.     

Toward eudaimonology: notes on a quantitative framework for the study of happiness

After noting factors (concern for others, ignorance, irrationality) accounting for the divergences between preference and happiness, the question of representing the preference of an individual by a utility function is discussed, taking account of lexicographic ordering, imperfect discrimination and the corresponding concepts of semiorder and sub-semiorder. Methods to improve upon the interpersonal comparability of measures of happiness such as pinning down the dividing line of zero happiness and the use of a just perceivable increment of happiness are discussed. The relation of social welfare to individual welfare (i.e. happiness) is then considered. Some reasonable set of axioms ensuring that social welfare is a separable function of and indeed an unweighted sum of individual welfares are reviewed. Finally, happiness is regarded as a function of objective, institutional and subjective factors; an interdisciplinary approach is needed even for an incomplete analysis.     

Instability of matchings in decentralized markets with various preference structures

In any two-sided matching market, a stable matching can be found by a central agency using the deferred acceptance procedure of Gale and Shapley. But if the market is decentralized and information is incomplete then stability of the ensuing matching is not to be expected. Despite the prevalence of such matching situations, and the importance of stability, little theory exists concerning instability. We discuss various measures of instability and analyze how they interact with the structure of the underlying preferences. Our main result is that even the outcome of decentralized matching with incomplete information can be expected to be “almost stable” under reasonable assumptions.     

模糊软集的相似测度和距离测度(英文)

In this paper we introduce several new similarity measures and distance measures between fuzzy soft sets, these measures are examined based on the set-theoretic approach and the matching function. Comparative studies of these measures are derived. By introducing two general formulas, we propose a new method to define the similarity measures and the distance measures between two fuzzy soft sets with different parameter sets.     

Intrafirm trade, arm’s-length transfer pricing rule, and coordination failure

This paper demonstrates that uniform imposition of the arm’s-length principle on transfer pricing leads to coordination failure among countries in terms of economic welfare if the countries trade products in the form of intrafirm transactions by multinational firms (MNFs). To highlight this implication, we first show that imposition of the arm’s-length principle on an MNF induces it to transfer a product among subordinate divisions at marginal cost, i.e., the competitive price, which is consistent with the purpose of the principle. Nonetheless, if regulators in each country impose the principle on MNFs, all of the following economic welfare measures decrease compared with the situation where the principle is not imposed: (1) consumer welfare in each of the trading countries, (2) profit of each MNF, and thus (3) total world economic welfare. This result indicates that it is possible that enforcement of the principle has no positive effect at all in the world because economic welfare of all economic agents deteriorates when the principle is imposed. A numerical analysis demonstrates that this possibility arises in a broad range of circumstances, even including the situation where a giant economic world power and a small underdeveloped country mutually trade products. In these circumstances, an agreement among trading countries that no country imposes the arm’s-length principle may encourage Pareto improvement of the world economy.     

基于基尼系数的区域创新投入产出熵权TOPSIS匹配性评价分析

采用匹配基尼系数对我国创新系统投入产出匹配性程度进行了测算。通过构建基于基尼系数的TOPSIS熵权评价模型,对我国大陆31个省市自治区的创新投入产出匹配性进行了评价,对各地区投入产出匹配性评价值聚类分析。研究结果表明我国创新系统投入产出呈现出不匹配的状态,形成了京津、长江三角洲和珠江三角洲三个极化区域。研究结果验证了本文构建模型的可行性和合理性,为区域创新投入产出的研究提供了新的思路。     

Nash equilibria in optimal reinsurance bargaining

We introduce a strategic behavior in reinsurance bilateral transactions, where agents choose the risk preferences they will appear to have in the transaction. Within a wide class of risk measures, we identify agents’ strategic choices to a range of risk aversion coefficients. It is shown that at the strictly beneficial Nash equilibria, agents appear homogeneous with respect to their risk preferences. While the game does not cause any loss of total welfare gain, its allocation between agents is heavily affected by the agents’ strategic behavior. This allocation is reflected in the reinsurance premium, while the insurance indemnity remains the same in all strictly beneficial Nash equilibria. Furthermore, the effect of agents’ bargaining power vanishes through the game procedure and the agent who gets more welfare gain is the one who has an advantage in choosing the common risk aversion at the equilibrium.     

The emergence of kinship behavior in structured populations of unrelated individuals

The paper provides an explanation for altruistic behavior based on the matching and learning technology in the population. In a infinite structured population, in which individuals meet and interact with their neighbors, individuals learn by imitating their more successful neighbors. We ask which strategies are robust against invasion of mutants: A strategy is unbeatable if when all play it and a finite group of identical mutants enters then the learning process eliminates the mutants with probability 1. We find that such an unbeatable strategy is necessarily one in which each individual behaves as if he is related to his neighbors and takes into account their welfare as well as his. The degree to which he cares depends on the radii of his neighborhoods. Received June 1996/Revised version October 1998     

The information value of logistics platforms in a freight matching market

The information asymmetry in the freight matching of the long-haul trucking industry usually pushes shippers to join a logistics platform that has better knowledge of truckers’ cost information. A logistics platform that is plugged into a freight transportation system helps shippers overcome their information disadvantage but produces the double marginalization effect. We investigate the equilibrium characteristics of a shipper and logistics platform in the freight matching market and find that the shipper prefers to cooperate with the logistics platform in a small-scale sales market but searches for truckers by himself in a large-scale sales market. We show that the information value of a logistics platform for the freight system consists of two aspects: (i) employ low-cost truckers for the shipper and avoid the shipper’s inefficient expansion of the selling quantity in a moderate-scale sales market with greatly heterogeneous truckers, and (ii) improve both the total profit and social welfare of the freight system in a small-scale sales market. We further find that the shipper’s private information may hurt the logistics platform and the logistics platform can mitigate her double marginalization disadvantage by improving value-added services or lowering the logistics price in a large-scale market. Our findings provide guidelines for the shipper and logistics platform on how to choose the appropriate transportation strategy and employment strategy in different logistics markets.     

Robust a Posteriori Error Estimation for a Singularly Perturbed Reaction–Diffusion Equation on Anisotropic Tetrahedral Meshes

We consider a singularly perturbed reaction–diffusion problem and derive and rigorously analyse an a posteriori residual error estimator that can be applied to anisotropic finite element meshes. The quotient of the upper and lower error bounds is the so-called matching function which depends on the anisotropy (of the mesh and the solution) but not on the small perturbation parameter. This matching function measures how well the anisotropic finite element mesh corresponds to the anisotropic problem. Provided this correspondence is sufficiently good, the matching function is O(1). Hence one obtains tight error bounds, i.e. the error estimator is reliable and efficient as well as robust with respect to the small perturbation parameter. A numerical example supports the anisotropic error analysis.     

Adaptive greedy approximations

The problem of optimally approximating a function with a linear expansion over a redundant dictionary of waveforms is NP-hard. The greedy matching pursuit algorithm and its orthogonalized variant produce suboptimal function expansions by iteratively choosing dictionary waveforms that best match the function’s structures. A matching pursuit provides a means of quickly computing compact, adaptive function approximations. Numerical experiments show that the approximation errors from matching pursuits initially decrease rapidly, but the asymptotic decay rate of the errors is slow. We explain this behavior by showing that matching pursuits are chaotic, ergodic maps. The statistical properties of the approximation errors of a pursuit can be obtained from the invariant measure of the pursuit. We characterize these measures using group symmetries of dictionaries and by constructing a stochastic differential equation model. We derive a notion of the coherence of a signal with respect to a dictionary from our characterization of the approximation errors of a pursuit. The dictionary elements slected during the initial iterations of a pursuit correspond to a function’s coherent structures. The tail of the expansion, on the other hand, corresponds to a noise which is characterized by the invariant measure of the pursuit map. When using a suitable dictionary, the expansion of a function into its coherent structures yields a compact approximation. We demonstrate a denoising algorithm based on coherent function expansions.     

基于FDI收益分成视角的FTA网络演化

本文假定双边自由贸易协定(bilateral free trade agreement,简称FTA)包含着无限制对外直接投资(foreign direct investment,简称FDI),并且通过FDI销售到非FTA伙伴国的收益按照一定比例在母国和东道国之间进行分配。基于Goyal和Joshi^[1],本文构建了FTA网络形成博弈模型。本文发现,FTA网络演化过程分为两个阶段:第一阶段,从空FTA网络到星状FTA网络,存在一条路径使得个体国家福利、世界总福利均改善,在此过程中,国家福利存在不对称性;第二阶段,从星状FTA网络到全连接FTA网络,存在一条路径使得个体国家福利改善,在此过程中,世界总福利不变,国家福利不对称性逐步消除。     

A graphical investigation of error bounds for moment-based queueing approximations

Many approximations of queueing performance measures are based on moment matching. Empirical and theoretical results show that although approximations based on two moments are often accurate, two-moment approximations can be arbitrarily bad and sometimes three-moment approximations are far better. In this paper, we investigate graphically error bounds for two- and three-moment approximations of three performance measures forGI/M/ · type models. Our graphical analysis provides insight into the adequacy of two- and three-moment approximations as a function of standardized moments of the interarrival-time distribution. We also discuss how the behavior of these approximations varies with other model parameters and with the performance measure being approximated.     

The generation of a social welfare function under ordinal preferences

Against the background of recent impossibility theorems, the paper establishes a number of rules for the formation of social preferences to ensure the generation of a Bergson-Samuelson social welfare function of the desired ‘individualistic’ form. It demonstrates that such welfare functions can indeed exist under conditions of simply ordinality of individual preferences and a lack of interpersonal comparability, for the general n-person case with only weak restrictions upon individual preferences. A valuable tool of social welfare theory for the single-profile case is therefore restored under a wide set of conditions. By examining Kemp and Ng's justification for their A3 condition in this context, we are able also to highlight a number of key differences between the conditions satisfied by many political constitutions and the requirements for achieving the positive existence of a Bergson-Samuelson social welfare function. In particular the paper focusses here on the weighting systems on individual preferences that are consistent with generating an individualistic welfare function and examines the information content of individual ordinal preferences which must be utilized if the desired welfare function is to result.