Values for two-stage games: Another view of the Shapley axioms

This short study reports an application of the Shapley value axioms to a new concept of two-stage games. In these games, the formation of a coalition in the first stage entitles its members to play a prespecified cooperative game at the second stage. The original Shapley axioms have natural equivalents in the new framework, and we show the existence of (non-unique) values and semivalues for two stage games, analogous to those defined by the corresponding axioms for the conventional (one-stage) games. However, we also prove that all semivalues (hence, perforce, all values) must give patently unacceptable solutions for some two-stage majority games (where the members of a majority coalition play a conventional majority game). Our reservations about these prescribed values are related to Roth's (1980) criticism of Shapley's -transfer value for non-transferable utility (NTU) games. But our analysis has wider scope than Roth's example, and the argument that it offers appears to be more conclusive. The study also indicates how the values and semivalues for two-stage games can be naturally generalized to apply for multi-stage games.Earlier versions of this study were presented at the International Conference on Game Theory and its Applications, organized by Ohio State University in 1987, and at the Workshop on Mathematical Economics and Game Theory at Tel Aviv Unversity. We gratefully acknowledge the valuable comments received on both occasions, especially those of Robert J. Aumann, Roy Gardner, Sergiu Hart, Ehud Kalai, Michael Maschler, Alvin E. Roth, and Lloyd S. Shapley, and also those ofIJGT's anonymous referees. Of course, all responsibility lies with us.     

Principal Submatrices of a Hermitian Matrix

Suppose k 1 ,<, k m and n are positive integers such that k 1 + … + k m h n . We characterize those k i × k i Hermitian matrices A i , i = 1, < , m that can appear as diagonal blocks of an n × n Hermitian matrix C with prescribed eigenvalues. The characterization will be given in terms of the eigenvalues of C and A i , i = 1, <, m . Our results extend those of Thompson and Freede, Horn, Fan and Pall.     

价值引领融入“无机化学与化学分析”的课程思政建设

将课程思政应用到"无机化学和化学分析"教学中,更好发挥其价值引领作用。开展课程思政建设,应做到守正与创新。本文以价值引领为切入点,介绍如何将思想政治教育有机融入课程内容设置和课堂讲授等环节,力求培养学生的家国情怀、国际视野、法治意识、生态意识、工程伦理、人文关怀等科学素养,深入践行立德树人,提高本科教学质量。     

水样中氨氮测定时试剂空白值偏高的原因分析

用纳氏试剂测定水体中氨氮时常常出现试剂空白偏高的现象,本文对氨氮分析过程进行检查,发现氨氮空白偏高的主要原因是分析的精密度不够高和校准曲线的应用存在误区所致。     

On the Semivalues and the Least Square Values Average Per Capita Formulas and Relationships

In this paper, it is shown that both the Semivalues and the Least Square Values of cooperative transferable utilities games can be expressed in terms of n^2 averages of values of the characteristic function of the game, by means of what we call the Average per capita formulas. Moreover, like the case of the Shapley value earlier considered, the terms of the formulas can be computed in parallel, and an algorithm is derived. From these results, it follows that each of the two values mentioned above are Shapley values of games easily obtained from the given game, and this fact gives another computational opportunity, as soon as the computation of the Shapley value is efficiently done.     

On the impact of low-balling: Experimental results in asymmetric auctions

The paper reports on a series of asymmetric auction experiments with private-independent values and two buyers. Maskin and Riley (2000) showed, under some conditions, that if one buyer has a greater probability than the other of not being able to bid, first-price auctions could yield lower revenues to the seller than second-price auctions. The data rejected this prediction because of an important overbidding when subjects received low values in first-price auctions. In this asymmetric setting, the observed overbidding cannot be explained by the usual risk aversion hypothesis and the detection of a learning pattern indicates that subjects used more an adaptive behaviour than a static one. An ad hoc bidding strategy for the buyers who are the most likely to bid explains the observed low bids better than the risk neutral equilibrium strategy. Finally, as subjects appear to have bid in equilibrium as if there were two other competitors instead of only one, their bidding behaviour can be thought to have displayed an over anxiousness about winning. Received: January 1999/Final version June 2001     

拟二次系统的广义焦点量与极限环分枝

本文给出了拟二次系统的前18个奇点量和可积性条件,由此统一解决了几类实平面微分自治系统的初奇点、高次奇点以及无穷远点的中心焦点判定与极限环分枝问题.     

Least absolute value and chebychev estimation utilizing least squares results

In exploratory data analysis and curve fitting in particular, it is often desirable to observe residual values obtained with different estimation criteria. The goal with most linear model curve-fitting procedures is to minimize, in some sense, the vector of residuals. Perhaps three of the most common estimation criteria require minimizing: the sum of the absolute residuals (least absolute value or L₁ norm); the sum of the squared residuals (least squares or L₂ norm); and the maximum residual (Chebychev or L norm). This paper demonstrates that utilizing the least squares residuals to provide an advanced start for the least absolute value and Chebychev procedures results in a significant reduction in computational effort. Computational results are provided.     

A novel method for detecting and counting overlapping tracks in SSNTD by image processing techniques

Overlapping object detection and counting is a challenge in image processing. A new method for detecting and counting overlapping circles is presented in this paper. This method is based on pattern recognition and feature extraction using “neighborhood values“ in an object image by implementation of image processing techniques. The junction points are detected by assignment of a value for each pixel in an image. As is shown, the neighborhood values for junction points are larger than the values for other points. This distinction of neighborhood values is the main feature which can be utilized to identify the junction points and to count the overlapping tracks. This method can be used for recognizing and counting charged particle tracks, blood cells and also cancer cells. The method is called “Track Counting based on Neighborhood Values” and is symbolized by “TCNV”.     

分担三个公共值的亚纯函数

主要讨论两个亚纯函数分担三个公共值时的唯一性问题，所得结果改进了仪洪勋、邱淦佛等的相应定理．