Pairwise symmetry conditions for voting equilibria

Necessary conditions are established for a point contained in the interior or boundary of a convex feasible subset of Euclidean space to be quasi-undominated in an anonymous simple game. Most of the conditions are behaviorally intuitive and imply pariwise symmetries among utility gradients.     

Refinements of rationalizability for normal-form games

There exist three equivalent definitions of perfect Nash equilibria which differ in the way “best responses against small perturbations” are defined. It is shown that applying the spirit of these definitions to rationalizability leads to three different refinements of rationalizable strategies which are termed perfect (Bernheim, 1984), weakly perfect and trembling-hand perfect rationalizability, respectively. We prove that weakly perfect rationalizability is weaker than both perfect and proper (Schuhmacher, 1995) rationalizability and in two-player games it is weaker than trembling-hand perfect rationalizability. By means of examples, it is shown that no other relationships can be found. Received: January 1997/final version: August 1998     

Proper rationalizability in lexicographic beliefs

Proper consistency is defined by the property that each player takes all opponent strategies into account (is cautious) and deems one opponent strategy to be infinitely more likely than another if the opponent prefers the one to the other (respects preferences). When there is common certain belief of proper consistency, a most preferred strategy is properly rationalizable. Any strategy used with positive probability in a proper equilibrium is properly rationalizable. Only strategies that lead to the backward induction outcome are properly rationalizable in the strategic form of a generic perfect information game. Proper rationalizability can test the robustness of inductive procedures. Final version: December 2001     

Proper rationalizability and backward induction

This paper introduces a new normal form rationalizability concept, which in reduced normal form games corresponding to generic finite extensive games of perfect information yields the unique backward induction outcome. The basic assumption is that every player trembles “more or less rationally” as in the definition of a ε-proper equilibrium by Myerson (1978). In the same way that proper equilibrium refines Nash and perfect equilibrium, our model strengthens the normal form rationalizability concepts by Bernheim (1984), B?rgers (1994) and Pearce (1984). Common knowledge of trembling implies the iterated elimination of strategies that are strictly dominated at an information set. The elimination process starts at the end of the game tree and goes backwards to the beginning. Received: October 1996/Final version: May 1999     

On the concepts of rationalizability in games

Rationalizability arises when the decision situations and rational behaviors of the players are common knowledge among them. We extend the notion of rationalizability, introduced by Bernheim [5] and Pearce [18] for Bayesian behavior, to some another kinds of player's behavior. We also present a representation of common knowledge consisting in introducing an additional player who sends messages to the players. This revised version was published online in June 2006 with corrections to the Cover Date.     

Pairwise sufficiency

Summary For an arbitrary experiment E we investigate the relation between its pairwise sufficient subalgebras and its sufficient sublattices in the M-space of E (in the sense of L. LeCam). By exhibiting an experiment without minimal pairwise sufficient subalgebra it is shown that this correspondence is in general not bijective. In view of this we introduce the rather large class of majorized experiments. They have a minimal pairwise sufficient subalgebra which can be described explicitely.As a natural subclass of the majorized experiments appear the coherent experiments that are distinguished by the coincidence of sufficiency and pairwise sufficiency. It is shown that the coherent experiments are characterized by the fact that they admit a majorizing measure which is localizable. As a consequence we obtain that the class of coherent experiments coincides with classes of experiments previously introduced by T.S. Pitcher, D. Mußmann, M. Hasegawa and M.D. Perlman.     

Proper belief revision and rationalizability in dynamic games

In this paper we develop an epistemic model for dynamic games in which players may revise their beliefs about the opponents’ utility functions as the game proceeds. Within this framework, we propose a rationalizability concept that is based upon the following three principles: (1) at every instance of the game, a player should believe that his opponents are carrying out optimal strategies, (2) a player, at information set h, should not change his belief about an opponent’s relative ranking of two strategies s and s′ if both s and s′ could have led to h, and (3) the players’ initial beliefs about the opponents’ utility functions should agree on a given profile u of utility functions. Common belief in these events leads to the concept of persistent rationalizability for the profile u of utility functions. It is shown that for a given game tree with observable deviators and a given profile u of utility functions, every properly point-rationalizable strategy is a persistently rationalizable strategy for u. This result implies that persistently rationalizable strategies always exist for all game trees with observable deviators and all profiles of utility functions. We provide an algorithm that can be used to compute the set of persistently rationalizable strategies for a given profile u of utility functions. For generic games with perfect information, persistent rationalizability uniquely selects the backward induction strategy for every player.     

Pairwise distance-based heteroscedasticity test for regressions

Science China Mathematics - In this study, we propose nonparametric testing for heteroscedasticity in nonlinear regression models based on pairwise distances between points in a sample. The test...     

两两NQD随机序列的 Lr 收敛性

该文讨论了两两NQD随机变量列在满足$r(1\leq r<2)$阶Ces\`aro一致可积条件下的 L^r 收敛性,获得了与独立情形一致的结果.     

两两独立序列加权和的L~r收敛性

讨论了两两独立随机变量列加权和在满足r(1≤r<2)阶Ces`aro一致可积条件下的Lr收敛性,获得了与独立情形一致的结果.用相似的方法,对于其它相依或混合序列(如两两NQD列,φ-混合序列,ρ-混合序列)也有相同的结果.     

Pairwise compatibility for 2-simple minded collections

In τ-tilting theory, it is often difficult to determine when a set of bricks forms a 2-simple minded collection. The aim of this paper is to determine when a set of bricks is contained in a 2-simple minded collection for a τ-tilting finite algebra. We begin by extending the definition of mutation from 2-simple minded collections to more general sets of bricks (which we call semibrick pairs). This gives us an algorithm to check if a semibrick pair is contained in a 2-simple minded collection. We then use this algorithm to show that the 2-simple minded collections of a τ-tilting finite gentle algebra (whose quiver contains no loops or 2-cycles) are given by pairwise compatibility conditions if and only if every vertex in the corresponding quiver has degree at most 2. As an application, we show that the classifying space of the τ-cluster morphism category of a τ-tilting finite gentle algebra (whose quiver contains no loops or 2-cycles) is an Eilenberg-MacLane space if every vertex in the corresponding quiver has degree at most 2.     

两两NQD随机序列的L^r收敛性

该文讨论了两两NQD随机变量列在满足r(1≤ r＜2)阶Cesàro一致可积条件下的Lr,收敛性,获得了与独立情形一致的结果.     

两两PQD序列的完全收敛性和强大数定律

本文给出两两PQD序列部分和的几个不等式，并研究了两两PQD序列的完全收敛性和强大数定律．     

Fast Trie-Based Method for Multiple Pairwise Sequence Alignment

Doklady Mathematics - A method for efficient comparison of a symbol sequence with all strings of a set is presented, which performs considerably faster than the naive enumeration of comparisons...     

Merging Mixture Components for Clustering Through Pairwise Overlap

Finite mixture models are well known for their flexibility in modeling heterogeneity in data. Model-based clustering is an important application of mixture models, which assumes that each mixture component distribution can adequately model a particular group of data. Unfortunately, when more than one component is needed for each group, the appealing one-to-one correspondence between mixture components and groups of data is ruined and model-based clustering loses its attractive interpretation. Several remedies have been considered in literature. We discuss the most promising recent results obtained in this area and propose a new algorithm that finds partitionings through merging mixture components relying on their pairwise overlap. The proposed technique is illustrated on a popular classification and several synthetic datasets, with excellent results.     

关于两两NQD随机序列的一个极限定理

设为两两NQD随机序列, 且, 是一列严格单调递增的凸序列. 本文将 Feller (1946)关于独立同分布期望不存在随机序列的极限定理推广到两两NQD随机 序列的情形.     

关于判断矩阵一致性检验与调整的一个注记

首先分析了判断矩阵不一致形成的原因,认为一个判断矩阵中的不一致是由强矛盾判断,弱矛盾判断,标度离散性,标度有限性共同作用的结果,并通过两个例子指出现有一致性检验与调整方法中存在的问题,最后在已有研究基础上给出了判断矩阵一致性调整的新步骤.     

Diagnostics for Pairwise Extremal Dependence in Spatial Processes

A measure of pairwise extremal dependence for spatial processes, that is marginally invariant, is introduced. This measure enables decisions to be made about whether a spatial process is asymptotically dependent, asymptotically independent or independent for any pair of locations, thus it provides fundamental diagnostic information for understanding or modeling the extreme values of a spatial process. We illustrate the properties and use of this measure through theoretical examples and applications in hydrology and oceanography.     

偏好的对子态可分性

本文提出了消费者偏好的对子态可分性概念，并用来揭示一般选择集合上偏好的效用函数表示的特征，证明了偏好关系可用效用函数表示的充分必要条件是该偏好具有对子态可分性和可数满足性，还证明了偏好关系具有长直线ｗ１—表示的充分必要条件是该偏好具有对子态可分性．这两个结果，使得对子态可分性成为用直线上的序来表示消费偏好序之本质所在．     

关于对半层空间

利用对$g$-函数和半连续函数给出对半层空间的一些刻画, 并讨论了具有半层拓扑的拓扑序$C$-空间的对半层性.