Collective Strategy Condensation: When Envy Splits Societies

Human societies are characterized by three constituent features, besides others. (A) Options, as for jobs and societal positions, differ with respect to their associated monetary and non-monetary payoffs. (B) Competition leads to reduced payoffs when individuals compete for the same option as others. (C) People care about how they are doing relatively to others. The latter trait—the propensity to compare one’s own success with that of others—expresses itself as envy. It is shown that the combination of (A)–(C) leads to spontaneous class stratification. Societies of agents split endogenously into two social classes, an upper and a lower class, when envy becomes relevant. A comprehensive analysis of the Nash equilibria characterizing a basic reference game is presented. Class separation is due to the condensation of the strategies of lower-class agents, which play an identical mixed strategy. Upper-class agents do not condense, following individualist pure strategies. The model and results are size-consistent, holding for arbitrary large numbers of agents and options. Analytic results are confirmed by extensive numerical simulations. An analogy to interacting confined classical particles is discussed.     

实二次域上理想类的zeta-函数在-1处的值

用连分数给出了实二次域理想类的zeta-函数-1处值的一个具体的计算公式.     

Rank 2 Ample Vector Bundles on Some Smooth Rational Surfaces

Several classification results for ample vector bundles of rank 2 on Hirzebruch surfaces, and on Del Pezzo surfaces, are obtained. In particular, we classify rank 2 ample vector bundles with _c2 less than seven on Hirzebruch surfaces, and with _c2 less than four on Del Pezzo surfaces.     

Fiberings with Fiber RP（κ）

Let κ be non-negative integer. The unoriented bordism classes, which can be represented as [RP（ξ^κ）] where ξ^κ is a k-plane bundle, form an ideal of the unoriented bordism ring MO.. A group of generators of this ideal expressed by a base of MO. and a necessary and sufficient condition for a bordism class to belong to this ideal are given.     

Oriented Cohomology Theories of Algebraic Varieties

This article contains proofs of the results announced by Panin and Smirnov (http://www. math.uiuc.edu/k-theory/0459/2000) in the part concerning general properties of oriented cohomology theories of algebraic varieties. It is constructed one-to-one correspondences between orientations, Chern structures and Thom structures on a given ring cohomology theory. The theory is illustrated by motivic cohomology, algebraic K-theory, algebraic cobordism theory and by other examples.     

A power-law distribution for tenure lengths of sports managers

We show that the tenure lengths for managers of sport teams follow a power law distribution with an exponent between 2 and 3. We develop a simple theoretical model which replicates this result. The model demonstrates that the empirical phenomenon can be understood as the macroscopic outcome of pairwise interactions among managers in a league, threshold effects in managerial performance evaluation, competitive market forces, and luck at the microscopic level.     

Classes polaires associées aux distributions holomorphes de sous-espaces tangents*

Résumé. Nous définissons des classes polaires associées à une distribution holomorphe singulière de sous-espaces tangents d’une variété projective lisse. Nous prouvons que ces classes polaires peuvent être calculées en fonction des classes de Chern-Mather du faisceau tangent de la distribution et réciproquement. Nous utilisons leurs degrés pour borner les degrés de certaines classes polaires associés à une variété invariante. *Ce travail a été soutenu par l’Accord de Coopération France-Brésil (CNRS/CNPq) et par la Fondation CAPES-Brésil.