Values for strategic games in which players cooperate

In this paper we propose a new method to associate a coalitional game with each strategic game. The method is based on the lower value of finite two-player zero-sum games. We axiomatically characterize this new method, as well as the method that was described in Von Neumann and Morgenstern (1944). As an intermediate step, we provide axiomatic characterizations of the value and the lower value of matrix games and finite two-player zero-sum games, respectively.The authors acknowledge the financial support of Ministerio de Ciencia y Tecnologia, FEDER andXunta de Galicia through projects BEC2002-04102-C02-02 and PGIDIT03PXIC20701PN.We wish to thank Professor William Thomson as well as an anonymous referee for useful comments.     

Finite element analysis of pressure formulation of the elastoacoustic problem

In this paper we analyze the non symmetric pressure/displacement formulation of the elastoacoustic vibration problem and show its equivalence with the (symmetric) stiffness coupling formulation. We introduce discretizations for these problems based on Lagrangian finite elements. We show that both formulations are also equivalent at discrete level and prove optimal error estimates for eigenfunctions and eigenvalues. Both formulations are rewritten such as to be solved with a standard Matlab eigensolver. We report numerical results comparing the efficiency of the methods over some test examples. Partially supported by Xunta de Galicia (Spain) through grant No. PGIDT00-PXI20701PR and by MCYT Research Project DPI2001-1613-C02-02Partially supported by Xunta de Galicia (Spain) through grant No. PGIDT00-PXI20701PR and by MCYT Research Project DPI2001-1613-C02-02Partially supported by FONDAP in Applied Mathematics (Chile) and by MCYT Research Projects DPI2001-1613-C02-02 and BFM2001-3261-C02-02Partially supported by FONDECYT (Chile) through grant No. 1.990.346 and FONDAP in Applied Mathematics (Chile)Mathematics Subject Classification (1991):65N30     

A non-cooperative approach to the cost spanning tree problem

We associate to each cost spanning tree problem a non-cooperative game, which is inspired by a real-life problem. We study the Nash equilibria and subgame perfect Nash equilibria of this game. We prove that these equilibria are closely related with situations where agents connect sequentially to the source.Finicial support from the Ministerio de Ciencia y Tecnologia and FEDER, and Xunta de Galicia through grants BEC2002-04102-C02-01 and PGIDIT03PXIC30002PN is gratefully acknowledged.     

Strategic absentmindedness in finitely repeated games

In this paper we consider finitely repeated games in which players can unilaterally commit to behave in an absentminded way in some stages of the repeated game. We prove that the standard conditions for folk theorems can be substantially relaxed when players are able to make this kind of compromises, both in the Nash and in the subgame perfect case. We also analyze the relation of our model with the repeated games with unilateral commitments studied, for instance, in García-Jurado et al. (Int. Game Theory Rev. 2:129–139, 2000). Authors acknowledge the financial support of Ministerio de Educaci ón y Ciencia, FEDER and Fundación Séneca de la Región de Murcia through projects SEJ2005-07637-C02-02, ECO2008-03484-C02-02, MTM2005-09184-C02-02, MTM2008-06778-C02-01 and 08716/PI/08.     

Random points on the boundary of smooth convex bodies

The convex hull of independent random points chosen on the boundary of a convex body according to a given density function is a random polytope. The expectation of its -th intrinsic volume for is investigated. In the case that the boundary of is sufficiently smooth, asymptotic expansions for these expected intrinsic volumes as are derived.

     

随机需求下三度价格歧视重复博弈的研究

基于随机需求函数,讨论了相互竞争的两厂商实施三度价格歧视无限次重复博弈和不定次重复博弈的均衡分析,在三度价格歧视无限次重复博弈分析中,得出了两厂商在贴现因子影响下的子博弈完美纳什均衡.在三度价格歧视不定次重复博弈分析中,设计了不同的方案并进行了Matlab仿真,比较了不同贴现因子下不同仿真方案的厂商得益,并对仿真结果进行了系统分析,得到了统计意义下的均衡分析.     

On the properties of solutions for NTU communication situations<Superscript>1</Superscript>

We consider the model of cooperative games in which the agents can restrict the communication, because agents are sometimes divided into subgroups in a natural way, for example by their political affinities or by the companies that employ them. More particularly we focus on cooperative games with non-transferable utility, where the communication restrictions are represented by a graph defined on the set of agents. For this class of games we consider two solutions that are modifications of the Shapley value. We axiomatically characterize these two solutions and study their relation to the strong core.The authors acknowledge the financial support of El Ministerio español de Ciencia y Tecnología, FEDER and Xunta de Galicia through projects BEC2002-04102-C02-02 and PGIDIT03PXIC20701PN. We would also like to thank Dr. Jo Dee Anderson for her linguistic support.     

Random polynomials having few or no real zeros

Consider a polynomial of large degree whose coefficients are independent, identically distributed, nondegenerate random variables having zero mean and finite moments of all orders. We show that such a polynomial has exactly real zeros with probability as through integers of the same parity as the fixed integer . In particular, the probability that a random polynomial of large even degree has no real zeros is . The finite, positive constant is characterized via the centered, stationary Gaussian process of correlation function . The value of depends neither on nor upon the specific law of the coefficients. Under an extra smoothness assumption about the law of the coefficients, with probability one may specify also the approximate locations of the zeros on the real line. The constant is replaced by in case the i.i.d. coefficients have a nonzero mean.

     

Convergence of zeta functions of graphs

The -zeta function of an infinite graph (defined previously in a ball around zero) has an analytic extension. For a tower of finite graphs covered by , the normalized zeta functions of the finite graphs converge to the -zeta function of .

     

Equilibrium existence and topology in some repeated games with incomplete information

This article proves the existence of an equilibrium in any infinitely repeated, un-discounted two-person game of incomplete information on one side where the uninformed player must base his behavior strategy on state-dependent information generated stochastically by the moves of the players and the informed player is capable of sending nonrevealing signals.

This extends our earlier result stating that an equilibrium exists if additionally the information is standard. The proof depends on applying new topological properties of set-valued mappings. Given a set-valued mapping on a compact convex set , we give further conditions which imply that every point belongs to the convex hull of a finite subset of the domain of satisfying .

     

Linearity of dimension functions for semilinear -spheres

In this paper, we show that the dimension function of every semilinear -sphere is equal to that of a linear -sphere for finite nilpotent groups of order , where , are primes. We also show that there exists a semilinear -sphere whose dimension function is not virtually linear for an arbitrary nonsolvable compact Lie group .

     

Study and modelling of two apple quality attributes: the soluble solids content and the firmness

Recently, the basic dynamics of fruit characteristics have been modelled using a stochastic approach. The time evolution of apple quality attributes was represented by means of a system of differential equations in which the initial conditions and model parameters are both random. In this work, a complete study of two apple quality attributes, the soluble solids content and the firmness, is carried out. For each of these characteristics, the system of differential equations is linear and the state variables and the parameters are represented as random variables with their statistical properties (mean values, variances, covariances, joint probability density function) known at the initial time. The dynamic behaviour of these statistical properties is analysed. The variance propagation algorithm is used to obtain an analytical expression of the dynamic behaviour of the mean value, the variance, the covariance and the probability density function. A Monte Carlo method and the Latin hypercube method were developed to obtain a numerical expression of the dynamic behaviour of these statistical quantities and particularly to follow the time evolution of joint probability density function which represents one but the best mean to characterize random phenomena linked with fruit quality attributes.     

On the least prime primitive root modulo a prime

We derive a conditional formula for the natural density of prime numbers having its least prime primitive root equal to , and compare theoretical results with the numerical evidence.

     

Asymptotic Dirichlet problem for the -Laplacian on Cartan-Hadamard manifolds

We show the existence of nonconstant bounded -harmonic functions on Cartan-Hadamard manifolds of pinched negative curvature by solving the asymptotic Dirichlet problem at infinity for the -Laplacian. More precisely, we prove that given a continuous function on the sphere at infinity there exists a unique -harmonic function on with boundary values

     

A Fejér type theorem to determine jumps in terms of the Abel-Poisson mean of double Fourier series

We extend from single to double Fourier series a theorem of Zygmund to determine the generalized jumps of a periodic integrable function at a simple discontinuity point. As a by-product of the proof, we obtain an estimate of the fourth mixed partial derivative of the Abel-Poisson mean of any integrable function at such a point where is smooth. We also consider the extension of the Zygmund classes and to the two-dimensional torus .

     

A continuum whose hyperspace of subcontinua is not -contractible

A topological space is said to be -contractible provided that there exists a continuous onto function such that is homotopic to a constant function. Answering a question by Sam B. Nadler, Jr., in this paper we construct a metric continuum such that its hyperspace of subcontinua is not -contractible.

     

New bases for Triebel-Lizorkin and Besov spaces

We give a new method for construction of unconditional bases for general classes of Triebel-Lizorkin and Besov spaces. These include the , , potential, and Sobolev spaces. The main feature of our method is that the character of the basis functions can be prescribed in a very general way. In particular, if is any sufficiently smooth and rapidly decaying function, then our method constructs a basis whose elements are linear combinations of a fixed (small) number of shifts and dilates of the single function . Typical examples of such 's are the rational function and the Gaussian function This paper also shows how the new bases can be utilized in nonlinear approximation.

     

On the centipede game with a social norm

In this paper, we present a formulation of the centipede game where inter-subjectivity between players is formalized through random costs that are an increasing function, in the sense of first-order stochastic dominance, of the number of iterations for which the game is played. This injection of a time-dependent social norm, one that also parametrizes player proximity, as an element of each player’s introspective calculations formalizes a setting under which subgame perfection dictates cooperative outcomes.