Necessary and sufficient conditions for interpolation with functions having monotoner-th derivatives

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Cooperation in an asymmetric Volunteer's dilemma game theory and experimental evidence

The symmetric Volunteer's dilemma game (VOD) models a situation in which each ofN actors faces the decision of either producing a step-level collective good (action C) or freeriding (D). One player's cooperative action suffices for producing the collective good. Unilateral cooperation yields a payoffU forD-players andU-K for the cooperative player(s). However, if all actors decide for freeriding, each player's payoff is zero (U>K>0). In this article, an essential modification is discussed. In an asymmetric VOD, the interest in the collective good and/or, the production costs (i.e. U or K) may vary between actors. The generalized asymmetric VOD is similar to market entry games. Alternative hypotheses about the behaviour of subjects are derived from a game-theoretical analysis. They are investigated in an experimental setting. The application of the mixed Nash-equilibrium concept yields a rather counter-intuitive prediction which apparently contradicts the empirical data. The predictions of the Harsanyi-Selten-theory and Schelling's focal point theory are in better accordance with the data. However, they do not account for the diffusion-of-responsibility-effect also observable in the context of an asymmetric VOD game.I am indebted to Wulf Albers, Norman Braun, Werner Güth, Norbert L. Kerr, Reinhard Selten, and the participants of the V^th International Social Dilemma Conference in Bielefeld for critical and helpful comments. I am grateful to Axel Franzen who organized the experiment at the University of Mannheim. This work was supported by a grant of the Deutsche Forschungsgemeinschaft (DFG).     

Sharpening of Stečkin's theorem to strong approximation

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Entropy control costs and entropic equilibria

Strategic errors may occur because of player trembles or because of noise in the communication channels. Suppose that the probability distribution of potential errors can be influenced at a cost proportional to the entropy reduction. This modified strategic-form game involves the choice of a probability distribution over strategies and a probability distribution over potential errors with weight on the latter. Each modified game has a Nash Equilibrium (NE), and any limit as 0 is called an -entropic equilibrium, -entropic equilibria always exist and constitute a subset of trembling-hand-perfect equilibria, but otherwise -EE are independent of other refinements such as Proper NE.The author is grateful to Larry Samuelson and an anonymous referee for helpful comments, but retains sole responsibility for any error.     

Riemannian tori without conjugate points are flat

The first author was supported by the Deutsche Forschungsgemeinschaft fellowship and enjoyed the hospitality of the University of Freiburg.     

Subexponential distributions and characterizations of related classes

LetL(),0, 0, denote the class of distributionsF satisfying

Large transversals to small families of unit disks

Summary It is proved that if the nonempty intersection of bounded closed convex sets AnB is contained in (A + F)U(B+F) and one of the following holds true: (i) the space X is less-than-three dimensional, (ii) AUB is convex, (iii) F is a one-point set, then AnBCA+F or AnBCB+F (Theorems 2 and 3). Moreover, under some hypotheses the characterization of A and B such that AnB is a summand of AUB is given (Theorem 3).     

Asymptotics of polynomials orthogonal with respect to varying measures

Letd be a finite positive Borel measure on the interval [0, 2] such that >0 almost everywhere; andW _n be a sequence of polynomials, degW _n =n, whose zeros (w _n ,1,,w _n,n lie in [|z|1]. Let d _n <> for each_nN, whered _n =d/|W _n (e ⁱ )|². We consider the table of polynomials _n,m such that for each fixednN the system _n,m,mN, is orthonormal with respect tod _n . If

Perturbation of hamiltonian systems with Keplerian potentials

Supported by Ministero P.I. Gruppo Nazionale Calcolo delle Variazioni (40%)     

Reflection groups and K-loops

The notion reflection group (, ) was introduced in order to give group theoretical characterizations of absolute planes. Here we consider reflection groups with midpoints and associate to each of them an incidence structure . Then is an incidence space which dimension can assume any value. The motion group together with the set of all reflections in points of a Euclidean or hyperbolic geometry are examples of reflection groups with midpoints. Furthermore the set can be turned into a K-loop. The precise results are summarized in the theorems at the end of the paper.Cordially dedicated to Sibylla Prieß on the occasion of her 60th birthdaySupported by the NATO Scientific Affairs Division grant CRG 900103.     

Spectral synthesis for Euler type operators

A=(a _ij) _i ^j=1 — k-o ,a _ij . :

A class of strongly nonlinear functional differential equations

Let H be a real Hilbert space, :H [0, + ] a proper l.s.c., convex function with L_k:={u H; u² + (u) k} compact for every k > 0, let > 0 be a given constant and . We prove an existence result for strong solutions to a class of functional differential equations of the form

Some remarks on Turán's inequality. III: The completion

. 0pq, 1–1/p+1/p0. f(x) — n, [–1,1],

On the Pólya conjecture concerning the maximum and minimum of the modulus of an entire function of finite order given by a lacunary power series

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Singularities of the Green function of a random walk on a discrete group

LetX be a countable discrete group and let be an irreducible probability onX. The radius of convergence of the Green function is finite, and independent ofx. Let 0} \right\}$$ " align="middle" border="0"> be the period of . We show that for eachxX the singularities of the analytic functionzG(x; z) on the circle {z:|z|=} are precisely the points e ^2ik/d k=0, ...,d–1. In particular, is the only singularity on the circle in the aperiodic cased=1 (which occurs, for example, when (e)>0). This affirms a conjecture ofLalley [5]. When is symmetric, i.e., (x ^–1)=(x) for allxX, d is either 1 or 2. As another particular case of our result, we see that- is then a singularity ofzG (x; z) if and only ifd=2, in which caseX is bicolored. This answers a question ofde la Harpe, Robertson andValette [2].     

Comparative cooperative game theory

Given two side-payment gamesv andw, both defined for the same finite player-setN, the following three welfare criteria are characterized in terms of the datav andw: (A) For everyy C(w) there existsx C(v) such thatyx; (A) For everyxC(v) there existsyC(w) such thatyx; and (B) There existyC(w) andxC(v) such thatyx. (HereC(v) denotes the core ofv.) Given two non-side-payment gamesv andw, sufficient conditions for the criteria (A) and (B) are established, by observing that an ordinal convex game has a large core.In memory of my teacher in Japan, Professor Ryuichi Watanabe, 1928–1986.     

Rational approximation to Lipschitz and Zygmund classes

In this paper, characterizations for lim _n(R _n (f)/(n ^–1)=0 inH and for lim _n(n ^r+ R _n (f)=0 inW ^r Lip ,r1, are given, while, forZ, a generalization to a related result of Newman is established.Communicated by Ronald A. DeVore.