On finding curb sets in extensive games

We characterize strategy sets that are closed under rational behavior (curb) in extensive games of perfect information and finite horizon. It is shown that any such game possesses only one minimal curb set, which necessarily includes all its subgame perfect Nash equilibria. Applications of this result are twofold. First, it lessens computational burden while computing minimal curb sets. Second, it implies that the profile of subgame perfect equilibrium strategies is always stochastically stable in a certain class of games.I am grateful to J. Kamphorst, G. van der Laan and X. Tieman, who commented on the earlier versions of the paper. I also thank an anonymous referee and an associate editor for their helpful remarks. The usual disclaimer applies.     

Lower semicontinuity for approximate social Nash equilibria

We introduce a suitable concept of approximate social Nash equilibrium and we determine sufficient conditions of minimal character which guarantee, for a parametric social Nash equilibrium problem, the lower semicontinuity of the set-valued function defined by these approximate solutions. Received: December 2001     

Shapley value for constant-sum games

It is proved that Youngs [4] axiomatization for the Shapley value by marginalism, efficiency, and symmetry is still valid for the Shapley value defined on the class of nonnegative constant-sum games with nonzero worth of grand coalition and on the entire class of constant-sum games as well.The research was supported by NWO (The Netherlands Organization for Scientific Research) grant NL-RF 047-008-010.I am thankful to Theo Driessen, Natalia Naumova and Elena Yanovskaya for interesting discussions and comments. The useful remarks of two anonymous referees are also appreciated.     

The core and the bargaining set in glove-market games

In a glove-market game, the worth of a coalition is defined as the minimum, over all commodities in the market, of the total quantity that the coalition owns of each commodity. We identify a subclass of these games for which the core and the bargaining set coincide with the set of competitive equilibrium outcomes. We present examples showing that these solution concepts differ outside that subclass. We also illustrate a peculiar behavior of the bargaining set with respect to replication of a glove-market. These examples provide a simple economic setting in which the merits of the various solution concepts may be discussed and compared.Correspondence with Michael Maschler is gratefully acknowledged.This authors work was partly done while visiting the Department of Mathematics, Massachusetts Institute of Technology. Research supported by the Fund for the Promotion of Research at the Technion.     

Unified approach to approximate solutions in games and multiobjective programming

Using a theorem of Tijs, we derive results about approximate solutions for Nash equilibrium theory and for multiobjective problems. We describe conditions under which one can replace an infinite strategy set, an infinite alternative set, or an infinite set of criteria by a finite subset without losing all approximate solutions of the problem under consideration.This work was done during the period when the second author was Visiting Professor of the Italian National Research Council at the Mathematical Department of the University of Pavia, Pavia, Italy.     

(φ,ξ,η,λ)‐Structures of Parabolic Type

We consider (,,,)structures of parabolic type on hypersurfaces of dual spaces and study the rank of the affinor . We consider almost contact metric structures of parabolic type of the first kind on hypersurfaces of 4dimensional dual metric space. We study the properties of these structures and give examples of normal, integrable, and Sasakian parabolic structures.     

Bankruptcy games

Bankruptcy problems are considered from a game theoretic point of view. Solution concepts from cooperative game theory are studied for bankruptcy games. A necessary and sufficient condition for a division rule for bankruptcy problems to be a game theoretic rule is given. A new division rule which is an adjustment of the proportional rule is given. This rule coincides with theT-value for bankruptcy games. Properties of the new rule are treated and a set of characterizing properties is given.

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Zusammenfassung In dieser Arbeit werden Bankrottprobleme von spieltheoretischer Warte aus behandelt; insbesondere werden Lösungskonzepte der kooperativen Spieltheorie für Bankrottspiele untersucht. Eine notwendige und hinreichende Bedingung wird angegeben dafür, Daß eine Aufteilungsregel für Bankrottprobleme spieltheoretischer Natur ist. Ferner wird eine neue Aufteilungsregel angegeben, welche eine passende Modellierung der Proportionalitätsregel ist. Diese Regel fällt mit dem-Wert für Bankrottspiele zusammen. Schließlich werden Eigenschaften dieser neuen Regel untersucht und eine Axiomatisierung angegeben.

     

On the Convergence of Cone Splitting Algorithms with ω-Subdivisions

We present a convergence proof of the Tuy cone splitting algorithm with a pure -subdivision strategy for the minimization of a concave function over a polytope. The key idea of the convergence proof is to associate with the current hyperplane a new hyperplane that supports the whole polytope instead of only the portion of it contained in the current cone. A branch-and-bound variant of the algorithm is also discussed.     

On Convergence of the Simplicial Branch-and-Bound Algorithm Based on ω-Subdivisions

The problem of minimizing a concave function over a polytope is considered. The simplicial branch-and-bound approach is presented and theoretical studies about the convergence of these algorithms are carried on. In particular, the convergence of the algorithm based on so-called -subdivisions is proved, which had been an open question for a long time.     

Essential spectral radius for Markov semigroups (I): discrete time case

Using two new measures of non-compactness (P) and _w (P) for a positive kernel P on a Polish space E, we obtain a new formula of Nussbaum-Gelfand type for the essential spectral radius r _ess (P) on b. Using that formula we show that different known sufficient conditions for geometric ergodicity such as Doeblins condition, drift condition by means of Lyapunov function, geometric recurrence etc lead to variational formulas of the essential spectral radius. All those can be easily transported on the weighted space b _u . Some related results on L ² () are also obtained, especially in the symmetric case. Moreover we prove that for a strongly Feller and topologically transitive Markov kernel, the large deviation principle of Donsker-Varadhan for occupation measures of the associated Markov process holds if and only if the essential spectral radius is zero; this result allows us to show that the sufficient condition of Donsker-Varadhan for the large deviation principle is in fact necessary. The knowledge of r _ess (P) allows us to estimate eigenvalues of P in L ² in the symmetric case, and to estimate the geometric convergence rate by means of that in the metric of Wasserstein. Applications to different concrete models are provided for illustrating those general results. Mathematics Subject Classification (2000):60J05, 60F10, 47A10, 47D07     

The Brownian loop soup

We define a natural conformally invariant measure on unrooted Brownian loops in the plane and study some of its properties. We relate this measure to a measure on loops rooted at a boundary point of a domain and show how this relation gives a way to chronologically add Brownian loops to simple curves in the plane.Cornell University; Research supported in part by the National Science FoundationUniversité Paris-Sud and IUFMathematics Subject Classification (2000):60J65, 81T40     

Maintaining convergence properties of BiCGstab methods in finite precision arithmetic

It is well-known that Bi-CG can be adapted so that hybrid methods with computational complexity almost similar to Bi-CG can be constructed, in which it is attempted to further improve the convergence behavior. In this paper we will study the class of BiCGstab methods.In many applications, the speed of convergence of these methods appears to be determined mainly by the incorporated Bi-CG process, and the problem is that the Bi-CG iteration coefficients have to be determined from the BiCGstab process. We will focus our attention to the accuracy of these Bi-CG coefficients, and how rounding errors may affect the speed of convergence of the BiCGstab methods. We will propose a strategy for a more stable determination of the Bi-CG iteration coefficients and by experiments we will show that this indeed may lead to faster convergence.     

Inequality of Petrović and Giaccardi for Convex Function of Higher Order

In this paper we use Lidstone polynomials to prove further generalization of Giaccardi generalization of the well-known Petrovis inequality.     

Production systems with interruptions, arbitrary topology and finite buffers

We consider a production system with finite buffers and arbitrary topology where service time is subject to interruptions in one of three ways, viz. machine breakdown, machine vacations or Npolicy. We develop a unified approximation (analytical) methodology to calculate the throughput of the system using queueing networks together with decomposition, isolation and expansion techniques. The methodology is rigorously tested covering a large experimental region. Orthogonal arrays are used to design the experiments in order to keep the number of experiments manageable. The results obtained using the approximation methodology are compared to the simulation results. The ttests carried out to investigate the differences between the two results show that they are statistically insignificant. Finally, we test the methodology by applying it to several arbitrary topology networks. The results show that the performance of the approximation methodology is consistent, robust and produces excellent results in a variety of experimental conditions.     

Spaces over a Category and Assembly Maps in Isomorphism Conjectures in K‐ and L‐Theory

We give a unified approach to the Isomorphism Conjecture of Farrell and Jones on the algebraicKandLtheory of integral group rings and to the Baum–Connes Conjecture on the topologicalKtheory of reducedC*algebras of groups. The approach is through spectra over the orbit category of a discrete groupG.We give several points of view on the assembly map for a family of subgroups and characterize such assembly maps by a universal property generalizing the results of Weiss and Williams to the equivariant setting. The main tools are spaces and spectra over a category and their associated generalized homology and cohomology theories, and homotopy limits.     

Some Properties of Isologism of Groups and Baer-Invariants

Let be a variety of groups defined by the set of laws V. In this paper we study the concept of -isologism of groups in terms of -extensions and their connections with the Baer-invariant of groups are also discussed.AMS Subject Classification (2000): primary 20F14, 20F19, secondary 20E10     

The quadratic convergence of the topological epsilon algorithm for systems of nonlinear equations

In this work we consider the topological epsilon algorithm for solving systems of nonlinear equations. In section 2, a sufficient condition for its quadratic convergence is given. In section 3, some geometrical remarks about this condition are made.     

Adhesion between Epoxy-Polysulfone Blends and Fibers

The adhesive strength of a fiber-polymer interface is determined, where epoxy resin blends and linear heat-resistant thermoplastics - polysulfone (PSF) and polyetherimide (Ultem) - are used as matrices. Steel wire and polyamide (nylon-6) fibers are taken as reinforcing fillers. It is shown that the addition of PSF to epoxy resin results in a maximum on the concentration curve corresponding to a 10% PSF content. It is also found that the adhesive strength of the ED-20+Ultem-steel wire interface is practically independent of the modifier content under low (up to 10%) Ultem concentrations.     

On Generalizations of Ostrowski Inequality and Some Related Results

Some generalizations of the Ostrowski inequality, the Milovanovi-Peari-Fink inequality, the Dragomir-Agarwal inequality and the Hadamard inequality are given.