A value for continuously-many-choice cooperative games

We extend a multi-choice cooperative game to a continuously-many-choice cooperative game. The set of all continuously-many-choice cooperative games is isomorphic to the set of all cooperative fuzzy games. A continuously-many-choice cooperative game and a cooperative fuzzy game have different physical interpretations. We define a value for the continuously-many-choice cooperative game and show that the value for the continuously-many-choice cooperative game has most properties as the traditional Shapley value does. Also, we give a probabilistic interpretation for the value. The probabilistic interpretation reveals some interesting properties of the value. Finally, we discuss the uniqueness of the value.     

A multiplicative model for volume and volatility

We first present prima facie evidence for the predictions generated by the mixture of distributions hypothesis, using daily German stock returns and their corresponding daily trading volumes and number of trades. These last two variables are used as proxies for the stochastic rate of information arrival when one wishes to explain GARCH effects by adhering to the mixture of distributions hypothesis. We show that there is no need for these proxies when the stochastic rate of information arrival follows an inverted gamma distribution. Daily trading volume and the daily number of trades, however, empirically provide an explanation for the occurrence of conditional heteroskedasticity of the GARCH form. We estimate several specifications where daily trading volume is included in the conditional variance equation additively and multiplicatively. The new multiplicative specification clearly outperforms the additive specification.     

A value for partially defined cooperative games

The Shapley value provides a method, which satisfies certain desirable axioms, of allocating benefits to the players of a cooperative game. When there aren players andn is large, the Shapley value requires a large amount of accounting because the number of coalitions grows exponentially withn. This paper proposes a modified value that shares some of the axiomatic properties of the Shapley value yet allows the consideration of games that are defined only for certain coalitions. Two different axiom systems are shown to determine the same modified value uniquely.     

A multiplicative method of solving boundary value problems of shell theory

The boundary conditions are transferred to an arbitrarily chosen point by multiplication of matrices (multiplicatively). The transfer matrices of the boundary conditions are an analytic solution of a system of first-order linear ordinary differential equations in canonical form of the mechanics of the deformation of shells in the form of values of Cauchy–Krylov functions. At an arbitrarily chosen point, the boundary conditions are combined in a system of algebraic equations in matrix form, columns of the unknown quantities of which are parameters of the required values of the problem. The effectiveness of the method – the simplicity with which it can be realized on a computer, the low costs of computer time and the RAM – is based on the multiplicative transfer of the boundary conditions into matrix form. The class of problems is limited by the possibilities of the Fourier method of separation of the variables in partial differential equations.     

A cooperative inventory policy with deteriorating items for a two-echelon model

A cooperative inventory policy between supplier and buyer is proposed. Unlike other studies, we consider the case of deteriorating items and permit the completed back-order in the problem. We solve the problem without the condition of equal replenishments periods during a specified planning horizon and present a procedure to find the optimal solution. A case is presented to demonstrate the application of the proposed approach. The sensitivity analysis for a cooperation policy between supplier and buyer also are explored.     

A savings-based model for two-shipper cooperative routing

We introduce a methodology for operational planning of cooperation between two independent shippers who manage their own fleets of vehicles in a given geographic area. We assume that shippers are willing to establish partial cooperation by sharing only a subset of customers. Our approach is based on the iterative attempt of identifying subsets of shareable customers which can be fruitfully exchanged between shippers. We resort to classic concepts of vehicle routing literature such as savings and insertion costs, providing both a heuristic and an exact approach.     

Analysis of a new variational model for multiplicative noise removal

In this paper we consider a new variational model for multiplicative noise removal. We prove the existence and uniqueness of the minimizer for the variational problem. Furthermore, we derive the existence and uniqueness of weak solutions for the associated evolution equation. Finally, some numerical experiments are shown to compare the proposed model with the model given by Aubert and Aujol.     

A reformulated Shapley-like value for cooperative games with interval payoffs

In this paper, a new value for cooperative interval games is proposed which may remedy the disadvantages of the interval Shapley-like value and of the improved interval Shapley-like value introduced by Han et al. (2012). Moreover, it is shown that the reformulated interval value uniquely satisfies the properties of efficiency, indifference null player, symmetry, and additivity.     

Coexistence in a strongly coupled system describing a two-species cooperative model

This paper is concerned with a cooperative two-species Lotka–Volterra model. Using the fixed point theorem, the existence results of solutions to a strongly coupled elliptic system with homogeneous Dirichlet boundary conditions are obtained. Our results show that this model possesses at least one coexistence state if the birth rates are big and cross-diffusions are suitably weak.     

Coexistence of two species in a strongly coupled cooperative model

In this paper, the cooperative two-species Lotka–Volterra model is discussed. We study the existence of solutions to a elliptic system with homogeneous Dirichlet boundary conditions. Our results show that this problem possesses at least one coexistence state if the birth rates are big and self-diffusions and the intra-specific competitions are strong.     

Numerical treatment of a finite strain viscoplasticity model based on a double multiplicative split

A viscoplastic material model of overstress type is analyzed. The model is based on the kinematic assumption of a double multiplicative split in order to simulate a nonlinear kinematic hardening. We investigate theoretically and numerically two implicit time–stepping methods, which were used lately in engineering literature to integrate the evolution equations in the context of multiplicative plasticity/viscoplasticity. A common feature of both methods is that the plastic incompressibility constraint is exactly satisfied. Moreover, we show that both methods preserve the symmetry of internal variables, which is inherent to the problem. According to testing results, both methods are equivalent regarding robustness, accuracy, and computational efficiency. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An average lexicographic value for cooperative games

For games with a non-empty core the Alexia value is introduced, a value which averages the lexicographic maxima of the core. It is seen that the Alexia value coincides with the Shapley value for convex games, and with the nucleolus for strongly compromise admissible games and big boss games. For simple flow games, clan games and compromise stable games an explicit expression and interpretation of the Alexia value is derived. Furthermore it is shown that the reverse Alexia value, defined by averaging the lexicographic minima of the core, coincides with the Alexia value for convex games and compromise stable games.     

A FPTAS for a class of linear multiplicative problems

In this paper we consider the problem of minimizing the product of two affine functions over a polyhedral set. An approximation algorithm is proposed and it is proved that it is a Fully Polynomial Time Approximation Scheme. We will also present and computationally investigate an exact version of the algorithm.     

Nonparametric inference in multiplicative intensity model by discrete time observation

This paper deals with nonparametric inference problems in the multiplicative intensity model for counting processes. We propose a Nelson–Aalen type estimator based on discrete observation. The functional asymptotic normality of the estimator is proved. The limit process is the same as that in the continuous observation case, thus the proposed estimator based on discrete observation has the same properties as the Nelson–Aalen estimator based on continuous observation. For example, the asymptotic efficiency of proposed estimator is valid based on less information than the continuous observation case. A Kaplan–Meier type estimator is also discussed. Nonparametric goodness of fit test is considered, and an asymptotically distribution free test is proposed.