A simple differential game

Necessary conditions and sufficient conditions are employed to deduce optimal strategies for a simple differential game with state equationd ² x/dt ²=au+v,a = Const, |u|1, |v|1, fixed transfer time, and terminal miss distance as payoff.This work was supported by the National Aeronautics and Space Administration, Contract No. NAS 12–114.     

Fitting the lognormal distribution to censored labour wastage data

In this paper an estimation technique is developed on the basis of the well-known lognormal hypothesis for labour wastage to estimate the early leavers for each entry cohort. Early leavers are those leavers who joined and left the company during the twelve-month period and are not recorded at the census data taken at the end of this period. The results of applying the lognormal model on the extended data in predicting survivors for several companies are then shown to be improved.     

A simple method for choosing between the lognormal and weibull models

A simple method for using a random sample to select a sampling distribution model from between the lognormal and Weibull distributions is developed. Simulation studies demonstrate that it performs just as well as more complicated alternatives.     

A simple game with a singular focal line

We propose a simple game whose solution contains a singular focal line, i.e., a focal line reached by optimal trajectories in a nontangential fashion. We also provide a discussion of how the optimal discriminating strategy can be approximated by a pure feedback.This work was prepared while the first author was visiting at INRIA-Sophia Antipolis, Valbonne, France.     

Some properties of the bivariate lognormal distribution for reliability applications

In this paper, we study the bivariate lognormal distribution from a reliability point of view. The conditional distribution of X given Y > y is found to be log‐skew normal. The monotonicity of the hazard rates of the univariate as well as the conditional distributions is discussed. Clayton's association measure is obtained in terms of the hazard gradient, and its value in the case of our model is derived. The probability distributions, in the case of series and parallel systems, are derived, and the monotonicity of their failure rates is discussed. Three real applications of the bivariate lognormal distribution are provided, two from financial economics and one from reliability. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical integration over a semi-infinite interval,using the lognormal distribution

Summary A method is described for numerical integration over a semiinfinite interval using a Gaussian formula, with the corresponding set of orthogonal polynomials constructed from a lognormal weight function.The lognormal weight function and hence the coefficients of the polynomials are functions of two arbitrary parameters; the mean and the logarithmic variance. The method is found to be of particular use for integration of bell-shaped or sharply spiked functions. Rapidly convergent results can be obtained in these cases, since the lognormal distribution can be used to provide a good approximation to the actual function to be integrated, by suitable choice of the two arbitrary parameters. Two examples are given for integrals with known solutions.     

The vetoers in a simple game with ordinal preferences

We consider a core of a simple game with ordinal preferences on a set of alternative outcomes Ω. When a player's strict preference relation takes any logically possible form of acyclic binary relation on Ω, necessary conditions for a simple game to have a nonempty core are given. If Ω is a finite set, the conditions are also sufficient. Further some related results are obtained.     

The core of a simple game with ordinal preferences

Michael Dummett andRobin Farquharson [1961] provided a sufficient condition for ann-person simple majority game with ordinal preferences to have a nonempty core. In the present paper we generalize this result to an arbitrary proper simple game. It is proved that their condition is also sufficient for this game to have a nonempty core. Our proof of this theorem is much simpler than the proof given byDummett andFarquharson. Finally some applications of the theorem are presented.     

A simple iterative method for water distribution network analysis

In this paper, a new method categorized as a modification to the Q–h equations is proposed for the analysis of pipe networks. The method is inspired by the Kani method which is used for analysis of structural frames. The new method can be considered as an iterative procedure which does not require a large system of nonlinear equations to be solved simultaneously. The main advantages of the proposed method are relative simplicity in formulation and programming, and rapid and smooth convergence of initially guessed values. To show the robustness and convergence of the present method, several pipe networks are analyzed, and the results are compared with those of the conventional methods.     

A game theoretic approach to measuring efficiency

Correspondence with a new mathematical programming definition for efficiency as proposed by Charnes, Cooper and Rhodes (CCR) is established by means of game theoretical models. Contact with all of the CCR results is also maintained so that their results extend to our new game theoretic interpretations. The latter proceeds by means of a family of games related to a linear programming problem. The games-to-programming relations which we establish also open new possibilities for further relations between families of games and linear programs.     

An exponential differential game which admits a simple Nash solution

This paper deals with a class ofN-person nonzero-sum differential games where the control variables enter into the state equations as well as the payoff functionals in an exponential way. Due to the structure of the game, Nash-optimal controls are easily determined. The equilibrium in open-loop controls is also a closed-loop equilibrium. An example of optimal exploitation of an exhaustible resource is presented.The helpful comments of Professor Y. C. Ho and Dipl. Ing. E. Dockner are gratefully acknowledged.     

Reconstructing a simple game from a uniparametric family of allocations

Several relationships between simple games and a particular type of solutions for cooperative games are studied in this paper. These solutions belong to the set of semivalues and they are related to a unique parameter that explicitly provides their weighting coefficients. Through the allocations offered by this family of solutions, so-called binomial semivalues, and also from their respective potentials, some characteristics of the simple games can be recovered. The paper analyzes the capacity of binomial semivalues to summarize the structure of simple games, and, moreover, a property of separation among simple games is given.     

Applying a new algorithm to derive nonclassical symmetries

In this paper we extend the procedure described for Bîlă and Niesen in [Bîlă N, Niesen J. On a new procedure for finding nonclassical symmetries. J Symbol Comp 2004;38:1523–33], to obtain the determining equations of the nonclassical symmetries associated with a partial differential equation system, to a different case. We offer some examples of how our method works. By using this procedure we obtain a new nonclassical symmetry for the 2 + 1-dimensional shallow water wave equation.     

A linear optimization problem to derive relative weights using an interval judgement matrix

In this paper, we propose a new Decision Making model, enabling to assess a finite number of alternatives according to a set of bounds on the preference ratios for the pairwise comparisons between alternatives, that is, an “interval judgement matrix”. In the case in which these bounds cannot be achieved by any assessment vector, we analyze the problem of determining of an efficient or Pareto-optimal solution from a multi-objective optimization problem. This multi-objective formulation seeks for assessment vectors that are near to simultaneously fulfil all the bound requirements imposed by the interval judgement matrix. Our new model introduces a linear optimization problem in order to define a consistency index for the interval matrix. By solving this optimization problem it can be associated a weakly efficient assessment vector to the consistency index in those cases in which the bound requirements are infeasible. Otherwise, this assessment vector fulfils all the bound requirements and has geometrical properties that make it appropriate as a representative assessment vector of the set of feasible weights.     

Modeling activity times by the Parkinson distribution with a lognormal core: Theory and validation

Based on theoretical arguments and empirical evidence we advocate the use of the lognormal distribution as a model for activity times. However, raw data on activity times are often subject to rounding and to the Parkinson effect. We address those factors in our statistical tests by using a generalized version of the Parkinson distribution with random censoring of earliness, ultimately validating our model with field data from several sources. We also confirm that project activities exhibit stochastic dependence that can be modeled by linear association.     

A stackelberg game approach to distributed spectrum management

We consider a cognitive radio system with one primary (licensed) user and multiple secondary (unlicensed) users. Given the interference temperature constraint, the secondary users compete for the available spectrum to fulfill their own communication need. Borrowing the concept of price from market theory, we develop a decentralized Stackelberg game formulation for power allocation. In this scheme, the primary user (leader) announces prices for the available tones such that a system utility is maximized. Using the announced prices, secondary users (followers) compete for the available bandwidth to maximize their own utilities. We show that this Stackelberg game is polynomial time solvable under certain channel conditions. When the individual power constraints of secondary users are inactive (due to strict interference temperature constraint), the proposed distributed power control method is decomposable across the tones and unlike normal water-filling it respects the interference temperature constraints of the primary user. When individual power constraints are active, we propose a distributed approach that solves the problem under an aggregate interference temperature constraint. Moreover, we propose a dual decomposition based power control method and show that it solves the Stackelberg game asymptotically when the number of tones becomes large.     

A fuzzy solution to a majority voting game

In the Fiorina-Plott majority voting game experiment several puzzling phenomena were discovered: (1) In the experiment series where the payoffs were small in general, the predictive performance of the core was markedly worse than in the high payoff series. (2) The core outcome was found to be defeatable by another proposal. (3) Some of the majority winning social outcomes were Pareto-suboptimal. (4) Even when there was no theoretical equilibrium point, there was a clear clustering of outcomes. The paper outlines a fuzzy decision making procedure which seems to be capable of explaining all the puzzling features (1)–(4). In the absence of data on membership functions the explanation provided is of non-predictive nature; it renders the observed outcomes plausible without precisely predicting each one of them.     

A technique to derive the analytical form of convex envelopes for some bivariate functions

In the recent paper (Locatelli and Schoen in Math Program, 2013) it is shown that the value of the convex envelope of some bivariate functions over polytopes can be computed by solving a continuously differentiable convex problem. In this paper we show how this result can be exploited to derive in some cases the analytical form of the envelope. The technique is illustrated through two examples.