Multicriteria Goal Games

In this paper, we deal with multicriteria matrix games. Different solution concepts have been proposed to cope with these games. Recently, the concept of Pareto-optimal security strategy which assures the property of security in the individual criteria against an opponent's deviation in strategy has been introduced. However, the idea of security behind this concept is based on expected values, so that this security might be violated by mixed strategies when replications are not allowed. To avoid this inconvenience, we propose in this paper a new concept of solution for these games: the G-goal security strategy, which includes as part of the solution the probability of obtaining prespecified values in the payoff functions. Thus, attitude toward risk together with payoff values are considered jointly in the solution analysis.     

k-边覆盖对策及其核心

本文针对从图的k-边覆盖问题引出的合作对策模型，利用线性规划对偶理论得到了其核心非空的一个充分条件和构造核心分配的多项式时间算法，并将这一结果推广到了一般的k-集合覆盖对策模型中．     

Recursive solution of linear-quadratic Nash games for weakly interconnected systems

A recursive method is developed for the solution of coupled algebraic Riccati equations and corresponding linear Nash strategies of weakly interconnected systems. It is shown that the given algorithm converges to the exact solution with the rate of convergence ofO(²), where is a small coupling parameter. In addition, only low-order systems are involved in algebrdic computations; the amount of computations required does not grow per iteration and no analyticity assumption is imposed on the system coefficients.This work was supported by Rutgers University Research Council under Grant No. 2-02188.     

The lion and man problem revisited

A pursuerP, whose speed is bounded by 1, wants to get closer to an evaderE, whose speed is bounded by >1.P wants to reduce his distancePE fromE below the capture radius . Both players are confined to a circular arena. This problem is equivalent to a problem discussed by Flynn, who characterized and gave numerical bounds to the least upper boundd* on the values ofPE thatE can maintain. He used direct methods and did not use Isaacs' theory.We solve our problem relying on the theory of singular surfaces in differential games. We construct and investigate barriers of the game of kind, and we replace Flynn's bounds ond* by analytical (exact) values for various speeds .The support of the TW Department of THT, Enschede, Holland, is gratefully acknowledged.     

Kinetics of cooperative conformational transitions of lineal biopolymers

Cooperative conformational transitions of proteins and nucleic acids are of decisive importance to many processes of molecular biology, and particularly to their regulation. They proceed via numerous interdependent elementary processes, and their kinetics are therefore often complicated. They are frequently also very fast. However, kinetic analyses can be carried out by chemical relaxation methods. The theoretical interpretation is comparatively simple in the case of linear biopolymers. When the linear Ising model extended for kinetics was applied to model peptides and polynucleotides, it provided an insight into the fundamental principles of cooperative transformations.     

On the population monotonicity of independent set games

An independent set game is a cooperative game dealing with profit sharing in the maximum independent set problem. A population monotonic allocation scheme is a rule specifying how to share the profit of each coalition among its participants such that every participant is better off when the coalition expands. In this paper, we provide a necessary and sufficient characterization for independent set games admitting population monotonic allocation schemes. Moreover, our characterization can be verified efficiently.     

A new approach to agglomeration problems

In this paper, we study a location problem with positive externalities. We define a new transferable utility game, considering there is no restriction on the transfer of benefits between firms. We prove that the core of this game is non-empty, provide an expression for it, and an axiomatic characterization. We also study several core allocations, selected by means of a certain bankruptcy problem.     

A game locating a needle in a circular haystack

A complete solution of the following Hider-Seeker zero-sum game is obtained. The hider hides a needle of lengtha, 0<a2, in the closed unit dise, and the seeker tries to locate it by shooting in a straight line across the disc. The payoff to the seeker is 1 if he hits the needle and 0 otherwise.     

Cooperative Competition Clustering for Gene Selection

Clustering analysis of data from DNA microarray hybridization studies is an essential task for identifying biologically relevant groups of genes. Attribute cluster algorithm (ACA) has provided an attractive way to group and select meaningful genes. However, ACA needs much prior knowledge about the genes to set the number of clusters. In practical applications, if the number of clusters is misspecified, the performance of the ACA will deteriorate rapidly. We propose the Cooperative Competition Cluster Algorithm (CCCA) in this paper. In the algorithm, we assume that both cooperation and competition exist simultaneously between clusters in the process of clustering. By using this principle of Cooperative Competition, the number of clusters can be found in the process of clustering. Experimental results on a synthetic and gene expression data are demonstrated. The results show that CCCA can choose the number of clusters automatically and get excellent performance with respect to other competing methods.     

Statistical mechanics of a dynamical system based on Conway's game of Life

We study a discrete dynamical system whose evolution is governed by rules similar to those of Conway's game of Life but also include a stochastic element (parametrized by a temperature). Statistical properties that are examined are density as a function of temperature and entropy (suitably defined). A phase transition and a certain thermodynamic constant of the motion are observed.Lady Davis Visiting Scientist at the Technion 1974–75.