We study players' behavior in the prisoner's dilemma by using two stability notions: the stable set of von Neumann and Morgenstern with indirect domination and the largest consistent set defined by Chwe. Both notions assume possibility of sequential deviations and farsightedness of players. When players use only pure strategies, these two stabliity concepts provide us with the same outcome: {(Cooperation, Cooperation), (Defect, Defect)}when players behave independently; and {(Cooperation, Cooperation)} when players' joint, but not binding, moves are also considered. In the prisoner's dilemma with many alternatives such as the mixed extension of the prisoner's dilemma, the two notions produce completely different outcomes. In the stable set, every individually rational outcome could be stable in the former case; and only a Pareto efficient outcome is essentially stable in the latter case. The largest consistent set consists of all individually rational outcomes in either case.

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Many real problems with uncertainties may often be formulated as Stochastic Programmming Problem. In this study, Genetic Algorithm (GA) which has been recently used for solving mathematical programming problem is expanded for use in uncertain environments. The modified GA is referred as GA in uncertain environments (GAUCE). In the method, the objective function and/or the constraint are fluctuated according to the distribution functions of their stochastic variables. Firstly, the individual with highest frequency through all generations is nominated as the individual associated with the solution presenting the best expected value of objective function. The individual with highest frequency is associated with the solution by GAUCE. The proposed method is applied to Stochastic Optimal Assignment Problem, Stochastic Knapsack Problem and newly formulated Stochastic Image Compression Problem. Then, it has been proved that the solution by GAUCE has excellent agreement with the solution presenting the best expected value of objective function, incases of both Stochastic Optimal Assignment Problem and Stochastic Knapsack Problem. GAUCE is also successfully applied to Stochastic Image Compression Problem where the coefficients of discrete cosine transformation are treated as stochastic variables.

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Topological design of centralized computer networks is an important problem that has been investigated by many researchers. Such networks typically involve a large number of terminals connected to concentrators, that are then connected to a central computing site. This paper focuses on the concentrator location problem among general topological network design problems. The concentrator location problem is defined as determining the following: (i) the number and locations of concentrators that are to be open, and (ii) the allocation of terminals to concentrator sites without violating the capacities of concentrators. An exact algorithm (fractional cutting plane algorithm/branch-and-bound) is proposed for solving this problem. In this approach an integer programming problem is formulated. Then a class of valid inequalities is derived and a greedy algorithm for a separation problem is shown. A good lower bound is obtained by a lifting procedures. We show how to implement the algorithm using a commercial software for LP and branch-and-bound. Finally, the computational efficiency of our algorithm is demonstrated.

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Multiple queue, cyclic service systems (called polling systems) have often been used as performance evaluation models in communication and production systems with cyclic resource allocation. However, most research has focused only on the mean waiting times due to prohibitively growing complexity in computing higher-order moments of the waiting time. This paper presents the explicit expressions for the second moments of the waiting time in symmetric exhaustive and gated service systems of two, three, and four queues with Poisson arrival processes. Numerical comparison reveals that they are ordered in the number of queues (increasingly/decreasingly for exhaustive/gated service systems, respectively) and bounded fairly tightly by those for single queue systems and by those for systems with infinitely many queues. Conjecture of their heavy traffic limits is also made.

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A stochastic version of a concentrator location problem is dealt with in which traffic demand at each terminal location is uncertain. The concentrator location problem is defined as to determine the following: (i) the numbers and locations of concentators that are to be open, and (ii) the allocation of terminals to concentrator sites. The problem is formulated as a stochastic multi-stage integer linear program, with first stage binary variables concerning network design and continuous recourse variables concerning expansion of capacity. Given a first stage decision, the series of realization of traffic demand may possibly imply a violation of the capacity constraint of the concentrator. Therefore from the second stage to the last stage, recourse action is taken to correct the violation. The objective function minimizes the cost of connecting terminals and the cost of opening concentrators and the expected recourse cost of capacity expansion. We propose a new algorithm which combines an L-shaped method and a branch-and-bound method. Under some assumptions it decomposes the problem into a set of problems as many as the number of stages in parallel. Finally we demonstrate the computational efficiency of our algorithm for the multi-stage model.

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This paper deals with a multi-facility location problem on a tree. Given the number of facilities and the tree structure, the problem is to find the optimal locations of facilities so as to maximize the service provider's gain obtained from customers accessing the nearest facility. Customers are located only at vertices of the tree. For each vertex, customers' demand function is given, which is nonincreasing piecewise linear in the distance from the vertex to the nearest facility location. We modify the algorithm proposed by Megiddo-Zemel-Hakimi (1983), and show that it yields the exact optimum within a polynomial time.

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