In completely symmetric systems that have homogeneous nodes (hosts, computers, or processors) with identical arrival processes, an optimal static load balancing scheme does not involve the forwarding of jobs among nodes. Using an appropriate analytic model of a distributed computer system, we examine the following three decision schemes for load balancing: completely distributed, intermediately distributed, and completely centralized. We show that there is no forwarding of jobs in the completely centralized and completely distributed schemes, but that in an intermediately distributed decision scheme, mutual forwarding of jobs among nodes is possible, leading to degradation in system performance for every decision maker. This result appears paradoxical, because by adding communication capacity to the system for the sharing of jobs between nodes, the overall system performance is degraded. We characterize conditions under which such paradoxical behavior occurs, and we give examples in which the degradation of performance may increase without bound. We show that the degradation reduces and finally disappears in the limit as the intermediately distributed decision scheme tends to a completely distributed one.

We consider a network shared by noncooperative two types of users, group users and individual users. Each user of the first type has a significant impact on the load of the network, whereas a user of the second type does not. Both group users as well as individual users choose their routes so as to minimize their costs. We further consider the case that the users may have side constraints. We study the concept of mixed equilibrium (mixing of Nash equilibrium and Wardrop equilibrium). We establish its existence and some conditions for its uniqueness. Then, we apply the mixed equilibrium to a parallel links network and to a case of load balancing.

This paper deals with the approximation of Nash equilibria in m-player games. We present conditions under which an approximating sequence of games admits nearequilibria that approximate near-equilibria in the limit game. We apply the results to two classes of games: (i) a duopoly game approximated by a sequence of matrix games, and (ii) a stochastic game played under the S-adapted information structure approximated by games played over a sampled event tree. Numerical illustrations show the usefulness of this approximation theory.

We model a pollution accumulation process through a nonlinear, nondifferentiable state equation and also as dependent on an environmental levy. Then the payoff function to an economic agent is defined piece‐wise. However, for a simple demand and cost structure, the combined payoff function of all agents is diagonally strictly concave. This implies that a steady‐state Nash equilibrium is unique and can be controlled by the levy. We analytically compute a steady‐state Nash equilibrium solution for the agents, and use a Decision Support Tool to determine a satisfactory solution for the interactions between the agents and a legislator responsible for the levy.

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