Chapter 15 - Paradoxical Degradation of Performance Under Nash Non-Cooperative Optimization in Symmetric Network Systems

Abstract

This chapter describes paradoxical degradation of performance under Nash non-cooperative optimization in symmetric network systems. The situation where no node can reduce its mean response time by unilaterally making another decision on forwarding jobs to other nodes is the Nash equilibrium. It is surprising that there exist cases of paradoxical performance degradation where the availability of communication means connecting nodes degrades the mean response time of every node in such a symmetric system. The condition under which the decentralized decision degrades the mean response time of every node are obtained, and the existence of the paradoxical cases where the ratio of the performance degradation can be unlimitedly large. The model of symmetrical nodes is investigated partly because in the preliminary investigation such counter-intuitive phenomena appeared most strongly in symmetrical models. It is found that there exist cases where paradoxes may bring unlimitedly large degradation of performance. The unique solution of the class optimum on the basis of only the special assumptions is also elaborated.