Pareto Set, Fairness, and Nash Equilibrium: A Case Study on Load Balancing

Various fairness objectives are studied in relation to Pareto optimal sets and Nash equilibria. We examine the already discussed general parameterized fairness objective that covers a variety of fairness criteria and the newly introduced Nash-proportionate-fairness objective. We study them mainly numerically on a simple static load balancing model with two identical servers (computers) each of which has an independent arrival process and its own queue. Through the numerical results, several intuitive results are shown. For example, we observe that the points that achieve the general parameterized fairness objectives may cover a part but not all of the Pareto set, and at times, do not cover the Nash-proportionate-fair Pareto optimal point. Keywords— Fairness, Nash equilibrium, noncooperative game, Pareto optimum and inefficiency, mathematical programming / optimization.