Pareto Efficiency and Approximate Pareto Efficiency in Routing and Load Balancing Games

We analyze the Pareto efficiency, or inefficiency, of solutions to routing games and load balancing games, focusing on Nash equilibria and greedy solutions to these games. For some settings, we show that the solutions are necessarily Pareto optimal. When this is not the case, we provide a measure to quantify the distance of the solution from Pareto efficiency. Using this measure, we provide upper and lower bounds on the "Pareto inefficiency" of the different solutions. The settings we consider include load balancing games on identical, uniformly-related, and unrelated machines, both using pure and mixed strategies, and nonatomic routing in general and some specific networks.

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