Multiobjective Prices of Stability and Anarchy for Multiobjective Games

We generalize the prices of stability and anarchy to multiobjective games. In the singleobjective case, the loss of overall efficiency induced by selfish behaviors is a deeply studied subject. While the price of anarchy bounds above the loss of efficiency of equilibria, the price of stability bounds it below. In a multiobjective game, each agent individually decides an action, creating an overall alternative which is valued by each agent using his multiobjective valuation function and compared by the Pareto-preference. We issue the study of multiobjective prices of stability and anarchy by discussing several possible definitions.