A Parametric Worst-Case Approach to Fairness in TU-Cooperative Games

We propose a parametric family of measures of fairness in allocations of TU-cooperative games. Their definition is based on generalized Rényi Entropy, is related to the Cowell-Kuga generalized entropy indices in welfare economics, and aims to parallel the spirit of the notion of price of anarchy in the case of convex TU-cooperative games. Since computing these indices is NP-complete in general, we first upper bound the performance of a “reverse greedy” algorithm for approximately computing worst-case fairness. The result provides a general additive error guarantee in terms of two (problem dependent) packing constants. We then particularize this result to the class of induced subset games. For such games computing worst-case fairness is NP-complete, and the additive guarantee constant can be explicitly computed. We compare this result to the performance of an alternate algorithm based on “biased orientations”. Department of Computer Science, West University of Timişoara, Bd. V. Pârvan 4, Timişoara, RO-300223, Romania and e-Austria Research Institute, Bd. V. Pârvan 4, cam. 045 B, Timişoara, RO-300223, Romania Corresponding Author. Center for the Study of Complexity, Babeş-Bolyai University, Fântânele 30, cam. A-14, Cluj Napoca, RO-400294, Romania and e-Austria Research Institute, Bd. V. Pârvan 4, cam. 045 B, Timişoara, RO-300223, Romania. email: [email protected]