On the performances of Nash equilibria in isolation games

On the performances of Nash equilibria in isolation games

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Article ID: iaor20119242
Volume: 22
Issue: 3
Start Page Number: 378
End Page Number: 391
Publication Date: Oct 2011
Journal: Journal of Combinatorial Optimization
Authors: , , ,
Keywords: Nash equilibrium
Abstract:

We study the performances of Nash equilibria in isolation games, a class of competitive location games recently introduced in Zhao et al. (Proc. of the 19th International Symposium on Algorithms and Computation (ISAAC), pp. 148–159, 2008). For all the cases in which the existence of Nash equilibria has been shown, we give tight or asymptotically tight bounds on the prices of anarchy and stability under the two classical social functions mostly investigated in the scientific literature, namely, the minimum utility per player and the sum of the players’ utilities. Moreover, we prove that the convergence to Nash equilibria is not guaranteed in some of the not yet analyzed cases.

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