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Journal of Applied Mathematics
Volume 2014, Article ID 415686, 7 pages
Research Article

Local Interactions and p-Best Response Set

1CREG, Université Pierre-Mendès-France-de Grenoble, 38400 Saint-Martin d’Hères, France
2GATE Lyon-St-Etienne, Université de Saint-Etienne, 42023 Saint-Etienne, France

Received 6 December 2013; Accepted 5 February 2014; Published 26 March 2014

Academic Editor: Pu-yan Nie

Copyright © 2014 J. Durieu and P. Solal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study a local interaction model where agents play a finite n-person game following a perturbed best-response process with inertia. We consider the concept of minimal p-best response set to analyze distributions of actions on the long run. We distinguish between two assumptions made by agents about the matching rule. We show that only actions contained in the minimal p-best response set can be selected provided that p is sufficiently small. We demonstrate that these predictions are sensitive to the assumptions about the matching rule.