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Second-order cone reformulation and the price of anarchy of a robust nash-cournot game

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Open access
Authors
Han, D.
Lo, H.K.
Sun, Jie
Yang, H.
Date
2010
Type
Journal Article

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Han, D. and Lo, H.K. and Sun, J. and Yang, H. 2010. Second-order cone reformulation and the price of anarchy of a robust nash-cournot game. Pacific Journal of Optimization. 6 (2): pp. 211-226.
Source Title
Pacific Journal of Optimization
ISSN
Faculty
Faculty of Science and Engineering
School
School of Elec Eng, Comp and Math Sci (EECMS)
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Abstract

We study an n-person Nash-Cournot game with incomplete information, in which the opponents' strategies are only known in a perturbed set and the players try to minimize their worst-case costs, which can vary due to data uncertainty. We show that in several interesting cases, this game can be reformulated as second-order cone optimization problems. We also derive a bound of the price of anarchy for this game, which is a bound on the ratio between the cost at the robust Nash-Cournot equilibria and the cost at the system optima. © 2010 Yokohama Publishers.