Research on Robust Cooperative Dual Equilibrium with Ellipsoidal Asymmetric Strategy Uncertainty

LUO Gui-mei

doi:10.13371/j.cnki.chin.q.j.m.2019.04.008

Chinese Quarterly Journal of Mathematics >

2019 , Vol. 34 >Issue 4: 431 - 440

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2019.04.008

Research on Robust Cooperative Dual Equilibrium with Ellipsoidal Asymmetric Strategy Uncertainty

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School of Financial Mathematics and Statistics, Guangdong University of Finance

Received date: 2019-06-05

Online published: 2020-08-21

Supported by

supported by Ministry of Education Planning Fund granted 15YJA790043； Guangdong Province Education Department Foundation granted 2016WTSCX079

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Abstract

In this paper,we investigate robust cooperative dual equilibria with two players in which each player minimizes the opponent’s cost and can not evaluate his own strategy while may estimate an asymmetric bounded set of the mixed strategy.Using dual theory and robust optimization technique,we obtain a result that the counterpart of the primitive uncertainty with ellipsoidal norm for each player can be formulated as a second-order cone programming(SOCP) and solving the corresponding equilibrium can be converted to solving a second-order cone complementarity problem(SOCCP).Then we present a numerical experiment to illustrate the behavior of robust cooperative dual equilibrium.

Key words： Robust cooperative dual equilibrium; Asymmetric strategy uncertainty; SOCP; SOCCP

Cite this article

LUO Gui-mei . Research on Robust Cooperative Dual Equilibrium with Ellipsoidal Asymmetric Strategy Uncertainty[J]. Chinese Quarterly Journal of Mathematics, 2019 , 34(4) : 431 -440 . DOI: 10.13371/j.cnki.chin.q.j.m.2019.04.008

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