On the existence and stability of solutions to stochastic equilibrium problems
RAIRO. Operations Research, Tome 55 (2021), pp. S705-S718

In this paper we consider stochastic equilibrium problems involving parameter of probability measures. Employing the fixed point theorem of Knaster, Kuratowski, Mazurkiewicz, and Fan (KKM-Fan), conditions for the existence of solutions to such problems are established. We then propose new metric concepts on the underlying stochastic spaces and study some properties corresponding to these metrics. Afterwards, we study sufficient conditions for the solution mappings of such problems, that are closed, upper (lower) semicontinuous and continuous with respect to the mentioned metrics. Finally, the special cases of stochastic optimization problems are taken into account as the applications.

DOI : 10.1051/ro/2020001
Classification : 49K40, 49K45, 90C15, 90C31
Keywords: Stochastic equilibrium problems, stochastic optimization, probabilistic metric spaces, existence and stability conditions, closedness and upper (lower) semicontinuity/continuity 
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     author = {Anh, Lam Quoc and Hai, Nguyen Xuan and Nguyen, Kien Trung and Quan, Nguyen Hong and Van, Dang Thi My},
     title = {On the existence and stability of solutions to stochastic equilibrium problems},
     journal = {RAIRO. Operations Research},
     pages = {S705--S718},
     year = {2021},
     publisher = {EDP-Sciences},
     volume = {55},
     doi = {10.1051/ro/2020001},
     mrnumber = {4223129},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ro/2020001/}
}
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Anh, Lam Quoc; Hai, Nguyen Xuan; Nguyen, Kien Trung; Quan, Nguyen Hong; Van, Dang Thi My. On the existence and stability of solutions to stochastic equilibrium problems. RAIRO. Operations Research, Tome 55 (2021), pp. S705-S718. doi: 10.1051/ro/2020001

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