Geodesic
An optimal strong equilibrium solution for cooperative multi-leader-follower Stackelberg Markov chains games
Kybernetika, Tome 52 (2016) no. 2, pp. 258-279.

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This paper presents a novel approach for computing the strong Stackelberg/Nash equilibrium for Markov chains games. For solving the cooperative $n$-leaders and $m$-followers Markov game we consider the minimization of the $L_{p}-$norm that reduces the distance to the utopian point in the Euclidian space. Then, we reduce the optimization problem to find a Pareto optimal solution. We employ a bi-level programming method implemented by the extraproximal optimization approach for computing the strong $L_{p}-$Stackelberg/Nash equilibrium. We validate the proposed method theoretically and by a numerical experiment related to marketing strategies for supermarkets.
DOI : 10.14736/kyb-2016-2-0258
Classification : 35K20, 93B05
Keywords: strong equilibrium; Stackelberg and Nash; $L_{p}-$norm; Markov chains 
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     author = {Trejo, Kristal K. and Clempner, Julio B. and Poznyak, Alexander S.},
     title = {An optimal strong equilibrium solution for cooperative multi-leader-follower {Stackelberg} {Markov} chains games},
     journal = {Kybernetika},
     pages = {258--279},
     publisher = {mathdoc},
     volume = {52},
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     year = {2016},
     doi = {10.14736/kyb-2016-2-0258},
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     zbl = {1374.35201},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2016-2-0258/}
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Trejo, Kristal K.; Clempner, Julio B.; Poznyak, Alexander S. An optimal strong equilibrium solution for cooperative multi-leader-follower Stackelberg Markov chains games. Kybernetika, Tome 52 (2016) no. 2, pp. 258-279. doi : 10.14736/kyb-2016-2-0258. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2016-2-0258/

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