An optimal strong equilibrium solution for cooperative multi-leader-follower Stackelberg Markov chains games

Kristal K. Trejo; Julio B. Clempner; Alexander S. Poznyak

Kybernetika (2016)

  • Volume: 52, Issue: 2, page 258-279
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Trejo, Kristal K., Clempner, Julio B., and Poznyak, Alexander S.. "An optimal strong equilibrium solution for cooperative multi-leader-follower Stackelberg Markov chains games." Kybernetika 52.2 (2016): 258-279. <http://eudml.org/doc/281546>.

@article{Trejo2016,
abstract = {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.},
author = {Trejo, Kristal K., Clempner, Julio B., Poznyak, Alexander S.},
journal = {Kybernetika},
keywords = {strong equilibrium; Stackelberg and Nash; $L_\{p\}-$norm; Markov chains; strong equilibrium; Stackelberg and Nash; -norm; Markov chains},
language = {eng},
number = {2},
pages = {258-279},
publisher = {Institute of Information Theory and Automation AS CR},
title = {An optimal strong equilibrium solution for cooperative multi-leader-follower Stackelberg Markov chains games},
url = {http://eudml.org/doc/281546},
volume = {52},
year = {2016},
}

TY - JOUR
AU - Trejo, Kristal K.
AU - Clempner, Julio B.
AU - Poznyak, Alexander S.
TI - An optimal strong equilibrium solution for cooperative multi-leader-follower Stackelberg Markov chains games
JO - Kybernetika
PY - 2016
PB - Institute of Information Theory and Automation AS CR
VL - 52
IS - 2
SP - 258
EP - 279
AB - 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.
LA - eng
KW - strong equilibrium; Stackelberg and Nash; $L_{p}-$norm; Markov chains; strong equilibrium; Stackelberg and Nash; -norm; Markov chains
UR - http://eudml.org/doc/281546
ER -

References

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