This paper studies the existence and the order structure of strong Berge equilibrium, a refinement of Nash equilibrium, for games with strategic complementarities à la strong Berge. It is shown that the equilibrium set is a nonempty complete lattice. Moreover, we provide a monotone comparative statics result such that the greatest and the lowest equilibria are increasing.
Mots-clés : strong Berge equilibrium, refinement, games with strategic complementarities, fixed point theory, supermodularity
@article{RO_2014__48_3_373_0, author = {Keskin, Kerim and \c{C}a\u{g}r{\i} Sa\u{g}lam, H.}, title = {Complementarities and the existence of strong {Berge} equilibrium}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {373--379}, publisher = {EDP-Sciences}, volume = {48}, number = {3}, year = {2014}, doi = {10.1051/ro/2014012}, mrnumber = {3264384}, zbl = {1296.91012}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ro/2014012/} }
TY - JOUR AU - Keskin, Kerim AU - Çağrı Sağlam, H. TI - Complementarities and the existence of strong Berge equilibrium JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2014 SP - 373 EP - 379 VL - 48 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2014012/ DO - 10.1051/ro/2014012 LA - en ID - RO_2014__48_3_373_0 ER -
%0 Journal Article %A Keskin, Kerim %A Çağrı Sağlam, H. %T Complementarities and the existence of strong Berge equilibrium %J RAIRO - Operations Research - Recherche Opérationnelle %D 2014 %P 373-379 %V 48 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2014012/ %R 10.1051/ro/2014012 %G en %F RO_2014__48_3_373_0
Keskin, Kerim; Çağrı Sağlam, H. Complementarities and the existence of strong Berge equilibrium. RAIRO - Operations Research - Recherche Opérationnelle, Tome 48 (2014) no. 3, pp. 373-379. doi : 10.1051/ro/2014012. http://www.numdam.org/articles/10.1051/ro/2014012/
[1] Théorie Générale des Jeux à n Personnes, Gautier Villars, Paris (1957). | Numdam | MR | Zbl
,[2] Non-cooperative games. Annal. Math. 54 (1951) 286-295. | MR | Zbl
,[3] Acceptable points in a general cooperative n-person games. in Contributions to the Theory of Games IV. Annal. Math. Study 40 (1959) 287-324. | MR | Zbl
,[4] Strong Berge equilibrium and strong Nash equilibrium: Their relation and existence, in Game Theory Appl., edited by L.A. Petrosjan and V.V. Mazalov. Vol. 15. Nova Science Publishers (2012) 165-180.
, and ,[5] Sur l'équilibre fort selon Berge. RAIRO Oper. Res. 35 (2001) 439-451. | Numdam | MR | Zbl
and ,[6] Intersection theorems and their applications to Berge equilibria. Appl. Math. Comput. 182 (2006) 1840-1848. | MR | Zbl
and ,[7] On the existence of Berge's strong equilibrium. Int. Game Theory Rev. 13 (2011) 325-340. | MR | Zbl
and ,[8] The set of Nash equilibria of a supermodular game is a complete lattice. Games Econ. Behavior 7 (1994) 295-300. | MR | Zbl
,[9] A short and constructive proof of Tarski's fixed-point theorem. Int. J. Game Theory 33 (2005) 215-218. | MR | Zbl
,[10] Supermodularity and Complementarity, Princeton University Press, Princeton (1998). | MR
,[11] Complementarities and games: New developments. J. Econ. Literature 43 (2005) 437-479.
,[12] Coordination Games: Complementarities and Macroeconomics, Cambridge University Press, Cambridge (1999). | Zbl
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