Complementarities and the existence of strong Berge equilibrium

Kerim Keskin; H. Çağrı Sağlam

RAIRO - Operations Research - Recherche Opérationnelle (2014)

  • Volume: 48, Issue: 3, page 373-379
  • ISSN: 0399-0559

Abstract

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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.

How to cite

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Keskin, Kerim, and Çağrı Sağlam, H.. "Complementarities and the existence of strong Berge equilibrium." RAIRO - Operations Research - Recherche Opérationnelle 48.3 (2014): 373-379. <http://eudml.org/doc/275083>.

@article{Keskin2014,
abstract = {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.},
author = {Keskin, Kerim, Çağrı Sağlam, H.},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {strong Berge equilibrium; refinement; games with strategic complementarities; fixed point theory; supermodularity},
language = {eng},
number = {3},
pages = {373-379},
publisher = {EDP-Sciences},
title = {Complementarities and the existence of strong Berge equilibrium},
url = {http://eudml.org/doc/275083},
volume = {48},
year = {2014},
}

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
PB - EDP-Sciences
VL - 48
IS - 3
SP - 373
EP - 379
AB - 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.
LA - eng
KW - strong Berge equilibrium; refinement; games with strategic complementarities; fixed point theory; supermodularity
UR - http://eudml.org/doc/275083
ER -

References

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  1. [1] C. Berge, Théorie Générale des Jeux à n Personnes, Gautier Villars, Paris (1957). Zbl0082.34702MR99259
  2. [2] J.F. Nash, Non-cooperative games. Annal. Math.54 (1951) 286–295. Zbl0045.08202MR43432
  3. [3] R. Aumann, Acceptable points in a general cooperative n-person games. in Contributions to the Theory of Games IV. Annal. Math. Study40 (1959) 287–324. Zbl0085.13005MR104521
  4. [4] R. Nessah, M. Larbani and T. Tazdaït, 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. Zbl1320.91013
  5. [5] M. Larbani and R. Nessah, Sur l’équilibre fort selon Berge. RAIRO Oper. Res.35 (2001) 439–451. Zbl1012.91002MR1896582
  6. [6] K.Y. Abalo and M.M. Kostreva, Intersection theorems and their applications to Berge equilibria. Appl. Math. Comput.182 (2006) 1840–1848. Zbl1151.91324MR2282626
  7. [7] M. Deghdak and M. Florenzano, On the existence of Berge’s strong equilibrium. Int. Game Theory Rev.13 (2011) 325–340. Zbl1259.91008MR2943857
  8. [8] L. Zhou, The set of Nash equilibria of a supermodular game is a complete lattice. Games Econ. Behavior7 (1994) 295–300. Zbl0809.90138MR1295306
  9. [9] F. Echenique, A short and constructive proof of Tarski’s fixed-point theorem. Int. J. Game Theory33 (2005) 215–218. Zbl1071.91002MR2211721
  10. [10] D.M. Topkis, Supermodularity and Complementarity, Princeton University Press, Princeton (1998). MR1614637
  11. [11] X. Vives, Complementarities and games: New developments. J. Econ. Literature43 (2005) 437–479. 
  12. [12] R.W. Cooper, Coordination Games: Complementarities and Macroeconomics, Cambridge University Press, Cambridge (1999). Zbl0941.91018

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