Next Article in Journal
Erev, I. et al. A Choice Prediction Competition for Market Entry Games: An Introduction. Games 2010, 1, 117-136
Previous Article in Journal
Backward Induction versus Forward Induction Reasoning
Games 2010, 1(3), 189-220; doi:10.3390/g1030189

Shapley Polygons in 4 x 4 Games

Department of Mathematics, University Vienna, c/o Josef Hofbauer, Nordbergstra├če 15, A-1090 Wien, Austria
Received: 9 June 2010 / Accepted: 14 July 2010 / Published: 15 July 2010
View Full-Text   |   Download PDF [361 KB, uploaded 15 July 2010]   |   Browse Figures


We study 4 x 4 games for which the best response dynamics contain a cycle. We give examples in which multiple Shapley polygons occur for these kinds of games. We derive conditions under which Shapley polygons exist and conditions for the stability of these polygons. It turns out that there is a very strong connection between the stability of heteroclinic cycles for the replicator equation and Shapley polygons for the best response dynamics. It is also shown that chaotic behaviour can not occur in this kind of game.
Keywords: evolutionary game theory; Shapley polygon; best response dynamics; periodic solutions evolutionary game theory; Shapley polygon; best response dynamics; periodic solutions
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Supplementary material

Share & Cite This Article

Further Mendeley | CiteULike
Export to BibTeX |
EndNote |
MDPI and ACS Style

Hahn, M. Shapley Polygons in 4 x 4 Games. Games 2010, 1, 189-220.

View more citation formats

Related Articles

Article Metrics

For more information on the journal, click here


[Return to top]
Games EISSN 2073-4336 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert