Shapley Polygons in 4 x 4 Games

Martin Hahn
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Martin Hahn: Department of Mathematics, University Vienna, c/o Josef Hofbauer, Nordbergstraße 15, A-1090 Wien, Austria

Games, 2010, vol. 1, issue 3, 1-32

Abstract: 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 (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2010
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