Shapley polygons in 4 x 4 games

Martin Hahn

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.

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Year of publication:	2010
Authors:	Hahn, Martin
Published in:	Games. - Basel : MDPI, ISSN 2073-4336, ZDB-ID 2527220-2. - Vol. 1.2010, 3, p. 189-220
Subject:	evolutionary game theory \| Shapley polygon \| best response dynamics \| periodic solutions \| Evolutionäre Spieltheorie \| Evolutionary game theory \| Spieltheorie \| Game theory \| Shapley-Wert \| Shapley value \| Evolutionsökonomik \| Evolutionary economics