Eur. Phys. J. B 56, 53-63 (2007)
https://doi.org/10.1140/epjb/e2007-00091-9

Evolution of imitation networks in Minority Game model

¹ Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Břehová 7, 11519,  Prague 1, Czech Republic
² Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-18221 Prague, Czech Republic and Center for Theoretical Study, Jilská 1, Prague, Czech Republic

Corresponding authors: ^a hynek.lavicka@fjfi.cvut.cz - ^b slanina@fzu.cz

Received: 20 December 2006
Published online: 4 April 2007

Abstract

The Minority Game is adapted to study the “imitation dilemma”, i.e. the tradeoff between local benefit and global harm coming from imitation. The agents are placed on a substrate network and are allowed to imitate more successful neighbours. Imitation domains, which are oriented trees, are formed. We investigate size distribution of the domains and in-degree distribution within the trees. We use four types of substrate: one-dimensional chain; Erdös-Rényi graph; Barabási-Albert scale-free graph; Barabási-Albert 'model A' graph. The behaviour of some features of the imitation network strongly depend on the information cost ϵ, which is the percentage of gain the imitators must pay to the imitated. Generally, the system tends to form a few domains of equal size. However, positive ϵ makes the system stay in a long-lasting metastable state with complex structure. The in-degree distribution is found to follow a power law in two cases of those studied: for Erdös-Rényi substrate for any ϵ and for Barabási-Albert scale-free substrate for large enough ϵ. A brief comparison with empirical data is provided.