Neworks underlying the minority game reflects different behavior of the model

INÉS CARIDI

Puebla, México

Conferencia; 1 ST LATIN AMERICAN CONFERENCE ON COMPLEX NETWORKS; 2017

BENEMÉRITA UNIVERSIDAD AUTÓNOMA DE PUEBLA

The Minority Game (MG) was introduced in 1997 by Challet and Zhang in anattempt to catch essential characteristics of a population competing for limited resources. As in the case of a traffic problem in whichpeople have to decide between two routes, in the MG an individualachieves the best result when she manages to be in the minoritygroup. In the model, there are N agents, who ateach step of the game must choose one of two sides, 0 or 1. The only information available for the agentsis the system state, which stores the best side choices for the last m steps and which is updated after each step of the game. The parameter m defines the information-processing capacity of the agents. Agents take decisions based on strategies. Although there is no explicit interaction among MG agents, it is known that they interact through the global magnitudes of the model and through their strategies. We have formalized the implicit interactions among MG agents as if they werelinks on a complex network. We have defined the link between two agents by quantifying the similarity between them, in terms of their strategies. We have analyzed the structure of the resulting network for different MG parameters, such as the number of agents N and the agents capacity to process information m. In the region of crowd-effects of the model, the resulting network structure is a small world network, whereas in the region where the behavior of the MG is the same as in a game of random decisions, MG networks become a random network of Erdös-Renyi. Finally, we have studied the resulting static networks for the Full Strategy Minority Game Model, a maximal instance of the Minority Game in which all possible agentstake part in the game. We have explicitly calculated the degree distribution of the Full Strategy Minority Game network and, on the basis of this analytical result, we have estimated the degree distribution of the minority game network, which is in accordance with computational results.