Characterizing the underlying static complex network of the Minority Game

CARIDI, INÉS

Villa Carlos Paz, Córdoba

Congreso; XIII LATIN AMERICAN WORKSHOP ON NONLINEAR PHENOMENA; 2013

The Minority Game (MG) is a well known agent-based model with no explicit interaction among its agents [1]. However, it is known that they interact through the global magnitudes of the model and through their strategies. In this work we intend to formalize the implicit interactions among MG agents as if they were links on a complex network. We have defined the link between two agents by quantifying the similarity among them. This link definition is based on the information of the instance of the game (the set of strategies assigned to each agent at the beginning) and it brings about a static, unweighted, and undirected network. This link denition only captures the underlying network of connections at the strategies level, without dynamic information. We have analyzed the structure of the resulting network for diferent MG parameters, such as the number of agents (N) and the capacity of information processing of the agents (m), always taking into account games with two strategies per agent. In the region of crowd-efects of the model, the resulting networks 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 Erdos-Renyi. The transition between these two networks is slow. We cannot say anything characteristic about the network in the region of the coordination among agents. Perhaps the instance (static) network may not be suficient to offer information about this region, and it might be necessary to consider the dynamic network, which should be obtained using information related with the strategies which the agents actually used. Finally, we have studied the resulting static networks for the Full Strategy Minority Game (FSMG) model, a maximal instance of the MG in which all possible agents take part in the game [2-3]. We have explicitly calculated the degree distribution of the FSMG network and, from this exact result, we have estimated the degree distribution of the MG network, which is in accordance with computational results.[1] D. Challet and Y. C. Zhang, Physica A, 246, 407, 1997; D. Challet and Y. C. Zhang, Physica A, 256, 514, (1998).[2] I. Caridi, H.Ceva, Physica A, 317, 247, (2003).[3] G. Acosta, I. Caridi, S. Guala, J. Marenco, Physica A 391, 217-230 (2012)