Crab effect, advantage law, silver medal and other applications of the minority game

Abstract

In this work we present a pedagogical introduction to the minority game and various new versions of it with interesting properties, focusing in its applications in socialphysics. For instance, some systems display a kind of social behavior that seems to play an important role in the advancement and survival of an organized society [see, for instance, J. B. Silk et al., Science 302, 1231 (2003)]. On the other hand, devious behavior may degrade a organized society specially when anti-social individual patterns becomes common to many members of a collectivity. In a, perhaps, somewhat far fetched application of a model for interacting agents, the well known minority game, applicable in many contexts, we have studied by computer simulation the effect of having a fraction of the members of a collectivity endowed with spurious strategies. In particular the so called advantage law, where there are some agents that always win, no matter if they play good or not, and another one is a realization of a popularly known ?crab effect?, where better performing agents may be suppressed by the mass of the medial players. As may be expected, this antisocial strategies deteriorate the collective organization of the system, but now studied within a measurable framework. In another application, positively minded, of the multi choice minority game we introduce different ways to reward also second place winners and compare the results with the one of the standard MG