  We study a modification of the Evolutionary Minority Game (EMG) in which
agents are placed in the nodes of a regular or a random graph. A neighborhood
for each agent can thus be defined and a modification of the usual relaxation
dynamics can be made in which each agent updates her decision scheme depending
upon the options made in her immediate neighborhood. We name this model the
Local Evolutionary Minority Game (LEMG). We report numerical results for the
topologies of a ring, a torus and a random graph changing the size of the
neighborhood. We focus our discussion in a one dimensional system and perform a
detailed comparison of the results obtained from the random relaxation dynamics
of the LEMG and from a linear chain of interacting spin-like variables at a
finite temperature. We provide a physical interpretation of the surprising
result that in the LEMG a better coordination (a lower frustration) is achieved
if agents base their actions on local information. We show how the LEMG can be
regarded as a model that gradually interpolates between a fully ordered,
antiferromagnetic system and a fully disordered system that can be assimilated
to a spin glass.
