Ecologists and economists try to explain collective behavior in terms of competitive systems of selfish individuals with the ability to learn from the past. Statistical physicists have been investigating models which might contribute to the understanding of the underlying mechanisms of these systems. During the last 3 yr one intuitive model, commonly referred to as the minority game (MG), has attracted considerable attention. Powerful yet simple, the minority game has produced encouraging results which can explain the temporal behavior of competitive systems. Here we switch the interest to the phenomena due to a distribution of the individuals in space. For analyzing these effects we modify the minority game and the local minority game (LMG) is introduced. We study the system both numerically and analytically, using the customary techniques already developed for the ordinary Minority Game. (C) 2002 Elsevier Science B.V. All rights reserved.