A number of papers have studied imperfect imitative learning as a utility-increasing activity (e.g. Dawid, McCain 2000). Some studies of imitative learning have taken account of the tendency of people to imitate others who are "near" them in some sense (e.g. McCain 2000, Bala and Goyal). As Axtell observed, however, imitation may not be utility-increasing and may be motivated by quite different motives. Indeed, as McCain (1992) observed, imitation may lead to destructive and self-destructive behavior, as in road rage. Imitation may arise from a variety of motives, including simple conformism, a sense of common identity (McCain 1992), and fairness (Rabin) in the sense of reciprocity (Berg, Dickhaut, and McCabe). This multiplicity of motives lends itself to an "impulse-filtering" model (McCain, 1992) which would generate a probablistic choice function (Chen, Friedman, and Thisse). Whatever the motives, however, nearness (perhaps in social rather than physical space) would seem to be an important determinant of imitation.This paper reports simulations of a population of semi-rational agents playing a simple aggression-retaliation game in space. Their interactions are set in motion by random impulses to aggress. The decision to act on that impulse or not and to retaliate or not are determined by a series of probablistic filters, any one of which may suppress the impulse to aggress or to retaliate with a probability that depends on the recent experiences of the agent and her neighbors. The agents (victims of aggression) are situated at the cells of a cellular automaton and they can only perceive, and so be influenced by, the experiences of nearby neighbors.Simple as this model is, it may be used for policy assessment. To illustrate this, outcomes are compared with those of a modified game in which an external authority uses two kinds of strategies to restrain conflict. In one -- implemented by the Washington State Police in 1998 (Watson) -- the aggressors are penalized. In the alternative strategy, retaliators are penalized. Simulations are compared in order to project the relative effectiveness of the two penalty strategies.
