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In this paper, we use principles from game theory, computer gaming, and evolutionary computation to produce a framework for investigating one of the great mysteries of the ancient Americas: why did the pre-Hispanic Pueblo (Anasazi) peoples leave large portions of their territories in the late A.D. 1200s? The gaming concept is overlaid on a large-scale agent-based simulation of the Anasazi. Agents in this game use a cultural algorithm framework to modify their finite-state automata (FSA) controllers following the work of Fogel (1966). In the game, there can be two kinds of active agents: scripted and unscripted. Unscripted agents attempt to maximize their survivability, whereas scripted agents can be used to test the impact that various pure and compound strategies for cooperation and defection have on the social structures produced by the overall system. The goal of our experiments here is to determine the extent to which cooperation and competition need to be present among the agent households in order to produce a population structure and spatial distribution similar to what has been observed archaeologically. We do this by embedding a "trust in networks" game within the simulation. In this game, agents can choose from three pure strategies: defect, trust, and inspect. This game does not have a pure Nash equilibrium but instead has a mixed strategy Nash equilibrium such that a certain proportion of the population uses each at every time step, where the proportion relates to the quality of the signal used by the inspectors to predict defection. We use the cultural algorithm to help us determine what the mix of strategies might have been like in the prehistoric population. The simulation results indeed suggest a mixed strategy consisting of defectors, inspectors, and trustors was necessary to produce results compatible with the archaeological data. It is suggested that the presence of defectors derives from the unreliability of the signal which increases under drought conditions and produced increased stress on Anasazi communities and may have contributed to their departure.