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Beating your Neighbor to the Berry Patch

This paper studies the situation in which multiple foragers compete for a resource that ripens (or otherwise improves) gradually. There is a unique mixed Nash Equilibrium (NE), which is stable against pure-strategy invaders provided that either the cost of visiting the resource or number of competitors is large. This equilibrium is not evolutionarily stable, however, because mixed strategies that are similar to the NE can invade. This mixed-strategy instability was not observed in computer simulations. The process converged to the neighborhood of the NE whenever the parameters implied stablity against pure-strategy invaders. Experiments with human subjects also failed to exhibit this mixed-strategy instability. After an initial period of familiarization, the behavior of human subjects was close to that predicted by the NE. This suggests that the NE may be useful as a prediction of behavior, and when that it true, strange conclusions emerge: the larger the number of foragers, the less likely it is that the resource will be harvested at all, and the greater the mean value of that resource when it is harvested.