Modeling the commons as a game with vector payoffs

Since Hardin first formulated the tragedy of the commons, researchers have described various ways that commons problems are solved, all based on the model of individual rationality. Invariably, these institutional solutions involve creating some system of property rights. We formulate an alternative model, one not founded on property rights but on decision-making around so-called vector payoffs. The model is formalized and an existence proof provided. The new model is shown to be effective in explaining some anomalous results (e.g., unanticipated cooperation) in the experimental games literature that run counter to the rational model. We then use the case of the buffalo commons to illustrate how the new model affords alternative explanations for examples like the rise and fall of the buffalo herds in the Great Plains. We find the vector payoff model to complement, though not displace, that of individual rationality.