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The Size of the Stag Determines the Level of Cooperation

Cooperation has long been a prominent aspect of research in human behavior. However, humans today cooperate on very different tasks than they did hundreds of years ago. Whereas previously a group of hunters may have worked together to hunt a stag, humans today work on large-scale projects, such as the extraction and refinement of crude oil. We build upon previous theories of cooperation modelled in a N-person stag hunt. Our model further related to the notion that leaps in economic development, such as revolutions in the use of natural resources, often require the cooperation of larger groups. Put easily, more cooperators are needed to derive energy from coal than to collect and burn wood. We thus incorporate multiple thresholds for returns from cooperation in an N-person stag-hunt model. That is, an increasing number of cooperators is needed to be reach one of the next thresholds with larger cooperative rewards. Furthermore, we consider the role of dynamic population size. As the size of a population increases, new cooperative thresholds are attainable, and as population size shrinks, previously attainable thresholds fall out of reach. Here we find that when a new threshold is accessible to a population, the level of cooperation will increase to reach this threshold. However, when the next threshold is out of reach, cooperation decreases as individuals refrain from costly cooperation. This model provides a framework to understand how levels of cooperation evolved and continue to evolve in the future.