On a Prey-Predator Nonzero-Sum Game and the Evolution of Gregarious Behavior of Evasive Prey

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Abstract
Following Hamilton (1971), gregarious behavior of a potential prey was examined on the basis of the selfish drive of each individual in the prey population to minimize its own probability of predation rather than to contribute to the welfare of the entire population. The asymmetric situation, where active pursuit and evasion endow faster individuals of the prey population with better chances to escape predation, was discussed. In such situations, a certain identity of interests between the predator and some of its potential prey can evolve. Conditions for formation of an evasive herd can be analyzed as a nonzero-sum prey-predator game. Under a wide variety of conditions the optimum behavior for a fast prey was always such as to maximize the predation probability of the slowest prey. Some other biological phenomena, typical to either evasive prey or its predators, were also suggested as following from the nonzero-sum model.

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