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Population Growth and Nash Equilibria Under Viability Constraints in the Commons

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  • Noël Bonneuil

    (Institut national d’études démographiques
    École des hautes études en sciences sociales)

Abstract

Population growth modifies the optimal equilibrium between a stationary population and its resource, producing instead a line of equilibria, characterized by fluctuating population size, resource quantity, harvest per head, and birth rates. The Pontryagin procedure allows the analytical expression of the Nash equilibria for two populations sharing a common resource and capable of growth. An alternative procedure, which avoids solving differential equations and inherently includes state constraints, involves building the capture-viability kernel of an auxiliary system. For two populations, all Nash equilibria under state constraints are obtained as the intersection of the boundaries of two capture-viability kernels. The two methods, Pontryagin and viability, yield concordant results. Viability is more flexible and avoids solving differential equations for each initial condition.

Suggested Citation

  • Noël Bonneuil, 2018. "Population Growth and Nash Equilibria Under Viability Constraints in the Commons," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 478-491, February.
    • Handle: RePEc:spr:joptap:v:176:y:2018:i:2:d:10.1007_s10957-017-1135-y
    DOI: 10.1007/s10957-017-1135-y
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