The tragedy of the commons revisited

Abstract

We formulate the Malthus-Hardin tragedy of the commons as a special case of dynamic game between tribes. At each date a member of a tribe desires more newborns of her/his type and more current consumption, harvested from the commons. Equilibrium in the dynamic game yields steady state level of per capita consumption for each person and a steady population level for each tribe (births equal deaths). We obtain four outcomes, depending on our assumptions about the discount rates of members of a tribe and about the mode of competition for large for each tribe. We compare Nash open loop and Nash feedback solutions with a quadratic current utility function and observe a larger populations under the feedback solution. The classic tragedy of the commons solution obtains as a special case of the open loop solution, one with an infinite rate of discount for players.