Tragedy of the commons: The extinction of the woolly mammoth

Consider Harrington’s model of the extinction of the woolly mammoth with the following modifications:

(a) Adopt the ‘egalitarian’ distribution of the meat from the effort of all hunters together that is mentioned in Harrington’s text. Note that direct costs of hunting are still borne individually and are equal to 100 times individual efforts. Derive the Nash equilibrium for this game.

(b) Compare the Nash equilibrium in (a) to Harrington’s result. Explain the difference between the two.

(c) Find a suitable definition of a ‘social optimum’ of the hunting-game and derive its numerical value. How can the social optimum be implemented?

Hint: In a ‘social optimum’ marginal social costs must be equal to marginal social benefits.

**Subject Mathematics Game Theory**