Consider the Tragedy of the Commons game with two shepherds, A and B. LetsA and sB denote the number of sheep each shepherd grazes on the common pasture. Assume the benefit per sheep equals 300−sA −sB
Assume the marginal cost of grazing sheep is zero since the common can be freely used.
a. Compute the flock sizes and shepherds’ total benefits in the Nash equilibrium.
b. Suppose A’s benefit per sheep rises to!330−sA −sB while B’s benefit remains the same. Compute the new Nash equilibrium flock sizes.
a. s(a)=s(b)=100
b. s(a)=120, s(b)=90