One famous game is a variant of the Prisonerâs Dilemma called the âTragedy of the Commons.â Assume there are two cattle herders who share a common plot of grazing land. The market price for a cow is given by P=300-10C, where C is the total number of cows grazed (this is because as more cows are grazed on the same plot of land, they become skinnier and less tasty). There is no cost associated with this activity, so Profit is simply P*C. Finally, let C1 be the number of cows grazed by the first cattle herder and C2 be the number of cows grazed by the second cattle herder, so C1+C2=C.
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Calculate the number of cows grazed by each cattle herder in the Nash equilibrium to this game. [5 marks]
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How much profit does each cattle herder earn? [2 marks]
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Is this arrangement Pareto Optimal (i.e., what would arise if the two
firms collude)? Show (mathematically) why/why not. (Pareto optimal means that you cannot make one player better off without making the other player worse off) [3 marks]
