This is Intermediate Microeconomics problem. Game Theory (Stag-Hunt Game): N pla

Question

This is Intermediate Microeconomics problem.

Game Theory (Stag-Hunt Game): N players go hunting; each can choose to hunt either stag or hare, so the set of actions available to each player is {S,H} (S stands for hunt stag, H stands for hunt hare). If all N players hunt S, then each gets payoff 2. If any players hunt hare, then each hare-hunter gets payoff 1, while all stag-hunters get zero. (Interpretation, the stag is only caught if all N players work together).
(a) Suppose first that N = 2 (i.e., that there are two players). Write out the payoff matrix.

(b) Now let N = 3: Show that it is not a Nash equilibrium for 2 players to choose S, and one player to choose H: specifically, show that if this is what players plan to do, and if all players correctly anticipate it, then somebody can improve his payoff by changing only his own action.

Explanation / Answer

a) If N = 2 players, the payoff matrix is drawn as follows:

b) Now if number of hunters becomes 3, and they follow the stragety where 2 players hunt stag and third one hunts hare, then the two hunting stag will get 0 and third one will get 1 where as another competing strategy exists there such as three of them hunt stag that will give them 2 payoff to each which is grater than earlier strategy's pay off hence this can not be an equilibrium.

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