Question

There are three cow shepherds, James (Player 1), Peter (Player 2) and John (Player 3), who share a common parcel of land on which each of them are entitled to let their cows graze. All of them can simultaneously choose between cooperate or not-cooperate actions in deciding the number of cows that can graze in their common land. The following matrix shows that payoff received by all shepherds given their and other's actions.
Player 3 Cooperate

	Cooperate	Not Cooperate
Cooperate	60, 60, 60	50, 70, 50
Not Cooperate	70, 50, 50	65, 65, 45

Player 3 Not Cooperate

	Cooperate	Not-Cooperate
Cooperate	50, 50, 70	45, 65, 65
Not-Cooperate	65, 45, 65	55, ,55, 55

Find The Nash Equilibrium from the game above

Answer 1

Player 3 is strictly better off by playing a non-cooperate strategy, since for any action of both the players playing a non-cooperate strategy will give a higher pay off as shown by the second table.

The Nash equilibrium will be 55,55,55. From table 2, simply this is because given that player 1 plays cooperate player 2 will be better off not cooperating and when Player 1 cooperates player 2 is better off not cooperating. Seeing the same from the point of view of the second player we find that all 3 players are better off not cooperating which is given by 55,55,55.