Question

Students believe that if everyone in the course studies for the final exam, then the average mark everyone can expect is 75. However, if no one studies, everyone does so poorly that grades are scaled and the average mark of 60 is achieved. If one person studies while everyone else doesn’t, the one who studies achieves 80, the rest achieve 45 (and no scaling takes place). This game is a one-off simultaneous game with the two players to be ‘You’ and ‘Everyone else’. If everyone colludes, then the Nash equilibrium is for no one to study.

Answer 1

Students believe that if everyone in the course studies for the final exam, then the average mark everyone can expect is 75.

However, if no one studies, everyone does so poorly that grades are scaled and the average mark of 60 is achieved.

If one person studies while everyone else doesn’t, the one who studies achieves 80, the rest achieve 45 (and no scaling takes place).

The game is a one-off simultaneous game with two players to be - Me and everyone else. The strategies and payoffs of both the players in the matrix firm can be shown as -

From above we can see that if we find generally, the Nash equilibrium of the game is to Study,study and hence get a payoff of 75(75 marks).

Collusion means the agreement between the two players in order to reduce competition and increase the joint profit. So here if everyone including me try to collude than we will decide to study because it gives all of us the highest marks. So even after collusion Nash equilibrium will be to Study.