Question

Suppose all the students in a class are asked to choose between α and β simultaneously. If a student chooses “β” he/she immediately gets B +. If the student chooses “α”, then his/her payoff depends on the choices made by the other students. If at least 90% students choose α, then all of those who chose α get A, otherwise they get F. Find the nash equilibrium

Answer 1

This can be simplified to form a two player game with both players having the choices and

The payoffs are shown in the table below:

Player 1/2	α	β
α	A,A	F,B+
β	B+,F	B+,B+

There are two Nash Equilibria in this game,

1. Both players choose and get a payoff of B+ each.

2. Both players choose and get a payoff of A each.

Because of the higher payoff, both players will choose

This can be extended to the given game since if at least 90% students choose , then all those who choose get A. There is no incentive to choose as choosing only reduces the payoff of all students.