A professor once gave this awesomely evil opportunity in the final test of a Gam

Question

A professor once gave this awesomely evil opportunity in the final test of a Game Theory class: ”Here you have the opportunity to earn some extra credit on your final test grade. Select whether you want 2 points or 4 points added onto your final test grade. But there’s a small catch: if more than 10 people in the class select 4 points, then no one gets any points.”

Your task is to identify all the pure-strategy Nash equilibria in this game. You can also assume that there are 40 students in that class

Explanation / Answer

two pure-strategy Nash equilibria in this game.

1) each person picks 4 and everyone gets 0.

2) if the maximum amount of people that is 10 pick 4 points and everyone else picks 2 points , then no one can individually do any better given what others are doing. This is also a Nash equilibrium.

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