Question

Nadia and Maddie are two college roommates who both prefer a clean common space in their dorm room, but neither enjoys cleaning. The roommates must each make a decision to either clean or not clean the dorm room's common space. The payoff table for this situation is provided below, where the higher a player's payoff number, the better off that player is. The payoffs in each cell are shown as (payoff for Nadia, payoff for Maddie).

Maddie Clean Clean Don't Clean (7, 50) (10, 10) (30, 30) (50, 7) Nadia Don't Clean

What is the Nash Equilibrium in this dorm room cleaning game?

Group of answer choices

Nadia: Clean / Maddie: Don't Clean

Nadia: Don't Clean / Maddie: Don't Clean

Nadia: Clean / Maddie: Clean

Nadia: Don't Clean / Maddie: Clean

Answer 1

- If Nadia chooses to Clean, then the best response of Maddie is to Don't Clean as it gives him higher payoff

- If Nadia chooses not to clean, then the best response of Maddie is to not clean

On the other hand,

- If Maddie chooses to Clean, then the best response of Nadia is not to clean.

- If Maddie chooses not to clean, then the best response of Nadia is not to clean.

Hence, both the players choose Not to Clean the dorm room

Hence, Nash Equilibrium of this game is (Don't Clean, Don't Clean)

So, 2nd option : Nadia: Don't Clean / Maddie: Don't Clean is Correct.

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