Use the following case from question
Two roommates John and Joe are playing a simultaneous game of cleaning the apartment.If neither of them clean,the apartment gets filthy and both get a utility of 2.If John cleans and Joe doesn't,John gets a utility of 1 and Joe gets a utility of 4.If Joe cleans and John doesn't,Joe gets a utility of 1 and John gets a utility of 4 and if both clean up the apartment,they each get a utility of 3.
-If the roommates played the game repeatedly where one roommate not cleaning this time would trigger the other roommate not cleaning next time,the Nash equilibrium is most likely to be
A)John cleans,Joe doesn't
B)Joe cleans,John doesn't
C)Both of them clean
D)Neither of them clean

Question

​Use the following case from question
Two roommates John and Joe are playing a simultaneous game of cleaning the apartment.If neither of them clean,the apartment gets filthy and both get a utility of 2.If John cleans and Joe doesn't,John gets a utility of 1 and Joe gets a utility of 4.If Joe cleans and John doesn't,Joe gets a utility of 1 and John gets a utility of 4 and if both clean up the apartment,they each get a utility of 3.
-​If the roommates played the game repeatedly where one roommate not cleaning this time would trigger the other roommate not cleaning next time,the Nash equilibrium is most likely to be
A)​John cleans,Joe doesn't
B)Joe cleans,John doesn't
C)Both of them clean
D)​Neither of them clean

Quizplus · Accepted Answer

In a repeated game where one player's action triggers the other player's action in the next round, the Nash equilibrium is often to cooperate (i.e., play the cooperative strategy) in the first round and then mimic the other player's action in subsequent rounds. This is known as a "tit-for-tat" strategy.

In this case, if John cleans and Joe doesn't, Joe will be incentivized to clean in the next round to avoid a dirty apartment. Similarly, if Joe cleans and John doesn't, John will be incentivized to clean in the next round. Therefore, cooperation (both cleaning) is the most likely Nash equilibrium strategy. If either player defects (i.e., doesn't clean), the other player will defect in the next round, leading to a suboptimal outcome for both.

Note: This assumes that the players are rational and have knowledge of each other's actions in previous rounds. If there is a possibility of miscommunication, lack of trust, or incomplete information, the equilibrium outcome may vary.

​Use the Following Case from Question

Use the Following Case from Question