Scenario: Consider the following non-cooperative, simultaneous-move game where each player knows her own and her opponent's payoffs. This game is called the dating dilemma. Hayley and Jack are a couple deciding what to do on a Saturday afternoon in the summer. Hayley wants to go to the Museum of Modern Art (MoMA), while Jack wants to go to a New York Mets game. Neither Jack nor Hayley will derive any benefit from going to their preferred activity without their partner. The payoff matrix for this game is presented below.

-Refer to the scenario above.Suppose Hayley and Jack face this quandary repeatedly.What might each individual do when faced with repeated play of this game?
A) Always choose their own preferred activity
B) Always choose their partner's preferred activity
C) Randomize their choice of their own and their partner's preferred activities
D) None of the above

Question

Scenario: Consider the following non-cooperative, simultaneous-move game where each player knows her own and her opponent's payoffs. This game is called the dating dilemma. Hayley and Jack are a couple deciding what to do on a Saturday afternoon in the summer. Hayley wants to go to the Museum of Modern Art (MoMA), while Jack wants to go to a New York Mets game. Neither Jack nor Hayley will derive any benefit from going to their preferred activity without their partner. The payoff matrix for this game is presented below.
 
-Refer to the scenario above.Suppose Hayley and Jack face this quandary repeatedly.What might each individual do when faced with repeated play of this game?
A) Always choose their own preferred activity 
B) Always choose their partner's preferred activity 
C) Randomize their choice of their own and their partner's preferred activities 
D) None of the above

Quizplus · Accepted Answer

If Hayley and Jack always choose their own preferred activity (A), they will always end up with 0 payoff. If they always choose their partner's preferred activity (B), the game will end up in a stalemate with a payoff of (5,5). However, if they randomize their choice of their own and their partner's preferred activities, they can both get a payoff of (3,3) on average. This is because, in any given round, each player has a 50% chance of getting their preferred activity, and a 50% chance of going along with their partner's preferred activity. Over time, this probability distribution will converge to (3,3) as the players adjust their strategies based on their past outcomes. Therefore, randomizing their choice is the best strategy for both players in the long run.

Scenario: Consider the Following Non-Cooperative, Simultaneous-Move Game Where Each Player