Friday, November 15, 2013

Dating Game

QUESTION: A man and a woman are trying to decide where to go on a date.  The woman prefers ballet, but the man prefers going to a football game.  There is some gain to going together, but each would rather go to their preferred activity alone, than together to their less preferred activity.  Diagram this game, and show how best to play.

 ANSWER:

                                                 Man
                                              Football             Ballet
                              Football   (1,4)                  (0,0)
Woman        
                                  Ballet   (2,2)                  (4,1)


The man does better by going to the football game, regardless what the woman does, and the woman does better by going to the ballet, regardless what the man does.  These are called "dominant strategies."  The equilibrium of the game is for each to go to their preferred activity.

Notice, however, that the two players could make themselves better off by cooperating.  Self interest is taking them to a place (2,2) with a lower group payoff than the cells on the main diagonal. 

There are two ways to change the game to increase group payouts.

1. Alternate.  If the couples take turns, their group payout goes up.

2. Have the player that receives the higher payoff, compensate the other player for going to their less preferred activity.

In this case, the man could give 1.5 units to the woman if they go to the football game, which would change the payoff in the upper left to (2.5, 2.5).  This would change the equilibrium of the game.

Alternatively, the woman could give 1.5 units to the man if they go to the ballet.  This is the premise of an off-color South Park episode.


3 comments:

  1. HAHA. I knew that was the South Park episode that you were thinking of before I clicked the link. I believe that compensation is a better than alternating. Alternating may introduce the Hold-Up effect.

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  2. As I read this article, I realized that relationships are torn between the men participating in women’s activities and vice versa. If a woman is into sports, like myself, I wouldn’t have an issue attending a basketball or football game, but many women aren’t interested. Men, on the other hand, aren’t too keen on going to the ballet.

    To put this situation into perspective, it was a clever idea to use a South Park episode called “Broadway Bro Down.” In this case, I consulted my son who is an avid South Parker viewer to analyze the episode for me and relate it to the article.

    This is point of view is from a 21 year old young man. In most relationships, men like to please their mate hoping that when the time comes to do “manly” activities there wouldn’t be a problem. Unbeknown to Randy, his co-workers informed him, that Broadway shows cause their wives to become sexually aroused. After this, Randy takes Sharon, his wife, to see Wicked and is confused and unimpressed with the lack of overt sexuality. Randy gets up during the play to get a drink, and at the bar a man tells Randy that there is 'sub-text' that he should listen for.

    Soon after, Randy apologizes to Sharon for tricking her before; she responds that she does not really mind because she got so much out of the plays. If it was something they both enjoyed and brought them closer together, then musicals are a good thing.

    Overall, since Randy has repeatedly play this is game, its win-win situation. Therefore, Randy’s wife, Sharon is happy and he gets thrilled!
    http://southpark.wikia.com/wiki/Broadway_Bro_Down


    Suzette Monteverde, Empire State College, Dr. Singh, ECO-65155X

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  3. Dating can be a logical representation of a prisoner’s dilemma that illustrates the tensions between self-interest and cooperation. I would agree with the case study that I would gain more by going to a football game as opposed to the ballet. Cooperation suggests that the group would be better off by going to the ballet together. Both the man and woman could use some suggestions as to how change the payoff structure and escape the prisoner’s dilemma. Suggestions include: be nice and cooperate, respond immediately to rivals, be forgiving, do not be envious, and have clear action (Froeb, McCann, Shor, & Ward, 2014). The case option #1 suggests to take turns, which is a difficult option for a dating couple and option #2 suggests to essentially bribe the other party. The classic tit-for-tat strategy seems to only work in theory but not in practice when applied to dating, given the complexity of emotion and interpersonal relationships. If while bargaining on which event to attend breaks down, defection seems a plausible solution. Defection is a strategy in the Prisoner's Dilemma, implies that there is a history of ties from which a person is departing. It would make sense in a practical application to dating, if the couple cannot decision on cooperating or it may be best to mutually defect the game as a whole.

    Froeb, L. M., McCann, B. T., Shor, M., & Ward, M. R. (2014). Managerial Economics: A problem Solving Approach. United States of America: South-Western Cengage Learning.

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