Thursday, November 19, 2015

REPOST: Dating Game

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.

1 comment:

  1. A practical view of the “dating game” predicament.

    Helen is my significant other. (She grew up in Illinois, she hates going to diners for breakfast, lunch, dinner, or after a concert for coffee & snack.) (I grew up in New Jersey, going to “the diner” was an accepted way of life. Anytime, any meal, or a place to meet, hang out, or discuss important & expensive business. I enjoy going to “the diner”.) She much prefers the foodie aspect of fine dining, a wine list bound in leather, and the chef’s signature dish (even better if the chef comes out from the kitchen to describe it in detail). (I take simple enjoyment in looking through a dozen pages of pictures, local creations, a dozen hamburger variations, and the joy of breakfast 24 hours a day. Unlimited coffee refills. And change from a “twenty.”)

    At first glance, one would expect the solution to be nearly identical to that presented in texts, and course materials - simple bargaining concepts, and diagram game theory (as in ballet and football game). Flip a coin, rock/scissors/paper, alternate this time//next time, or consult a psychologist! Or any common variation of how a couple finds a solution to a vexing problem. If only (1, 4) and (4, 1) were truly a viable solution.

    Instead, this more of the prisoner’s dilemma. (No matter what I may offer as for her “opponent’s gain” – my actual bargaining power dilutes with each passing utterance of “No!”) Indeed, if I ever actually drove the car into the parking lot of “the diner”, the judge would declare me criminal and only 8 months in jail would be a bargain.

    Sometimes, one needs to creatively think out of the box. I take her to the restaurant. I go with friends (and my sister) to the diner. Perhaps Nash would proud, a reasonable outcome for all. Score (1, 4) for the couple (I’m getting the 1, in case there was any doubt for going fancy.) And! (5, 0) if I meet a friend at “the diner.”
    Lee Lichtenstein

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