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Topic: An interesting game theory problem
Replies: 8   Last Post: Jun 25, 2013 11:14 AM

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ksoileau

Posts: 83
From: Houston, TX
Registered: 3/9/08
An interesting game theory problem
Posted: Jun 24, 2013 10:16 AM
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Hello All,
Have any of you seen this problem or some problem isomorphic to it, addressed in the literature ? Any advice is appreciated.
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Suppose a young lady is eagerly anticipating the upcoming prom. Of course, she will need a date. For each of the $n$ young men whom she thinks might ask her, she has estimated the probability that he will ask, together with his desirability, with the most desirable boy having value equal to 1, and every boy having a value greater than 0. These data are represented by the variables $p_1,p_2,p_3,\dots,p_{n-1},p_n$ and $x_1,x_2,x_3,\dots,x_{n-1},x_n$, respectively. Since she has included only boys whom she thinks might ask her, all of the $p_i$ are positive. She knows neither which boys will actually ask her nor the order in which they will ask. She assumes that the boys who are willing to ask her will do so in no particular order, so every possible ordering of these boys' invitations is equally likely. Once she refuses a boy, he will not ask again. If she happens to refuse every boy that is willing to ask her, she will end up with no date for the prom, a payoff of 0. It's possible that no boy will ask her, yielding her a payoff of 0. Her objective is to find a strategy of acceptance or refusal that maximizes the expected desirability of the boy she accepts.
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Thanks,
Kerry Soileau



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