Via MR, a wonderful profile and interview with the economist Avinash Dixit. Avinash has made fundamental contributions to international trade, political economy and the theory of real options. Avinash has a Schelling-esque style and has a great sense of humor. It turns out that for many years he has kept hidden in his drawer an analysis of Elaine’s decision problem in an episode of Seinfeld:
Elaine Benes uses a contraceptive sponge that gets taken off the market. She scours pharmacies in the neighborhood to stock a large supply, but it is ﬁnite. So she must “re-evaluate her whole screening process.” Every time she dates a new man, which happens very frequently, she has to consider a new issue: Is he “spongeworthy”?
Avinash studies Elaine’s problem formally. And his model displays all the great qualities one might expect. First, simplifying assumptions: To get intuition for the key issue – how does the finite supply of sponges affect Elaine’s decision problem – it is good to make the rest of the model stationary. Hence:
Suppose Elaine believes herself to be inﬁnitely lived; this is a good approximation in relation to the number of sponges she has and her time-discount factor or impatience. She meets a new man every day.
Let Q be the “quality” of a man Elaine meets where Q is drawn from the uniform distribution on [0,1]. Let Vm be Elaine’s expected utility when she has m sponges left. Her per-day discount factor is b – Elaine lives in NYC and meets a lot of men! At her optimum, a man is spongeworthy iff
Given the assumptions made, Avinash can actually explicitly work out the details of the solution to this problem by cranking out Vm. But here are some qualitative insights.
1. Elaine should have a threshold strategy: There is a threshold Qm where a man is spongeworthy iff his Q is greater than this threshold when Elaine has m sponges left.
2. Qm is decreasing: The more sponges Elaine has left, the lower her standards.
3. Vm is decreasing: As Elaine runs our of sponges, her expected utility declines as there are fewer “interactions” remaining.
There are other insights and extensions. For those, I recommend Avinash’s lovely paper.