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→Question B.2: Opportunistic sellers
===Question B.2: Opportunistic sellers===
Consider an economy with many identical Buyers that can each engage in a transaction with one of many sellers. For concreteness, imagine that there are more buyers than sellers and that the market for transactions must clear. The transaction can either succeed or fail. Each buyer’s value of "success" is 1 and of "failure" is 0.
There are two kinds of Sellers. A proportion <math>1 - \beta\,</math> are "good" and they succeed with probability <math>p > 0\,</math>. A proportion <math>\beta\,</math> are "opportunistic" and can choose some effort, <math>e \in [0,1]\,</math> at a personal cost of <math>c(e)\,</math> where <math>c'(0) = 0, c'(1) = \infinityinfty\,</math> and <math>c''(e) > 0 \;\forall e = 0\,</math>. The opportunistic types succeed with probability <math>ep\,</math>.
The economy operates for 2 periods. Sellers live for two periods but a new cohort of buyers is active in each period, and second period buyers can observe the first period outcome of transactions.
