As noted, the buyer must be given incentives to invest and the seller incentives not
to overcharge. These conditions are, respectively, equivalent to
87
Taking the limit as δ→ 1, (6.5.20) and (6.5.21) imply
By definition (6.5.22) holds—indeed is a strict inequality—if
ˆ
I=I
∗
. By continuity, it
follows that if the parties are sufficiently patient (δ is large enough), then an equilibrium
of the repeated game exists in which the buyer invests. Observe, critically, that such an
equilibrium requires that the seller not capture all the surplus—she must leave the buyer
with some.
88
6.5.4 Semi-Cooper ...
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