Different Signal Qualities
In this section I will explore what happens if there is a lender with better
information technology than all the rest. Consider the following two cases.
Case /: 92(02-01) > 1. This inequality will be true when there is a high difference in
S"
risk among borrowers and the profit margin of the safe borrower is not very high. A high
probability the risky project succeeds also increases the probability of being in this case.
Let there be a lender such that its probability of being correct and the borrower is
indeed safe when an H is observed, is greater than that of other lenders, p, > p,. Call
S
this the "accurate" lender and the rest, "inaccurate" lenders. Note that, PH* > L-. By
1-pH PH
strategy OS, if all inaccurate lenders offer in the first period R1 = k + 01 then the offer of
the accurate lender, R*, will be k + 01.
The strategy OS still applies in periods two and higher, only now probabilities will
be updated according to a high accuracy of the first signal and lower accuracy for the
following ones.
In this case 1, it is possible that the signal of the accurate lender satisfies (2-2) but
the inaccurate signals do not, and ps is still greater than pr. If this were true, all
inaccurate lenders will offer k + 02 for all observations in the first period while the
accurate lender is separating according to its signal. Hence, all borrowers weakly prefer
to apply first to the best technology in the market, and those who obtain an L signal will
approach the worst lenders afterwards. This case is similar to the results in the literature
studying lending to informationally opaque firms where borrowers will tend to approach