Although it might seem like a strong assumption the modeled ability of lenders to
observe the interest rate policy offered by their competitors and to adjust their own
interest rates in response, recall that most banks advertise some of their interest rates
policies at their offices or through media advertising and the internet, and that the
increasing scrutiny in bank lending practices makes some of their actions publicly
available.
After a pricing policy function is defined, when the borrowers apply for loans to all
banks, each lender observes a signal, then interest rate offers are made simultaneously
and independently based on the signal observed such that profits are greater than or
equal to zero9. Each borrower will accept the lowest interest rate from among those
offered by the lenders.
Thus, the model has the following timing:
Stage 1 is a game in pricing policies. Each lender finds an equilibrium function as
defined above that determines interest rates offers according to the borrower's signal.
In stage 2 borrowers apply for loans to all banks and lenders make their offers
simultaneously. The offer will be dictated by the pricing function specified in stage 1.
Borrowers accept the lowest interest rate from among the rates offered by the
lenders. If the two lenders offer the same interest rate, the borrower randomly selects a
lender.
Note that the policies, but not the outcome of the signal, can always be observed
by all lenders. Notice too that profits will not be earned until a price structure has been
91t could also be considered the case of profits greater than or equal to rl, where ris the interest on some
safe investment or the cost of lenders to get the capital, but the conclusions would be the same. For
simplicity I will assume r=0. As will be addressed latter, if profits could not be made positive, no offer will
be made. This occurs if it is almost certain that the borrower if of type /.