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Baye Morgan Scholten (2006) - Information Search and Price Dispersion (view source)
Revision as of 17:39, 25 April 2010
, 17:39, 25 April 2010→Information Clearinghouses
<center><math>\mathbb{E}\pi(p) = (p-m) \left ( L + \left ( \sum_{i=0}^{n-1} \binom{n-1}{i} \alpha^i (1-\alpha)^{n-1-i}(1-F(p))^i \right ) S \right ) - \phi\,</math></center>
To solve this note that the expected profits must be the same across the entire support (for it to be a mixed strategy) and are equal to the profit from the outside option. The inside option (above) is made up of the following components:
*(p-m) is difference between the price and consumer's willingness to pay
*This is gained for sure for the L loyal consumers
*This is gained for the S shoppers on the basis of:
*\sum_{i=0}^{n-1} is the sum over the number of people on the site
*\binom{n-1}{i} is the n-1 choose i ways that this could occur
*\alpha^i is the probability that i firms list
*(1-\alpha)^{n-1-i} is the probability that the other firms (n-1-i) didn't list
*(1-F(p))^i is the probability that everyone who did list prices above p
Using the [http://en.wikipedia.org/wiki/Binomial_theorem binomial theorem]:
