October 29, 2001  4 October 2005

Eric Rasmusen notes, erasmuse@indiana.edu 


http://rasmusen.org


Notes on Item 30: Farrell (1987)


 p. 156. The assumption that B>0 is crucial. It says that a firm does better
staying out of the market when the other firm *enters* the market than when both
stay out (and get payoffs of zero).
 
This is a special assumption; ordinarily, we would expect the payoff from
staying out to be 0 regardless of what the other firm does. The assumption here
would be justified if the firms are rivals in some other market and one's rival
entering market A means that he has higher costs of competing in market B.
 
 p. 157. Property 2 is the key: in the good cheap talk equilibrium, a firm
saying In when the other says Out indicates which firm will enter.
 
 Property 3  matters because the Dixit-Shapiro mixed strategy is a bad outcome
for both firms-- they dissipate all the rents from entry. So it is undesirable
to say IN if the other firm is also going to say IN.

 
 The second part of equation (4) is reached because u_1= pB. That is because in
the Dixit-Shapiro mixed strategy equilibrium, the payoff of  a firm is the same
as the payoff from the pure strategy of not entering, which is pB + (1-p) *0.
  Farrell alludes to "the fact that M> 2pB." This is not obvious. Here is how to
see it is true.  Since p = M / (B + L + M) in the mixed equilibrium strategy, M
= pB + pL +pM. It follows that M = pB + pL +pM > 2pB,  since L > 0 and M > B.

 (I thank Martin Caley of the Isle of Man Treasury for helpful comments on this)