What is the logit models prediction of (s1, s2, s3) post-entry, according to IIA

[bubbles930]

*iia = independence of irrelevant alternatives.

Hi guys, this is actually just a question for fun outside of my homework.

Consider a market with three firms, with existing market shares (s1, s2, s3) = (1/4, 1/3, 5/12).
Suppose a new firm enters and captures a market share of s4 = 1/3.
What is the logit model's prediction of (s1, s2, s3) post-entry, according to the IIA property.?

I suppose my real query here is, when the fourth firm enters the market, what happens to the ratios (under IIA)?

Thanks to anyone who comments any ideas! I know this one might be a bit left-field for some of you

 

[afos]

The logit model would not be applicable to this situation because, presumably, it has been estimated on panel data characterizing the original 3 firms. Your question is a reason why empirical microeconomics exists. A lot of it is optimization and dynamic (near-)equilibria.