How to capture competitive spatial interactions between multiple stores and customers I am estimating sales with data on customer and store locations and attributes using a Huff-style model, where sales decay with drive time and increase with attractiveness of the store.
One hypothetical instance of the problem is illustrated below. The 3 pushpins represent stores and the white flag represents the site where the customers live.** The size of the pins represents the attractiveness of the store (like floor space). The problem I am having is that I would expect red store's sales at the site to be lower than the the green store's even though they are just as far away and have identical attractiveness, because the purple store is somewhat in between the the red store and the site. I would like to translate this intuition into rigorous (but tractable) math so that I add it into my statistical model. I am also having trouble figuring out what this is called in the literature (other than the n-body gravity problem in physics).  

** For the daltonic folks, the red store is in the upper left corner. The green store is in the bottom right. Purple store is to the left of the site.
 A: One of the assumptions of the Huff model (which we call multinomial logit in economics) is Independence of Irrelevant Alternatives.  IIA says that the ratio of red store to green store sales is independent of the existence and characteristics of all other alternatives --- it only depends on red and green store characteristics.  Your intuition is that this assumption should be violated in this application.
What you want is one of the alternatives to multinomial logit which relaxes the IIA assumption.  There are a number of these, including multinomial probit, nested logit, and logit models using the generalized extreme value distribution, sometimes called generalized logit.  There are large literatures in this in both Industrial Organization and in Marketing.
Though these models are all defined at the individual level, they can be estimated with data at the market level (like total sales at each store in your example).  There is a nice free online book by Kenneth Train.  Actually, there are two.
A: You are right, the original model seems to calculate individual attractiveness and probabilities but does not take into account the interactions.
Let's say you calculate P(i,j) Using the definition of huff-model from -
http://www.directionsmag.com/articles/retail-trade-area-analysis-using-the-huff-model/123411
then to translate your intuition -
P'(i,j) = P(i,j) * [k / [sum(A(i,j')]]
where k is some constant. sum(A(i,j')) is the attractiveness (numerator of earlier formula) of all stores except this one. This will introduce dampening and penalize a store for being close to other desirable stores.
