To me the most striking/exciting way to extend this model and what assumption to question is the zero sum assumption.
If the equilibrium is such that both ice cream sellers stay near the median, we might also imagine that the # of customers available to both sellers depends on how far they have to walk. I don't think it's unrealistic to imagine that the # of willing customers decreases as distance to the nearest seller increases. So in the case described by the article, some of the people on both ends of the beach might decide agaist buying ice cream at all, given they have to walk half way across the beach.
This is exciting to me because it might indicate that if both sellers were to cooperate (@ .33 and .66 distances along the dimension) both sellers could be better off in the aggregate because the potential number of customers they are splittig could be larger than at the nash equilibrium described in the article.
Expading the scope beyond even the sellers, we might also imagine that as a result the entire system is better off because the average customer saves time walking by having more evenly spaced ice cream sellers. That means even if we were to imagine the demand function was completely inelastic with respect to distance to nearest seller, at the very least the customers save time on average walking to the stands. This time could more productively be used to dream, plan, create the next startup, come up with the next big idea for society, etc.
The value of cooperation, expading the pie, and not assuming a zero sum game...as an optimist, these are the themes I take away from something like this.
If the equilibrium is such that both ice cream sellers stay near the median, we might also imagine that the # of customers available to both sellers depends on how far they have to walk. I don't think it's unrealistic to imagine that the # of willing customers decreases as distance to the nearest seller increases. So in the case described by the article, some of the people on both ends of the beach might decide agaist buying ice cream at all, given they have to walk half way across the beach.
This is exciting to me because it might indicate that if both sellers were to cooperate (@ .33 and .66 distances along the dimension) both sellers could be better off in the aggregate because the potential number of customers they are splittig could be larger than at the nash equilibrium described in the article.
Expading the scope beyond even the sellers, we might also imagine that as a result the entire system is better off because the average customer saves time walking by having more evenly spaced ice cream sellers. That means even if we were to imagine the demand function was completely inelastic with respect to distance to nearest seller, at the very least the customers save time on average walking to the stands. This time could more productively be used to dream, plan, create the next startup, come up with the next big idea for society, etc.
The value of cooperation, expading the pie, and not assuming a zero sum game...as an optimist, these are the themes I take away from something like this.