Case Scenario:
Suppose there is a circle with numbered locations from 0-60 (with 0/60 at the top; like a clock in minutes). Customers are evenly distributed at locations around the circle. Three firms will locate at locations in order, so that firm F knows where previous firms located (i.e. 1 goes first, then 2 knowing what 1 did, then 3 knowing what 1 and 2 did). All the customers which are closest on the circle to a particular firm shop there (e.g. if it a customer is at 18 and firms are at 12 and 20, the customer shops at firm location 20). The firms desire to maximize the * expected * percentage of customers who shop at their store. If firms locate between two other firms, they choose a spot that maximizes their market share of customers, and equalizes the market share to the other two firms.
Without loss of generality, suppose firm 1 locates at 0 (=60).
(1) Where should firm 2 locate?
(2) Where should firm 3 locate?
(3) Is there an advantage or disadvantage—in theory—to going first or last?