Along a stretch of beach there are 300 children, in 3 groups of 100 each, at locations A, B, and C, as follows: Paddle and Pop, two ice-cream vendors, will each make a decision on where to locate: at A, B or C. If there is only one vendor at one location, then all the 100 children who are there will buy from him. If both ice-cream vendors are at the same location, then each vendor sells to 50 out of the total 100 children who are there. If there is no vendor at one location, then all 100 children there walk to an adjacent location. If the adjacent location has only one vendor, then all 100 children who walked there buy from him. If the adjacent location has two vendors, then each vendor sells to 50 out of the total 100 children who walked there. If there are two equidistant adjacent locations, with one vendor each, then 50 children walk to one of these locations and buy from the vendor there, and 50 children walk to the other location and buy from the vendor who is there. If there is no vendor at one location, children can walk to an adjacent location, but cannot walk further away. For example, if both vendors are located at C, then children from B could walk to C, but children from A cannot walk all the way to C, as C is too A B C 100 children 100 children 100 children 2 far away from them. Ice-cream melts quickly, so you should assume that children who walk to another location cannot buy for children who do not walk. Suppose Paddle and Pop make choices simultaneously on where to locate:

a) Construct the payoff matrix for this game. Please explain how you arrived at the answer.