Suppose two merchants have to choose a location along the straight road.

Suppose two merchants have to choose a location along the straight road.

They may choose any point in {1, 2,…, n}. Assume there is exactly one customer at each of these points and a customer will always go to the nearest merchant. If the two merchants are equidistant to a customer then they share that customer, that is, 1 2 the customer goes to each store. For example, if n = 11 and if player I chooses location 3 and player II chooses location 8, then the payoff to I is 5 and the payoff to II is 6. (a) Suppose n = 5. Find the bimatrix and find the Nash equilibrium. (b) What do you think is the Nash equilibrium in general if n = 2k + 1, that is, n is an odd integer
Suppose two merchants have to choose a location along the straight road.