Two bus companies, Comfy Bus and Cheapo, run the same route in a UK town. Each has enough busses to run a service once an hour. Passengers prefer to ride on Comfy Bus because, well it's more comfortable. But will take whatever bus is at the bus stop when they get there rather than waiting. Passengers arrive at the bus stop at a constant rate, perhaps one a minute. Both companies can schedule their service at the top of the hour or on the half hour. Both companies wish to maximize the number of their riders.

(a) a payoff matrix to describe this game.

(b) What are the equilibria to this game?

(c) If there is a mixed strategy equilibrium compute the bus companies optimal strategies.