100 drivers are planning their morning commute. Each driver has two options, either to take the toll road or the back roads. Assume that the payoff of using toll road is 800 - m for each drive, where m is the number of drivers on the toll road. Note that payoff decreases as the number of users increase. Also, assume that the payoff of using back roads is 850 - 2n, where n is the number of drivers on the back roads. Drivers make simultaneous decisions as to whether to take the toll road or the back roads.

a. Find out whether it is a stable equilibrium where we have 30 drivers on toll road and 70 on back roads. Justify your answer.

b. Find a Nash equilibrium for this game.

c. Draw payoff functions of toll road and back roads users in the same graph.

4. 100 drivers are planning their morning commute. Each driver has two options, either to take the to}! mad or the ban- main Assume that the payoff of using toll road is 800 m for each drive, where m is the number of drivers on the toll road. Note that payoff decreases as the number of users increase. Also, assume that the payoff of using back roads is 850 2, where r: is the number of drivers on the back roads. Drivers make simultaneous decisions as to whether to take the toll road or the back roads. a. Find Out whether it is a stable equilibrium where we have 30 drivers on toll road and 7'0 on back roads. justify your answer. b. Find a Nash equilibrium for this game. c. Draw payoff functions of toll road and back roads users in the same graph