Question: It's spring break and you're traveling south on Interstate 95, heading toward Fort Lauderdale. Do you travel the legal limit of 65 miles per hour, or do you crank it up to 80 and hope that there's no speed trap? And what about the state police? Do they set a speed trap or instead head into town and find out whether the "Hot and Fresh" neon sign is lit up at the Krispy Kreme? The police like to nab speeders, but they don't want to set a speed trap if there won't be any speeders to nab. Hence, in this game the driver can either go the legal limit of 65 mph or speed at 80 mph. The police officer can set a speed trap or head into town and grab some of those delicious high-carb doughnuts. The best outcome for the driver is that she speeds and isn't caught:the payoff for that case is 70. The worst outcome is that she speeds and is nailed by the police, for which the payoff is 10. If she chooses to drive the legal limit, then her payoff is 50 and is the same regardless of what the state police do. (In other words, the driver doesn't care about the caloric intake of the trooper.) As for the police officer, his best outcome is setting a speed trap and nailing a speeder, giving him a payoff of 100. His worst outcome is sitting out there in a speed trap and failing to write a ticket:this outcome delivers a payoff of only 20. His payoff is 40 when he chooses to go to the Krispy Kreme.

(a) Write this game in strategic form.

(b) Find all Nash equilibrium using only pure strategies.

(c) Find the Nash equilibrium in mixed strategies.