It’s spring break and you’re traveling south on US-54, heading toward Lake of the Ozarks. 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 Eldon (a small town nearby) to grab some of those delicious Krispy Kreme doughnuts?
Consider the following simultaneous-move game between a driver (she) and a police officer (he):.
police officer driver speed trap Krispy Kreme 80 mph 10, 100 70, ∗ 65 mph ∗, ∗ ∗, ∗
1. The best outcome for the driver is that she speeds up and isn’t caught; the payoff for that case is 70.
2. The worst outcome is that she speeds and is nailed by the police officer, for which the payoff is 10.
3. If she chooses to drive the legal limit, then her payoff is 40 and is the same regardless of what the police officer does.
4. As for the police officer, his best outcome is setting a speed trap and nailing a speeder, giving him a payoff of 100.
5. 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.
6. His payoff is 50 when he chooses to go to Krispy Kreme.