The Car Onwer and the Thief (10 points) Suppose the following conditions for a game between a thief and the owner of a vehicle. Both their benefits are measured for the car's valuation (higher is better) and the years of imprisonment (lower is better) The car has a value of $50. If the owner chooses to install an alarm, they must pay a cost of $5. If the thief decides to steal the vehicle, they will face a penalty of -10 years when the car has an alarm. Otherwise, he can enjoy the full value of the car for himself. If the thief decides not to commit any crime he will enjoy his freedom. 1. Define the strategies for the players players = {Owner, Thief} 2. Represent the normal-form of the game when it is played simultaneously. 3. Define the Best response for each player. Is there a Nash Equilibrium? 4. Write the extensive form of the game, one when the owner moves first and the other when the thief moves first. Explain the process of backward induction to reach the SPE.