Reference no: EM132446058

Consider a game between a police officer (player 3) and two drivers (players 1 and 2). Player 1 lives and drives in the Clairemont neighborhood of San Diego, whereas Player 2 lives and drives in the downtown area. On a given day, players 1 and 2 each have to decide whether (U) or not (N) to use their cell phones while driving. They are not friends, so they will not be calling each other. Thus, whether player 1 uses a cell phone is independent of whether player 2 uses a cell phone. Player 3 (the police officer) selects whether to patrol in Clairemont (C) or Downtown (D). All of these choices are made simultaneously and independently. Note that the strategy spaces are S₁ = {U, N}, S₂ = {U, N}, and S₃ = {C, D}. 

Suppose that using a cell phone whole driving is illegal. Furthermore, if a driver uses a cell phone and player 3 patrols in his or her area (Clairemont for Player 1 and Downtown for Player 2), then this driver is caught and punished. A driver will not be caught if player 3 patrols the other neighborhood. A driver who does not use a cell phone gets a payoff of zero. A driver who uses a cellphone and is not caught obtains a payoff of 2. Finally, a driver who uses a cell phone and is caught gets a payoff of -y, where y>0. Player 3 gets a payoff of 1 if she catches a driver using a cell phone, and she gets zero otherwise.

Does this game have a pure-strategy Nash equilibrium? If so, describe it. If not, explain why.

Suppose that y = 1. Calculate and describe a mixed-strategy equilibrium of the police officer and argue whether he can make both player 1 and player 2 obey the law. 

Suppose that y = 3. Calculate and describe a mixed-strategy equilibrium of the police officer and argue whether he can make both player 1 and player 2 obey the law.