Cops and Robbers: Player 1 is a police officer who must decide whether to patrol the streets or to hang out at the coffee shop. His payoff from hanging out at the coffee shop is 10, while his payoff from patrolling the streets depends on whether he catches a robber, who is player 2. If the robber prowls the streets then the police officer will catch him and obtain a payoff of 20. If the robber stays in his hideaway then the officer's payoff is 0. The robber must choose between staying hidden or prowling the streets. If he stays hidden then his payoff is 0, while if he prowls the streets his payoff is –10 if the officer is patrolling the streets and 10 if the officer is at the coffee shop. a. Write down the matrix form of this game. b. Draw the best-response function of each player. c. Find the Nash equilibrium of this game. What kind of game does this game remind you of?

Question
Cops and Robbers: Player 1 is a police officer who must decide whether to
patrol the streets or to hang out at the coffee shop. His payoff from hanging out
at the coffee shop is 10, while his payoff from patrolling the streets depends on
whether he catches a robber, who is player 2. If the robber prowls the streets
then the police officer will catch him and obtain a payoff of 20. If the robber
stays in his hideaway then the officer's payoff is 0. The robber must choose
between staying hidden or prowling the streets. If he stays hidden then his
payoff is 0, while if he prowls the streets his payoff is –10 if the officer is
patrolling the streets and 10 if the officer is at the coffee shop.
a. Write down the matrix form of this game.
b. Draw the best-response function of each player.
c. Find the Nash equilibrium of this game. What kind of game does this
game remind you of?
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Transcribed Image Text

Cops and Robbers: Player 1 is a police officer who must decide whether to patrol the streets or to hang out at the coffee shop. His payoff from hanging out at the coffee shop is 10, while his payoff from patrolling the streets depends on whether he catches a robber, who is player 2. If the robber prowls the streets then the police officer will catch him and obtain a payoff of 20. If the robber stays in his hideaway then the officer's payoff is 0. The robber must choose between staying hidden or prowling the streets. If he stays hidden then his payoff is 0, while if he prowls the streets his payoff is –10 if the officer is patrolling the streets and 10 if the officer is at the coffee shop. a. Write down the matrix form of this game. b. Draw the best-response function of each player. c. Find the Nash equilibrium of this game. What kind of game does this game remind you of?