Suspect A (A), suspect B. (B), and a police officer (P) interact in the following way....

 

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Suspect A (A), suspect B. (B), and a police officer (P) interact in the following way. A has just robbed a store and is fleeing. He has a choice of two routes to take to try to escape: X and Y. Route Y goes by a club that plays louds music that A does not like so it entails a cost of 20 to him. The music is not payoff relevant for the other two players. P would like to catch A. B would also like to catch A to settle a score from their previous criminal dealings. Being caught by either P or B yields an immediate payoff of -100 to A. If A is not caught (by either P or B), his payoff is 0. The three players simultaneously and independently choose between routes X and Y. Assume that if either A or B (or both) chooses the same route as P. P catches that suspect (or both). If A and B select the same route and P selects a different route. B catches A. If P catches A, P's payoff is 150. P cares only about catching A. So if P catches both A and B, P's payoff is also 150. If P catches only B, P's payoff is 0. If P catches no one, P's payoff is 0. If B catches A, B's payoff is 110. If B is caught by P (regardless of whether A is also caught by P), B's payoff is -110. If B does not catch A and B is not caught by P, B's payoff is 0. Describe a Nash equilibrium of this game. Please show any calculations used. Suspect A (A), suspect B. (B), and a police officer (P) interact in the following way. A has just robbed a store and is fleeing. He has a choice of two routes to take to try to escape: X and Y. Route Y goes by a club that plays louds music that A does not like so it entails a cost of 20 to him. The music is not payoff relevant for the other two players. P would like to catch A. B would also like to catch A to settle a score from their previous criminal dealings. Being caught by either P or B yields an immediate payoff of -100 to A. If A is not caught (by either P or B), his payoff is 0. The three players simultaneously and independently choose between routes X and Y. Assume that if either A or B (or both) chooses the same route as P. P catches that suspect (or both). If A and B select the same route and P selects a different route. B catches A. If P catches A, P's payoff is 150. P cares only about catching A. So if P catches both A and B, P's payoff is also 150. If P catches only B, P's payoff is 0. If P catches no one, P's payoff is 0. If B catches A, B's payoff is 110. If B is caught by P (regardless of whether A is also caught by P), B's payoff is -110. If B does not catch A and B is not caught by P, B's payoff is 0. Describe a Nash equilibrium of this game. Please show any calculations used.

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To find the Nash equilibrium in this game we need to analyze the strategies of each player and determine their best responses given the strategies of ... View the full answer