A city police department and a gang of drug dealers play a game every day where the police must decide whether to focus their department resources on either street patrol or parks patrol, and the drug gang must make the same decision regarding where to focus their drug selling activities. If both focus on street sales the police make 90 arrests and the dealers avoid 10 arrests. If both focus on park selling. The police arrest 80 dealers and 20 dealers avoid capture. If the PD focuses on streets, while the DDs focus on parks, 5 arrests are made and 95 dealers escape arrest. If the PD focuses on parks while the DD focus on streets, then 10 arrests are made and 90 dealers get away. a) Find the Nash equilibrium in mixed strategies for the police department and for the drug dealers. b) Explain in simple terms what will play out in this game between the PD and the DDs. c) If the PD gets better at park patrol (measured by more arrests in parks than before), in which direction will the mixing strategies change? Explain. (It is not necessary to re-calculate answers, just use economic logic)
A city police department and a gang of drug dealers play a game every day where the police must decide whether to focus their department resources on either street patrol or parks patrol, and the drug gang must make the same decision regarding where to focus their drug selling activities. If both focus on street sales the police make 90 arrests and the dealers avoid 10 arrests. If both focus on park selling. The police arrest 80 dealers and 20 dealers avoid capture. If the PD focuses on streets, while the DDs focus on parks, 5 arrests are made and 95 dealers escape arrest. If the PD focuses on parks while the DD focus on streets, then 10 arrests are made and 90 dealers get away. a) Find the Nash equilibrium in mixed strategies for the police department and for the drug dealers. b) Explain in simple terms what will play out in this game between the PD and the DDs. c) If the PD gets better at park patrol (measured by more arrests in parks than before), in which direction will the mixing strategies change? Explain. (It is not necessary to re-calculate answers, just use economic logic)
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter14: Game Theory
Section14.3: Linear Programming And Zero-sum Games
Problem 4P
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A city police department and a gang of drug dealers play a game every day where the police must decide whether to focus their department resources on either street patrol or parks patrol, and the drug gang must make the same decision regarding where to focus their drug selling activities. If both focus on street sales the police make 90 arrests and the dealers avoid 10 arrests. If both focus on park selling. The police arrest 80 dealers and 20 dealers avoid capture. If the PD focuses on streets, while the DDs focus on parks, 5 arrests are made and 95 dealers escape arrest. If the PD focuses on parks while the DD focus on streets, then 10 arrests are made and 90 dealers get away.
a) Find the Nash equilibrium in mixed strategies for the police department and for the drug dealers.
b) Explain in simple terms what will play out in this game between the PD and the DDs.
c) If the PD gets better at park patrol (measured by more arrests in parks than before), in which direction will the mixing strategies change? Explain. (It is not necessary to re-calculate answers, just use economic logic)
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