1 / 1 | - 100% + 0 Econ 690, Economics of Crime Problem Set 3 (Due 10/19, in lecture) 1. Suppose police and citizens play the following game, where a, b, c, x, y, z > 0 and x > z. Police can choose to stop or not stop a citizen, and a citizen can choose to carry or not carry contraband. Carry Do Not Carry Stop a, -x Do Not Stop c, -c, y || b, z 0,0 (a) Show that there is no pure strategy equilibrium of this game. (b) Let a be the probability that the police plays stop, and be the probability that the citizen plays carry. Solve for the mixed strategy Nash Equilibrium values of a and (a will be a function of x, y, and z, and will be a function of a, b, and c). (c) Show that is decreasing in a and c, but increasing in b. Briefly give an interpretation for what that means. (d) In the document "Racial Profiling: Understanding the Practice of Stop-and-Frisk in NYC in the Readings module on Canvas, find the data for stop and frisk arrest rates by race for the year 2019. Calculate the arrest rate (arrests per stop) for white and black individuals. Briefly discuss whether you think the data looks consistent with the equilibrium of the game above. 2. Suppose you are writing a grant proposal to run a policing experiment in Madison, WI. You would like to test whether installing visible "shot detector" technology will reduce gun violence within the neighborhoods it is placed. Your first draft suggests putting the technology in the first 10 blocks both east and west of the capital, and using the neighborhoods that are 11-20 blocks east/west from the capital as a control. Explain one reason this research design may lead to a biased result, and suggest one way to improve it. WW X