Part A: Consider a simple game theoretic version of "cops and robbers". In this game, there will be a cop (Player 1), and a robber (Player 2). The cop will choose a level of effort (e1) in order to catch the robber, and the robber will choose a level of effort (e2) used to commit crimes. The best responses will work as follows: The higher the level of effort e2 of the robber, the more effort e1 the cop will want to exert to catch him/her. Alternatively, the higher the level of effort e1 exerted by the cop, the less effort the robber will be willing to commit to crime. One example of best responses which we'll use to capture this intuition will be the following: e1 = 25 + e2 e2 = 75 - e1. What would the graph of these best responses look like?

\fe2 75 ez = 75 - e1 25 91 = 25 + e2 75 e1