Consider the following law enforcement game. There is a law enforcement official, labeled L, and a criminal, labeled C. C has broken the law and L is making the arrest. In a simple game situation, C chooses whether to resist arrest, r, or to comply, c. At the same time, L chooses whether to use deadly force, d, or to use non-deadly force, n, to make the arrest. Assume that these choices must be made simultaneously. Regarding payoffs, if the arrest occurs with non-deadly force and compliance from C (the strategy profile < c, n >, then each receives a payoff of 10. Instead, if C complies but L chose to use deadly force (the strategy profile ), the presence of the gun opens up the possibility that is injured. This is bad for both C and L. Hence, let the payoff from this strategy profile be 10 - 0 for both players. If C chooses to resist arrest, it is possible that he escapes, which is better for him but worse for the officer. If C resists and L does not use deadly force (the strategy profile), then receives a payoff of 10 +e and L receives the payoff of 10 - c. Finally, deadly force is useful when the criminal resists arrest. Since he is resisting the potential for being shot is much greater. Thus, C receives 10 - 20 in the strategy profile , while L ensures arrest (but may have to shoot) generating a payoff of 10+ 0-0. Assume that the parameters a, 0, and e are all positive. 1. What must be true of the parameters a, 0, and to generate a mixed strategy Nash equilibrium of the game being the only equilibrium? 2. In this mixed strategy Nash equilibrium how does the potential harm from the gun, 0, affect the probability of resisting arrest? 2 a 3. Is there a pure strategy Nash equilibrium where the criminal complies and the law enforcement official does not use deadly force? If so, explain why (and when it is possible. If not, explain why not. 4. Suppose, in an attempt to reduce deaths, policymakers punish law enforcement officials who use deadly force one can think of it as an expected punishment where with some small probability the use of deadly force will be determined to not be justified when it is). Thus, and additional cost of - ) is incurred by L in any situation where deadly force is used (regardless of C's decision to resist). How would this punishment affect the rate at which criminals resisted arrest?