Strong Invigilation (,140) Cheat Lenient Invigilation (, -20 (,140) ,140) (,0) Not Cheat(No Prep) Not Cheat(Good Prep) (,0) If the student decides to cheat and faces strong invigilation, then his payoff is 140 while lenient invigilation will give him a payoff of 140. But if he does not cheat and has good prep), then he gets a payoff of 140 regardless of the type of invigilation. Lastly, if he does not cheat and his preparation is not good either, then strong invigilation gives him a payoff of 70 while weak invigilation also gives him a payoff of 70. 1. Complete the utility matrixormal form by filling in the utilities of the student. [4] 2. Write down the player set N, action profile A, and utility profile u of this game. [6] 3. Find the best response of the student given that (a) The proctor decides to go with strong invigilation [2] (b) The proctor decides to go lenient invigilation [2] 4. Find the best response of the proctor given that (a) The student decides to cheat [2] (b) The student decides not to cheat [2] 5. Find the Nash Equilibrium of this game. Given the student is rational, what should be his action? [1 + 1] Strong Invigilation (,140) Cheat Lenient Invigilation (, -20 (,140) ,140) (,0) Not Cheat(No Prep) Not Cheat(Good Prep) (,0) If the student decides to cheat and faces strong invigilation, then his payoff is 140 while lenient invigilation will give him a payoff of 140. But if he does not cheat and has good prep), then he gets a payoff of 140 regardless of the type of invigilation. Lastly, if he does not cheat and his preparation is not good either, then strong invigilation gives him a payoff of 70 while weak invigilation also gives him a payoff of 70. 1. Complete the utility matrixormal form by filling in the utilities of the student. [4] 2. Write down the player set N, action profile A, and utility profile u of this game. [6] 3. Find the best response of the student given that (a) The proctor decides to go with strong invigilation [2] (b) The proctor decides to go lenient invigilation [2] 4. Find the best response of the proctor given that (a) The student decides to cheat [2] (b) The student decides not to cheat [2] 5. Find the Nash Equilibrium of this game. Given the student is rational, what should be his action? [1 + 1]