Part I: Prisoner's Dilemma We discussed the Prisoner's dilemma in class. If you don't recall it, let's review it here: Bonnie and Clyde were an American criminal couple who traveled the Central United States with their gang during the Great Depression, known for their bank robberies, although they preferred to rob small stores or rural funeral homes. Assume they are arrested and charged with crimes. They're questioned separately, unable to communicate. The police deputy chief lays out their possible choices and the consequences of their actions as follow: - If they both proclaim mutual innocence cooperating), they will be found guilty anyway and get one year sentences for robbery - If one confesses (defecting) and the other doesn't cooperating), the confessor is rewarded with zero-year sentence and the other gets a severe 20 year sentence. - if both confess (defecting), then the judge sentences both to a moderate 10 years jail time in prison a. Construct the pay off matrix for this prisoner's dilemma case. b. Do they have a dominant strategy? Support your answer with a full explanation c. What should Bonnie do? What should Clyde do? d. What is the Nash Equilibrium? Explain why?