2. In the original Prisoners' Dilemma, two prisoners were incarcerated in a prison after having committed an unspecified crime. Both have the choices of either to confess (c) or not confess (c) and take their actions simultaneously. The payoff matrix is given by C C c (0, 0) (7, -2) C (-2, 7) (5, 5) However, a variant of this game exists, whereby the payoff matrix is now C C c (-2, -10) (0, 2) E (2, 0) (10, 3) Assume that in the prison, the original game is played 80% of the time and the variant only 20% of the time. This is common knowledge to both prisoners. However, the prisoner, whose actions are represented in the columns of the above payoff matrices, i.e., Prisoner 2, is the only one aware which game is being played. a) Explain why this is game of incomplete information. Who are the players and what are their strategies? b) Portray the extensive form of the game, including payoffs at the terminal nodes. c) Display the normal form of the game. Check the normal form for the existence of any pure strategy Bayes - Nash equilibrium point