Problem 3.(4.5 points total) Follow closely the instructions and answer all the following questions: A) (1 Points) create your own two player simultaneous prisoners' dilemma game and show both the extended and the normal form (i.e. matrix) of the game. In the case of the extended form name each nod and indicate which nods are the root, terminal and non-terminal. How many information sets does each player have and how many nods does each info set contain? B) (1 Points) create your own two player sequential prisoners' dilemma game (P1 plays first) and show both the extended and the normal form (i.e. matrix) of the game. In the case of the extended form name each nod and indicate which nods are the root, terminal and non-terminal. How many information sets does each player have and how many nods does each info set contain? C) (1 Points) create your own two player sequential Battle of the Sexes game (P1 plays first) and show both the extended and the normal form (i.e. matrix) of the game. Define clearly the strategy sets of each player. In the case of the normal form indicate all the "normal" NE. D) (1.5 Points) Consider the following extended form game. Define clearly the strategy sets of each player. Provide the Normal form representation of this game and find all "normal" Nash Equilibria. 1 c 2 c 10 20 (3,3) N n N n 1 1 0 3 2 2 4 Problem 3.(4.5 points total) Follow closely the instructions and answer all the following questions: A) (1 Points) create your own two player simultaneous prisoners' dilemma game and show both the extended and the normal form (i.e. matrix) of the game. In the case of the extended form name each nod and indicate which nods are the root, terminal and non-terminal. How many information sets does each player have and how many nods does each info set contain? B) (1 Points) create your own two player sequential prisoners' dilemma game (P1 plays first) and show both the extended and the normal form (i.e. matrix) of the game. In the case of the extended form name each nod and indicate which nods are the root, terminal and non-terminal. How many information sets does each player have and how many nods does each info set contain? C) (1 Points) create your own two player sequential Battle of the Sexes game (P1 plays first) and show both the extended and the normal form (i.e. matrix) of the game. Define clearly the strategy sets of each player. In the case of the normal form indicate all the "normal" NE. D) (1.5 Points) Consider the following extended form game. Define clearly the strategy sets of each player. Provide the Normal form representation of this game and find all "normal" Nash Equilibria. 1 c 2 c 10 20 (3,3) N n N n 1 1 0 3 2 2 4