step by step explanations, diagrams , thank you!

Question 12 (a) Consider a game with two players and two actions, A and B. If both players choose action A, they each get a payoff of 2; if both players choose B, they each get a payoff of 6. If one of them chooses A while the other one chooses B, the one that chose A gets 10 while the one who chose B gets nothing. Write down the payoff matrix for this game and find the Nash equilibrium. What kind of game is this? How do you know? (b) How (if at all) would the equilibrium you found in the one-stage game be different in an evolutionary context where the players' are matched with successive strangers whose types (Type A or Type B) were freely and reliably observable? Support your answer with a graph. (c) How (if at all) would the equilibrium you found in the one-stage game be different in an evolutionary context where the players' types were not at all observable? Support your answer with a graph. (d) How (if at all) would the equilibrium you found in the one-stage game be different in an evolutionary context where the players' types were observable, but only after the would-be observer paid a real cost? (Suppose the cost is equal to 2 units.) Support your answer with a graph