Please anwser them precisely

(12. (a) Consider a game with two players (Din 8'. Grogu) and two actions, A and B. If both players choose action A, they each get a payoff of 10; if both players choose B, they each get a payoff of 20. If one of them chooses A while the other one chooses B, the one who chose B gets zero, while the one who chose A gets 10. Write down the payoff matrix for this game and find any pure strategy Nash equilibria. What kind of game is this? How do you know? (b) Consider a game with two players {Din 8i. Grogu} and two actions, A and B. If both (Cl players choose action A, they each get a payoff of 10; if both players choose B, they each get a payoff of 20. If one of them chooses A while the other one chooses B, the one who chose B gets 15, while the one who chose A gets 25. Write down the payoff matrix for this game and find any pure strategy Nash equilibria. What kind of game is this? How do you know? Consider a game with two players (Din 8; Grogu} and three actions, A and B and C. If both players choose action A, they each get a payoff of 10; If both players choose action B, they each get a payoff of 25; if both players choose C, then Din gets a payoff of 20 while Grogu gets a payoff of 30. If they choose different actions from one another, then they both get payoffs of zero. Write down the payoff matrix for this game and nd any pure strategy Nash equilibria. Of the games we considered in class, which does this game most closely resemble? Why