Answer Happy

please solve it with explanation thx
an upvote is promised
Question 4: (30 marks] Consider the following card game with two players P and P. To start the game, both players ante 2 dollars into the pot. From a three-card deck consisting of a king, queen and jack, each player is dealt one card. Plooks at the dealt card, and then has the choice to either raise or pass. If he passes, the player with the higher card wins the pot (under the order king>queen>jack). If Praises, he adds 4 dollars into the pot, and then P2, after looking at her card, can either call or fold. If she folds, wins the pot. If P, calls, she adds 4 dollars to the pot, and then the player with the higher card wins the pot. (a) Show that there are six possible deals. (b) Determine that each of Pand has exactly 8 pure strategies. 8 2

(c) Show that has nothing to gain by passing when he has a king, and P, has nothing to gain by folding when she has a king. (d) Show that has nothing to gain by calling when she has a jack, and that then, after these considerations, P, has nothing to gain by raising when he has a queen. (e) The viable pure strategies for each player are then reduced to two: Praises on a king, passes on a queen, and either raises or passes or a jack; P, in response to a raise by P. calls on a king, folds on a jack, and either calls or folds on a queen. Suppose the cards are dealt properly, i.e., uniformly at random, compute the associated 2 x 2 payoff matrix (f) Solve the game.