Use Game theory.PLZ be detailed. Show all the processes if possible. Thanks a lot.

Alice and Bob play the following Bayesian game. Alice has only one type, Bob has two types: H, L. Both Alice and Bob assign probability 0.5 to each type before Bob learns his type. Before making a decision, Bob knows his type and Alice's type, but Alice does not know Bob's type. Each Alice has two actions: (Contribute, Not Contribute); and each type of Bob has two actions: (Contribute, Not Contribute). If Bob's type is H, then the payoffs of player i E { Alice, Bob} are as follows: 2 if both players contribute, 0 if he/she does not contribute, and 1 if he/she contributes and the other player does not contribute. If Bob's type is L, then the payoffs of player i E { Alice, Bob} are as follows: 1 if both players contribute, 0 if he/she does not contribute, and -4 if he she contributes and the other player does not contribute. (a) (3 marks) Model this problem as a Bayesian game. In your answer provide the payoff matrices. (b) (5 marks) Solve for all Bayesian-Nash equilibria of this game (in pure and mixed strategies)