Consider a two-player game where player A chooses Up or Down and player B chooses Left, Center, or Right. Their payoffs are as follows: When player A chooses Up and player B chooses Lg? player A gets $5 while player B gets $5. When player A chooses Up and player B chooses Center they get $6 and $1 correspondingly, while when player A chooses Up and player B chooses Right player A loses $2 while player B gets $4. Moreover, when player A chooses Down and player B chooses Le they get $6 and $1, while when player A chooses Down and player B chooses \"Center they both get $1. Finally, when player A chooses Down and player B chooses Right player A loses $1 and player B gets $2. Assume that the players decide simultaneously (or, in general, when one makes his decision doesn't know what the other player has chosen)- a) Solve for the pure strategy Nash Equilibrium using nom'ial form. b) Suppose player A chooses up with probability p and down with probability (I-p) and player B chooses left with probability q and right with probability (Iq). Determine player A's best response to any choice of q by player B, and player B's best response to any choice of p by player A. What happened to Center? c) Find the mixed strategy Nash equilibrium. Show these best Response functions and all the possible equilibria on a graph. d) Now suppose that player B moves rst, and Player A moves second. Show the game information in extensive form. What is the Nash equilibrium in this case