1. (33%) Considerthe following game Column Left Right Top 4:2 0:3 Row Bottom 1:1 2:0 (a) Are there any pure strategy equilibria (b) Assuming that Row chooses a mixed strategy with probability p of playing top , what are the column player's expected payo's to each of her pure strategies! (c) Let q denote the mixed strategy in which column plays left' with probability q. Show Column 's best response function in a tgure with p and q on the two axes. (d) Find the value of q that makes Row indiferent between 'top and bottom. (c) Find the mixed strategy equilibrium 2. (33%) Consider the following simultaneous-move game: Column Left Right Top 10: 10 21;0 Row Bottom 0;21 11: 11 Find all pure-strategy Nash equilibria What kind of game is it? Assume that the game is repeated every period for N periods. What are the Nash equilibria in this tnitely repeated game? Bricy explain your answer. Now let the time horizon be intnite. Can the outcome (bottom; right ) be sustainedas a Nash equilibriumif there is no discountingbetween periods' If so, explain how, if this is not possible then explain why not. Can the outcome (bottom; right ) be sustained as a Nash equilibrium if the discountrate between periods is r =0:25? If so, explain how; if this is not possible then explain why not. 3. (334) Considera group of 10 people If n of them participatein a common project each participant gets a net payo of p(n) = n while the non- participants get a payo/ of s(n) = 5 + n