3. This is a long question, which should give you enough practice in computing mixedstrategy equilibria. Suppose Ben and Jerry play the following game, in which Ben is the row player and Jerry is the column player. l m r U 1,1 1,0 4,1 M 2,3 2,2 2,5 D 5,3 1,1 2,2 a. Are there dominant or strictly dominated strategies in this game? b. Are there any completely mixedstrategy equilibria in the game (that is, equilibria in which each player chooses each of his pure strategies with positive probability)? If yes, find them. c. Are there any mixedpure strategy equilibria in the game (i.e., equilibria in which one player plays a pure strategy and the other mixes)? If yes, find them. Guidance: for each pure strategy of one player, check what the best response is of the other player. Only if the other player has more than one best response could he be mixing, so you only have to check pure strategies such that the other player has more than one best response. In these cases, you have to find probabilities of mixing for the other player such that the first player would like to play the pure strategy and not deviate. d. Are there any mixedstrategy equilibria in which each player mixes between two strategies? If yes, find them. Guidance: consider all the combinations of mixing for each player (there are ((3/2)(3/3))=9 such combinations). For each combination and each player compute the probabilities of mixing that make the other player indifferent between the pure strategies he is mixing over. Then check if any of the players want to deviate to the strategy they are not mixing over.