Consider the following game of incomplete information between Row and Column. Row's set of possible actions is SR = {U, D}, and Column's set of possible actions is SC = {L, R}. Row's preferences over pure strategy combinations are well known and are given in the following matrix: U D L R Row's Payoffs: 1 0 0 2 Column's preferences are not perfectly known. Column is either a type a or a type b, and the associated payoffs for Column are as follows: U D U D L R L R Payoffs to Column if of type a: Payoffs to Column if of type b: 2 0 0 1 0 2 2 0 Suppose Nature chooses Column to be type a with probability 1/2 and type b with probability 1/2. Column learns his type before choosing an action; Row does not observe the outcome of Nature's choice (i.e., Column's type is private information known only to Column). Assume the above structure is common knowledge. Find all of the Bayesian Nash equilibria to this game when players choose their actions simultaneously