2. (Nondeterministic Trading Mechanisms) Consider the bilateral exchange problem studied in class, in which the buyer's valuation v and the seller's cost c are both continuously distributed on [0, 1]. Let a and B both belong to [0, 1], and define the following probability of trade function: p ( c, v ) = 5pa (c, v) + 5p5 (c, v ) , where p" (c, v) and p (c, v) are the probability of trade functions associated with the single-price mechanisms with prices a and B, respectively. (a) Find a transfer function t(c, v) such that the direct trading mechanism {p(., .), t(., .) } is truthfully implementable in dominant strategies. (b) Give an economic interpretation of the above trading mechanism