Consider a trading network in which there are two buyers (B1 and B2), two sellers (S1 and S2), and one trader (T1). All of the buyers and the sellers are allowed to trade with the trader. The sellers each have one unit of the object and value it at 0; the buyers are not endowed with the object, but they each want one unit; buyer B1 attaches a value of 1 to one unit, while buyer B2 attaches a value of 2 to one unit.
(a) Draw the trading network, with the trader as a square, the buyers and the sellers as circles, and edges representing pairs of people who are able to trade with each other. Label the nodes as T1, B1, B2, S1, and S2. Find Nash equilibrium bid and ask prices. (You do not have to provide an explanation for your answer.)
(b) Suppose now that we add a second trader (T2) who can trade with each seller and each buyer. In the new network, is there a Nash equilibrium in which each trader’s bid price to each seller is 1, each trader’s ask price to buyer B1 is 1, each trader’s ask price to buyer B2 is 2, one unit of the good flows from S1 to B1 through trader T1, and one unit of the good flows from S2 to B2 through trader T2? Draw the new trading network and give a brief (one- to three-sentence) explanation for your answer.
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