Consider a trading network with intermediaries in which there is one seller S, two buyers B1 and B2, and two traders (intermediaries) T1 and T2. The seller is allowed to trade with either trader. The buyers can each trade with only one of the traders: buyer B1 can only trade with trader T1, and buyer B2 can only trade with trader T2. The seller has one unit of the object and values it at 0; the buyers are not endowed with the object. Buyer B1 values a unit at 1 and buyer B2 values a unit at 2.
(a) Draw the trading network, with the traders as squares, the buyers and the seller as circles, and edges representing pairs of people who are able to trade with each other. Label each node as S, B1, B2, T1, or T2.
(b) Suppose the traders offer prices as follows:
Trader T1 offers a bid price of to S and an ask price of 1 to B1.
Trader T2 offers a bid price of to S and an ask price of 2 to B2.
Are these bids and asks Nash equilibrium prices? If you think the answer is yes, give a brief (one- to three-sentence) explanation. If you think the answer is no, describe a way in which one of the traders could change its prices so as to increase its profit.
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