Consider a trading network with intermediaries in which there are two sellers S1 and S2, three…

Consider a trading network with intermediaries in which there are two sellers S1 and S2, three buyers B1, B2, and B3, and two traders (intermediaries) T1 and T2. Each seller can trade with either trader. Buyer B1 can only trade with trader T1. Buyer B2 can trade with either trader. Buyer B3 can only trade with trader T2. The sellers each have one unit of the object and value it at 0; the buyers are not endowed with the object. Buyer B1 values a unit at 1, buyer B2 values a unit at 2, and buyer B3 values a unit at 3.

(a) Draw the trading network, with the traders as squares, the buyers and the sellers as circles, and edges representing pairs of people who are able to trade with each other. Label each node as S1, S2, B1, B2, B3, T1, or T2.

(b) Suppose the prices and the flow of goods are as follows:

 Trader T1 offers a bid price of 1 to each seller, an ask price of 1 to B1, and an ask price of 2 to B2.

 Trader T2 offers a bid price of 1 to each seller, an ask price of 2 to B2, and an ask price of 3 to B3.

 One unit of the good flows from seller S1 to buyer B2 through trader T1 and one unit of the good flows from seller S2 to buyer B3 through trader T2.

(If it is useful, it is okay to write these prices and this flow of goods on the picture you drew for part (a), provided the picture itself is still clear.) Do these prices and this flow of goods form a Nash equilibrium? 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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