# Consider a trading network with intermediaries in which there are three sellers S1, S2, and S3,…

Consider a trading network with intermediaries in which there are three sellers S1, S2, and S3, two buyers B1 and B2, and two traders (intermediaries) T1 and T2. Sellers S1 and S2 can trade only with trader T1, and seller S3 can trade only with trader T2. 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 sellers each have one unit of the object and value it at 0. The buyers are not endowed with the object and they each value a unit at 1.

(a) Draw the trading network, with the traders as squares, the buyers and sellers as circles, and edges connecting nodes that are able to trade with each other. Label each node as S1, S2, S3, B1, B2, T1, or T2.

(b) Find a Nash equilibrium of this trading game, including both prices and the flow of goods. Give an explanation for your answer.

(c) Suppose now that we add an edge between buyer B2 and trader T1. We want to examine whether this new edge changes the outcome in the game. To do this, take the equilibrium from your answer to part (b), keep the prices and the flow of goods on the edges from part (b) the same as before, and then suppose that the ask price on the new B2-T1 edge is 1, and that no good flows on this new edge. Do these prices and this flow of goods still form an equilibrium? If you think that the answer is yes, give a brief (oneto three-sentence) explanation. If you think the answer is no, describe a way in which one of the participants in the game would deviate.

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