Economists’ Untold Secrets 017: Nash Bargaining II

In 1950, Nash produced an important paper on bargaining. This video proves that his theory leads to inefficient exchange. Nash contemplated a social utility framework for two persons. If they have several alternatives of utility-combination as represented by a concave set, its Pareto Efficiency must be one on its upper-right corner, as shown in this graph, which is taken directly from Nash’s paper. To verify his theory, Nash offered a numeric example: Bill has 5 goods, and their utility levels to Bill and Jack are listed in the upper part of this Table; Jack has 4 other goods, and their utility levels to the two are listed in the lower part of this Table. I plot the set of all alternatives in a scatter diagram, where the * represents Bill’s products, while the diamond Jack’s. It looks like Nash’s graph. Then, I follow Nash’s advice of exchange, “Bill gives Jack: book, whip, and bat, Jack gives Bill: pen, toy, and knife.” The alternatives remain unchanged, but not their ownership. Now, Bill possesses those products on the lower right part of the set, while Jack those on the upper left part. instead of coming to a vertex, the exchange leads to polarisation. why? Perhaps, Nash’s exchange is wrong. Perhaps, Nash’s definition of efficiency is wrong. Perhaps, Nash’s bargaining theory is wrong.

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