Abstract
The two person exchange game is analysed using core theory, the Nash solution and the competitive equilibrium. It is shown for specific utility functions that relative to the other trader, the less wealthy trader does better under the Nash solution than he would under the competitive solution. Conversely, the trader with the lower initial utility level does better under the competitive solution than he would under the Nash solution. If traders have disparate initial endowments, it is argued that outcomes should be restricted to a reduced core containing the Nash and competitive solutions as endpoints.
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References
Crawford, V. P. and Varian, H. R.: 1979, ‘Distortion of Preferences and the Nash Theory of Bargaining’, Economics Letters III 203–206.
Hildenbrand, W. and Kirman, A. P.: 1976, Introduction to Equilibrium Analysis, North Holland, Amsterdam.
Roth, A. E.: 1979, Axiomatic Models of Bargaining, Springer-Verlag, Berlin.
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Hughes, W.R. A note on the two person exchange game. Theor Decis 17, 11–19 (1984). https://doi.org/10.1007/BF00140052
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DOI: https://doi.org/10.1007/BF00140052