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The Complete Idiot's Guide to Game Theory by Edward Rosenthal, Ph.D., Edward C. Rosenthal

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The Kalai-Smorodinsky Solution

Seeing as the Nash solution to the Bankruptcy game examples does not appear to take some important information into account, game theorists have tried to develop other solutions that are more appealing.
The main focus of the newer approaches has been to single out condition N4—independence of irrelevant alternatives—as the troublemaker, and replace it with a different, less contentious, axiom. The best-known of the alternative solutions was published by Ehud Kalai and Meir Smorodinsky in 1975. They noticed that it was possible in some bargaining games for the feasible set S to expand and yet for the Nash allocation to one of the players to decrease.
Kalai and Smorodinsky sought to remove the irrelevant alternatives ...

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