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

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Nash’s Standard Model

The way John Nash considered the problem of two-player bargaining was to suppose there is a set of different outcomes represented by coordinate points (u1,u2) that are available to the players. Even though the players are bargaining over money, the outcomes can be measured more generally as utilities (hence the u notation). The players need to agree on one of the joint outcomes or else they both end up at an inferior disagreement point.
Instead of modeling a back-and-forth “haggling” process where two players are trying to narrow a monetary gap between them, let’s represent the bargaining problem as one of sharing a sum M of money. This sum could be the amount of money “on the table” in a negotiation, the amount left over ...

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