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Glossary · Game Theory

Nash Bargaining Solution

also: bargaining theory · bargaining problem · Rubinstein bargaining · alternating-offers bargaining · outside option · BATNA

Definition

The Nash bargaining solution is the division of surplus that maximizes the product of the two parties' gains over their outside options. Nash (1950) derived it from four axioms; Rubinstein (1982) showed alternating-offer bargaining converges to it as offers become frequent. Its lesson for negotiators: payoff is set by outside options and relative patience, not by splitting the difference.

Nash's axiomatic approach asked what a fair and efficient split should satisfy, and the unique answer maximizes the product of each side's surplus above its disagreement payoff. Rubinstein's strategic approach asked what impatient players would actually agree to when offers alternate, and found the same split in the limit, with the more patient player taking the larger share. Binmore, Rubinstein, and Wolinsky (1986) connected the two, and Binmore, Shaked, and Sutton (1989) showed experimentally that outside options only shift the split when they bind. Enterprise procurement, vendor renewals, and partnership term sheets are all governed by these parameters. The practitioner error is to negotiate the number when the leverage lives in the outside option and the deadline.

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