Nash Bargaining, explained.
Nash bargaining models a negotiated outcome by comparing each side's gain from agreement with what it would receive if no agreement were reached.
Why it happens
The disagreement point is part of the bargain. An equal final split can produce unequal gains when the alternatives differ. The Nash solution maximizes a product of gains within a feasible set under specified assumptions.
The Nash bargaining solution selects a feasible agreement by maximizing the product of gains above disagreement payoffs, under its axioms.
Read the result
Move the disagreement payoffs and inspect the surplus each party receives above its fallback. Distinguish an equal division of the total from an equal division of the gains available through agreement.
A worked example
A ten-unit agreement
One person can secure two units without a deal and the other can secure zero.
A six–four allocation gives each four units above their fallback. A five–five allocation gives gains of three and five.
The fallback changes how the same total is interpreted in the symmetric bargaining model.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
A receives x and B receives 100−x. Feasible gains require x≥a and 100−x≥b. With equal bargaining weights, x*=a+(100−a−b)/2 when a+b≤100. If a+b>100, there is no individually rational agreement and each takes its outside option.
Where this idea is useful
A practical use
A credible alternative supplier or job offer can affect negotiations by changing the payoff available without agreement.
A common misconception
“A fair bargain always divides the total equally.”
The model evaluates gains above disagreement, so different alternatives can justify different total allocations under its assumptions.
What this explanation leaves out
- This is a cooperative solution with transferable, linear utility and equal weights. It does not simulate a sequence of offers or say that all negotiations follow this solution.
Does the Nash solution predict every negotiation?
No. It is a structured solution concept. Time pressure, bargaining power, incomplete information, indivisible goods, and unequal weights can alter the process and the appropriate model.
What does each side actually get if the negotiation fails?
Associated thinkers
Further reading
Explore the original research or the teaching reference behind this experiment.