John Nash's Bargaining Parabola

When a damages expert derives a reasonable royalty as a remedy for patent infringement from Nobel laureate John Nash’s bargaining solution, the expert reports a division of surplus that the parties’ conduct never produced. The U.S. Court of Appeals for the Federal Circuit rejected that methodology in VirnetX v. Cisco on a narrow ground: the Nash bargaining solution says nothing about which real-world disputes satisfy its premises. Left unexamined in VirnetX was the equal weighting built into Nash’s multiplication.

The Nash bargaining solution maximizes the multiplicative product of the parties’ gains above their disagreement payoffs. In the symmetric case, the objective function is a parabola and the even split sits at its vertex. But that symmetry is not a fact about the parties. It is an axiom of Nash’s mathematical model. Because each party’s utility scale is separately calibrated, one party’s utility unit cannot be treated as commensurable with the other’s. Multiplying the two therefore builds equal weighting into the model arbitrarily and reports the resulting split of surplus as though it had been measured from the parties’ bargaining power, rather than assumed by construction.

Reasonable-royalty litigation requires a case-specific estimate of the license that the parties would have struck in a hypothetical negotiation. An expert economic witness on patent-infringement damages who begins with the Nash multiplicative product instead supplies the vertex of a function that fixes symmetry before any inquiry into the case-specific evidence—such as bargaining power, outside options, and patience—that the Georgia-Pacific factors are designed to elicit. In Daubert terms, the expert has not supplied a basis for the division of surplus; he has supplied an assumption disguised as a conclusion. That method does not multiply; it measures.

Federal Rule of Evidence 702, as amended in 2023, and the Federal Circuit’s en banc decision in EcoFactor, Inc. v. Google LLC in 2025 require the proponent of expert testimony to establish the sufficiency of the basis for an opinion, not merely its relevance. For the equal division of surplus at the heart of Nash’s bargaining parabola, no such basis exists, because the 50-percent split was never measured from facts concerning the parties, their patience, or their alternatives. The split of surplus was merely assumed by the choice of a symmetric, multiplicative objective function—the same choice that recurs, under other names, in disputes over fair, reasonable, and nondiscriminatory (FRAND) royalties for standard-essential patents (SEPs).