Swanson-Baumol Prior Theoretical Work

The Swanson-Baumol 2005 work is a seminal paper in antitrust and patent law. Swanson and Baumol argue that once a technology is adopted into a standard, the patent holder gains immense market power. This is not necessarily due to the inherent superiority of the technology, but because the industry is now locked in. After firms have invested in the standard, the SEP holder can demand royalties that capture the value of the standard itself, rather than just the value of the patented invention. As a solution, the authors propose that “reasonable” royalties must be determined based on the ex ante (before the standard is set) value of the technology when alternatives were still available.

The authors suggest a conceptual theoretical framework for the pricing of patents based on the theory of auctions. Before a standard is finalized, different technology owners should compete before an SSO to be included. Technology owners would “bid” by offering specific FRAND royalty commitments. The SSO chooses the technology that offers the best combination of technical merit and low cost. This ensures that the royalty reflects the incremental value of the technology over the next best alternative.

Dr. Silva’s Pricing Of FRAND Via Regression

The Swanson-Baumol reasoning provides a plausible way of thinking regarding pricing of FRAND royalties. Regardless, it is a theoretical exercise and the authors have not provided clear steps to empirically implement their approach.

In Ednaldo Silva’s formulation of the pricing of FRAND royalties, he postulates that for a licensing agreement i:

Y_i = a + b_1 Q(i) + b_2 C(i) + b_3 D(i) + u(i)

where:

Y(i) = Total licensing revenue
a = floor amount
Q(i) = Net Revenue or Volume
C(i) = indicator variable for cross-licensing
D(i) = indicator variable for the product practicing a standard

One can think of this FRAND formulation, in terms of the Shapley regression where the marginal contribution of each explanatory variable is provided in terms of a coalitional game framework where each explanatory variable is represented by an agent in the game and the set function is the predictive power or R² suitable characterized.

Some Game Theoretical Intuition

In the rest of this article, the author shall attempt to reconcile the Swanson-Baumol theoretical framework with Silva’s empirical methodology. The author shall suggest a dynamic game whose solution would be the FRAND licensing of a standard technology. As it was already mentioned, one can think of the standard being set as part of an auction, which would be the first step of this dynamic game. This is the core of the Swanson-Baumol theoretical argument regarding FRAND as the outcome of such an auction would, provide a basis for what constitutes “reasonable” license fees, because it would fully reflect the state of competition among potential IP providers existing prior to the selection of a standard. In the auction or the first step, the parties representing competing technologies submit offers in terms of licensing fees competing for the standard to be implemented.

Once a standard is set though the game progresses to the second stage of pricing with a given standard and the hold-up problem appears as the winner can extract rents from the downstream users who now have to abide by the standard.

Game Theoretical Foundation

Let’s consider a dynamic game with two periods, 1 and 2.

Starting in period 2, a standard is set and a patent holder can extract rents from n licensees. Each licensee obtains revenue R so total surplus to be obtained is n x R. It is standard that using the Shapley solution the payoff to the patent holder is given by 0.5 x n x R, while each licensee obtains 0.5 x R.

In period 1, think of m potential standard setters of IP holders vying for a standard. They participate in a sealed bid auction where we assume that the valuation R is uniformly distributed in [a, b], so we have [0.5na, 0.5nb] uniformly in terms of payoff to the IP holder. It can be shown that for each player they bid the following to the SSO:

b(R) = 0.5 n a + \frac{m-1} {m} [0.5nR - 0.5na]

For the winning bid, the ex-ante return to the licensing game is given by:

0.5nR - b(R) = 0.5 \frac{n}{m} R - 0.5 \frac{n}{m} a

Or one can think of b(R) as the hold-up premium and therefore we get ex-post:

0.5nR = -0.5\frac{n}{m} a + 0.5 \frac{n}{m} R + b(R)

This is equivalent to the regression approach above where generally we have:

Royalties = a + b_1 Licensee Royalty + b_3 D(i) + u(i)

Conclusion

Swanson and Baumol’s work remains the intellectual bedrock for many court decisions regarding SEP royalties. Their insistence on an ex-ante perspective successfully shifted the burden of proof: it is no longer enough for a patent holder to show their technology is used; they must show what it was worth before the industry became captive to it and other rival technologies vied for the standard.

In this article we show that Ednaldo Silva’s regression analysis trying to capture the FRAND contribution to royalties has theoretical underpinnings in game theory. We can think of the regression analysis as a reduced form formulation of a two-period game where in the second stage standard patent holder distributes the surplus or economic rent with the licensees via the Shapley values framework. In the first period, different potential standard setters vie for standard setting via a sealed bid auction. This game-theoretic formulation captures the essence of the Swanson-Baumol work while through Ednaldo Silva’s regression analysis makes it empirically tractable.

References

1. Daniel G. Swanson and William J. Baumol (2005). Reasonable And Nondiscriminatory (RAND) Royalties, Standards Selection, And Control Of Market Power. Antitrust Law Journal, Vol. 73, No. 1, 1-58.
2. Stan Lipovetsky and Michael Conklin (2001). Analysis Of Regression In Game Theory Approach. Applied Stochastic Models In Business And Industry, 17, 319-330.
3. Christopher P. Adams (2025). Game Theory For Applied Econometricians. Chapman & Hall/CRC Series On Statistics In Business And Economics, Ch. 10, 177-179.
4. Ednaldo Silva (2026). A FRAND Regression Model: Defensibility and Data Feasibility.