Bargaining Theory Lends IP Litigation a New Negotiating Approach

How Nash’s work on bargaining theory has gone beyond the purview of academia

 IP litigation benefits from Bargaining Theory

Jeffrey Klenk

Consider this scene from the film A Beautiful Mind. It is the late 1940s. Mathematician John Nash is in a bar with friends. Several women walk in, including a blonde woman who immediately provokes competitive banter among
the friends. 

“Every man for himself, gentlemen,” says one of them. 

In Nash, this eruption of competition inspires a revelation: If all of the men compete to talk to the blonde woman, the likely outcome is that she turns them all down. But if none of them talks to the blonde women, and they instead talk with her friends, then they avoid competing with each other and potentially insulting the other women.

This is clearly a Hollywood concoction. But it illustrates a core Nash principal of governing dynamics: In the ideal bargaining solution, no one has an incentive to deviate. Or, as the Hollywood Nash concludes, “The best result comes when everyone in the group does what’s best for himself and the group.”  

Nash’s work on bargaining theory, once the purview of academia, is being applied more broadly. Its core principles can provide a formidable advantage to business negotiators, and, in recent years, federal courts have considered the tenets of bargaining theory as a possible element in calculating damages in intellectual property litigation. 

A bargaining theory definition for unauthorized use of intellectual property

A bargaining model offers a way to divide a certain economic surplus or “pie.” It can be used in negotiating anything from employment agreements to supplier contracts to mergers and acquisitions. In those situations, a negotiator may gain an advantage by considering a few key principles of bargaining theory. 

There are two common approaches to modeling a negotiation. The first is axiomatic bargaining, based on Nash’s work. The second is strategic bargaining, based on the work of Ariel Rubinstein and Ken Binmore, who published their groundbreaking theses in the 1980s. Both approaches agree on two key principles: the bargain must be 1) Pareto optimal (there’s no alternative bargain that makes one of the parties better off without making the other party worse off); and 2) individually rational (the solution is not worse than either side would achieve without it). Taking the case of President Trump’s desire to renegotiate NAFTA, these principles essentially say that—short of unilaterally ending the trade agreement—any new deal would be expected to make at least one of the parties, presumably the US, better off while remaining palatable to both Mexico and Canada. 

Understanding the Nash bargaining theory of axiomatic negotiations

The party that is better positioned to wait generally ends up with a larger share.

The Nash, or axiomatic, approach is constrained by two additional rules: the independence of irrelevant alternatives and symmetry. The first of these is at the heart of what economists mean by “rational” and simply means that individuals will continue to have consistent preferences, even if certain choices are eliminated. As an example, let’s say someone prefers listening to Bach over Beethoven; removing Chopin from the set of available options should not change that person’s preference for Bach over Beethoven. The second of these additional rules means that individuals with identical preferences would realize identical solutions. 

Based on this set of axioms, a wide variety of negotiations can be modeled. A key variable in these negotiations is the disagreement payoff—or what each party would be left with if a deal is not reached. The larger a party’s disagreement payoff, the more power it has to achieve a favorable solution. 

In contrast to Nash’s axiomatic approach, Rubinstein’s strategic approach models the bargaining process so that the parties take turns making an offer, until either an offer is accepted or negotiations are discontinued. This process stresses the time value of a negotiation. Parties to a negotiation typically are eager to reach an agreement because the size of the pie they are sharing declines over time. In a commercial setting, for instance, a product feature may be delayed, diluting a competitive advantage. Thus, the party that is better positioned to wait generally ends up with a larger share once the deal is reached.

A real-world application of bargaining theory

As a practical illustration of the principles above, let’s say that a star athlete is expected to significantly increase a team’s revenue. For his agent, a starting point for negotiations could be to request a portion of that incremental revenue. A Nash bargaining outcome would be reached when neither the team nor the athlete would have any incentive to suggest an alternative offer. However, if the team did not make an acceptable offer, the agent could recommend that the athlete accept a deal from a different team, which would represent the athlete’s disagreement payoff.

Now, suppose the beginning of the season is quickly approaching and the athlete threatens not to accept the team’s offer. The athlete risks losing a large paycheck. The team’s performance also may suffer, which would hurt revenue. A Rubinstein bargaining outcome would account for each party’s ability to wait and would favor the more patient party. If, for example, the athlete had already accumulated significant savings or had other sources of revenue, those factors might favor the athlete waiting for a better offer. Conversely, if the team knew its chances of winning were bleak without its star, it might be compelled to make a more favorable offer.

Bringing bargaining theory into intellectual property law 

Amid a profusion of IP disputes, courts have sought to balance the rights of patent holders (to monetize IP) with the interests of technology users (such as manufacturers or service providers), who are often unaware that they are using patented technology. To determine appropriate damages, the parties present analyses indicating what a willing licensee and a willing licensor would have agreed to for the use of intellectual property if licensing negotiations had taken place prior to the first infringing use of the patented technology.

Given that these negotiations never in fact took place, the court’s hypothetical exercise is vulnerable to speculation. Economists have historically used various approaches to modeling these hypothetical negotiations, but courts have dismissed certain approaches as too speculative. Then, in the early 2000s, courts began to consider damages models based on bargaining theory, but admonished that the models be sufficiently tied to the facts of each case. 

As one recent example, involving Limelight Networks and XO Communications, the plaintiff’s economist used the parties’ weighted average cost of capital as a proxy for impatience, arguing that a company with higher capital costs would be in a greater rush and would settle for a smaller slice of the pie. Although the court accepted that a Rubinstein bargaining model was a feasible way of reaching a reasonable outcome, it noted that the economist’s particular model amounted to “fancy guesswork,” as it failed to account for certain case-specific evidence. The takeaway from this case, then, is that courts are willing to consider sophisticated bargaining models for patent disputes, but are requiring that they accurately reflect the particular facts and situations of the parties.

Bargaining theory permeates the world around us, not just IP litigation

Thus, the core principles behind the Nash and Rubinstein bargaining methods—that negotiations are shaped by each side’s disagreement payoff and level of impatience—can be applied intuitively across a variety of negotiations, ranging from high-stakes trade disputes or the valuation of IP to the more mundane. In negotiating with a 4-year-old, for example, although parents of an obstinate child might be frustrated by their child’s ability to delay going to bed, they can still take solace in extensive research consistent with the Rubinstein model. This includes the famous Stanford marshmallow study—showing that children able to exercise patience and stand their ground have preferable outcomes later in life.

In presenting the Nobel Prize to Nash in 1994, the Royal Swedish Academy of Sciences noted that “[m]any situations in society, from everyday life to high-level politics, are characterized by what economists call strategic interactions.” Through the work of Nash and Rubinstein, negotiators now have systematic ways of modeling and understanding those interactions, even when those interactions may be nothing more than figuring out how to talk to a an attractive person at the bar.

Jeffrey Klenk is a director for Berkeley Research Group. He has extensive experience with economic consulting and intellectual property matters.