Several formulations of bargaining power have been devised. A popular one from 1951 and due to American economist Neil W. Chamberlain is: In another formulation, bargaining power is expressed as a ratio of a party's ability to influence the other participant, to the costs of not reaching an agreement to that party: These formulations and more complex models with more precisely defined variables are used to predict the probability of observing a certain outcome from a range of outcomes based on the parties' characteristics and behavior before and after the negotiation. One potential application is in patent infringement lawsuits, when the jury must determine for the patent holder and the potential licensee a mutually-agreeable royalty for use of the patent holder's proprietary technology. One economist suggests a methodology to calculate the royalty whereby the total surplus of the transaction is calculated first, then split among the negotiating parties based on, in part, their relative bargaining power. The model explains that a patent holder with more bargaining power—for example, a patent holder that licenses its patents on an exclusive basis or that owns a commercially-successful technology—would capture a larger share of the total surplus than the licensee, and vice versa, as well as shows how that insight could guide a court's determination of a reasonable royalty in a patent infringement lawsuit.
Buying power
Buying power is a specific type of bargaining power relating to a purchaser and a supplier. For example a retailer may be able to dictate price to a small supplier if it has a large market share and or can bulk buy.
Economic theory
In modern economic theory, the bargaining outcome between two parties is often modeled by the Nash Bargaining solution. An example is if party A and party B can collaborate in order to generate a surplus of 100. If the parties fail to reach an agreement, party A gets a payoff X and party B gets a payoff Y. If X+Y<100, reaching an agreement yields a larger total surplus. According to the generalized Nash bargaining solution, party A gets X+π and party B gets Y+, where 0 < π < 1. There are different ways to derive π. For example, Rubinstein has shown that in a bargaining game with alternating offers, π is close to 1 when party A is much more patient than party B, while π is equal to ½ if both parties are equally patient. In this case, party A's payoff is increasing in π as well as in X, and so both parameters reflect different aspects of party A's power. To clearly distinguish between the two parameters, some authors such as Schmitz refer to π as party A's bargaining power and to X as party A's bargaining position. A prominent application is the property rights approach to the theory of the firm. In this application, π is often exogenously fixed to ½, while X and Y are determined by investments of the two parties.
