### The Bargaining Model Approach

#### User Damages and the Hypothetical Negotiation

Historically, courts have hesitated to award damages to plaintiffs in data breach and data misuse cases because of a lack of a clear theory of harm. Plaintiffs who have not been directly and provably affected by credit card fraud have generally not suffered a direct monetary loss.

The premise of the recent Lloyd v. Google decision in the UK is that data subjects possess their personal data in the manner of an economic asset. Anyone using this data without the subject’s permission has deprived them of control over this asset. This “loss of control” suggests that data breach victims are entitled to a form of damages known as “user” or “negotiating” damages. Harm in such a case stems from the idea that the owner of an asset ought to be able to decide the terms on which he or she is willing to lend it out for others’ use.

Crucially, for the question of data valuation, this right exists even if the proposed use of the asset does not damage or use it up. Under user damages, there is no need for the owner to demonstrate that they have been directly harmed, merely that they have been deprived of control of their property. In principle, the harmed party was unlawfully denied the opportunity to bargain with the “user” of his or her property.

The “user damages” framework, as a legal precept, establishes that personal data valuation can be framed as the outcome of a negotiation between the owner of the personal data, i.e. the data subject herself, and the infringer who used this information without consent, i.e., a first or third-party data collector such as Google.

#### Outline of the Nash Bargaining Solution

As it turns out, the problem of modeling a hypothetical negotiation between two parties has been articulated at length in game theory and microeconomics. The classic approach is to estimate a result known as the Nash bargaining solution (“NBS”), which resolves the negotiation by choosing the only outcome that satisfies a series of mathematical assumptions about the options and preferences of each party.

The key insight of the NBS framework lies in posing all negotiations as a discussion over how to split up the rewards of a collective venture. Suppose that two parties can either

§ Come to an agreement and cooperate with one another, generating a “pot” of money through some common enterprise, which they then must decide how to split between themselves; or

§ Walk away from the negotiation (an outcome sometimes referred to as the status quo option) and devoting their time and resources to other uses

Under these conditions, neither party will accept any division of the pot that results in a worse outcome than their status quo option, because if either party tried to force such an outcome, the other party would simply walk away from the negotiation.

An important implication is that the range of possible negotiating outcomes is not determined by any questions of how much “value” each party adds. Instead, NBS is only interested in three things: the collective total value of the agreement, and the value that each party would realize in the absence of an agreement.

Even without further elaboration, this relatively simple and intuitive framework clarifies a few crucial points about the nature of the hypothetical negotiation. It defines the stakes of the bargaining and puts firm upper and lower boundaries on the outcome of the hypothetical negotiation.

#### Example Calculation of Personal Data Value Using a Nash Bargaining Model

As discussed above, the NBS requires only three pieces of information to put upper and lower boundaries on how much the data collector might have paid: the value of the status quo outcome for the individual, the value of the status quo outcome for the data collector, and the total value that can be realized if the individual allows her data to be used.

§ If no transaction occurs, the individual retains her privacy, which has a significant subjective personal value to her. Assume that she puts a price of around $X on the status quo outcome of retaining her privacy

§ For the data collector, not having access to the data might mean lower computing or server costs. There would be no need to store the additional data point on their servers or apply their algorithms. Call this value $Y

§ The “total value” of the potential deal is the amount that the data processor can expect to earn by processing and reselling the individual’s personal data to advertisers and the like. Call this value $Z

From these parameters, we estimate that the amount that the data collector might have paid the individual for her data, had she been afforded the opportunity to bargain for it, falls somewhere between $X and $(Z-Y).

These bounds hold regardless of the external conditions of the bargaining, such as the impatience or beliefs of the two parties. In the original framework proposed by Nash, the assumption of symmetric time-preferences and information leads to a unique point within this range that “solves” the bargaining model. This is the point which maximizes the “Nash Product,” which is given by the formula

where S1 and S2 represents the utility value of the share received by each of the parties, while Q1 and Q2 represent the utility value of each party’s status quo options. Solving for this maximum in the example given above, for instance, results in an NBS of (X + (Z-Y))/2.

#### Extending the Model

The basic version of the bargaining model discussed above has seen several elaborations and extensions since the initial publication of Nash’s pathbreaking paper in 1950. A commonly used extension of the model, for instance, is to relax the assumption that both parties have the same degree of time-sensitivity and of information. This results in the more generalized “asymmetrical” Nash product given by the formula

where β is a number between 0 and 1 that represents the bargaining power of the first party in the negotiation. Where both parties have the same bargaining power, β = 50%, and the solution is identical to the standard “symmetrical” case. Where the first party has higher (or lower) bargaining power than the second party, β shifts up (or down) and the solution shifts away from (or toward) that party’s lower bound.

Further elaborations involve game-theoretic “sequential” bargaining models, known as Rubenstein models, in which parties make offers and counter-offers over a hypothetically infinite period of time. These models are popular in the academic literature because they quantify the advantages of time-sensitivity and because they have a game-theoretic “equilibrium” solution. Like the asymmetric Nash product models, they are based on the same fundamental underlying framework.

### Conclusions

The bargaining model proposed here, in combination with the ‘user damages’ theory of harm, may represent a way forward in valuing personal data for litigation in the US and the UK. A hypothetical negotiation between plaintiffs or claimants and an infringer would not require individualized analysis of harm nor, indeed, individual proof of harm (though establishing a class wide figure for the valuation of privacy, for instance, might prove more difficult). The NBS, for its part, represents an intuitive and lightweight model with low data requirements that could help to balance the respective economic positions of the litigants in data breach cases and beyond.