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Nash Bargaining Theory and Intangible Property Transfer Pricing

Posted on Sep. 30, 2019
[Editor's Note:

This article originally appeared in the September 30, 2019, issue of Tax Notes Federal.

]
Benjamin M. Satterthwaite
Benjamin M. Satterthwaite

Benjamin M. Satterthwaite is pursuing his LLM in taxation at the University of Florida Levin College of Law. He is a 2019 graduate of the University of South Carolina School of Law. Satterthwaite thanks professor Clint Wallace of the University of South Carolina School of Law for his guidance on this article, and Jason DeBacker and Yash Gad for their invaluable input on its economic and mathematical portions.

In this article, Satterthwaite proposes a transfer pricing framework for unique intangibles that integrates the economic fundamentals of John Nash’s bargaining theory with the “realistic alternatives” language of amended sections 367(d) and 482.

This article was the winning entry in Tax Analysts’ annual student writing contest and received the 2019 Christopher E. Bergin Award for Excellence in Writing.

Copyright 2019 Benjamin M. Satterthwaite.
All rights reserved.

I. Introduction

In classical game theory, the “bargaining problem” describes the ubiquitous scenario of two players negotiating over the apportionment of something desirable. John Nash’s bargaining theory models the outcome of this scenario by providing an algorithm that calculates the most efficient allocation of utility between the bidding parties relative to their respective alternatives to entering into the transaction. As discussed later, the outcome is unique in that it provides each player with the largest apportionment of utility possible without harming the other party. In this way, the solution to Nash bargaining theory effectively gives each party to a negotiation the fairest split of benefits.

Tax authorities confronted with this same problem in the transfer pricing context have tried to address it by circuitously defining an appropriate allocation between related parties as what would result from independent parties negotiating at arm’s length. The voluminous statutes and regulations giving shape to this arm’s-length principle rely primarily on subjective comparisons with similar exchanges and fail to give the taxpayer any objective measure of a transaction’s adequacy. Nash bargaining theory may be able to satisfy tax authorities’ need to objectively measure the merits of transactions, and it may provide much-needed clarity to this pressing issue in global commerce.

A transfer price is the price charged between related entities, such as a parent multinational corporation (MNC) and a controlled foreign subsidiary in an intraorganizational transaction. Although intracompany transactions like this are ignored when the financial outcomes of the enterprise are consolidated,1 they are not ignored for tax purposes.2 This is because the tax rates governing the parent and the subsidiary differ and therefore tempt the taxpayer corporation to apportion more income than necessary to the lower-taxed jurisdiction to reduce its overall tax liability.

For enterprises with sufficient contacts in the United States, section 482 gives the IRS the power to make adjustments to the taxpayer’s income if profit from an intracompany intangible property transfer doesn’t reflect the true amount of income attributable to each corporate entity.3 The goal of section 482 is to place the controlled taxpayer on parity with the uncontrolled taxpayer by requiring that the prices charged and profit allocation from the controlled transaction be the same as if it were an uncontrolled transaction with an independent entity.4 The scope of intangibles covered by section 482 is applicable to a vast array of business structures5 and includes any intangible of significant worth existing independent of the goods or services provided.6

This rule comports with the OECD’s substantively similar arm’s-length principle. Under that rule, if conditions are imposed between two enterprises that differ from those that would be made between independent enterprises negotiating at arm’s length, that difference must be included in the profits of that enterprise and taxed accordingly.7 In sum, the arm’s-length rules are designed to prevent companies from buying or selling intangible property to related companies under terms or prices that would not be agreed to if they were negotiating with an independent organization they didn’t own or control.

The necessity of intangible property transfers, coupled with the ease with which they may intentionally or unintentionally distort income, has baffled both tax planners and authorities. The problem has grown in size and complexity8 as commerce continues to become increasingly global, and as companies’ most valuable assets morph from the physical to data, goodwill, trade secrets, patents, and general know-how. Compounding this problem is tax authorities’ insistence on reaching an arm’s-length allocation by valuing intracompany transfers of intangibles based on comparables that don’t exist. Indeed, as discussed later, the IRS has hedged its bet on comparable transactions with an alternative commensurate with income approach that has been shown to produce woefully different results.

I argue that Nash bargaining theory can provide clarity and thus help practitioners formulate and evaluate controlled intangible property transfers so that they comply with these established measures of a transaction’s adequacy. This solution is not only consistent with the spirit of transfer pricing law, it also comports with amendments made by the Tax Cuts and Jobs Act that emphasize the “realistic alternatives” of controlled transactions. Realistic alternatives happen to be the most important input in Nash’s solution to the bargaining problem.

II. Background

A. History

Section 482’s functional predecessors trace back to the War Revenue Act of 1917, which gave the commissioner authority to require related corporations to file consolidated returns “whenever necessary to more equitably determine the invested capital or taxable income.” This led to section 482’s earliest direct predecessor, which authorized the commissioner to consolidate the accounts of related corporations “for the purpose of making an accurate distribution or apportionment of gains, profits, income, deductions, or capital between or among such related trades or business.”9 And in 1928 Congress enacted section 45, which expanded the scope and set of rules for calculating the correct apportionment of income.10

The familiar arm’s-length standard of today traces its roots to regulations issued under section 45, which were not published until 1934.11 In describing the scope and purpose of section 45, Treasury made clear that the ultimate end was to place the controlled taxpayer on par with an uncontrolled taxpayer by determining, “according to the standard of an uncontrolled taxpayer, the true net income from the property and business of a controlled taxpayer.” This was to be accomplished by applying “the standard of an uncontrolled taxpayer dealing at arm’s length with another uncontrolled taxpayer.”12

Courts struggled with the dearth of information provided by section 45 and its regulations. Section 45 was changed to section 482 in a 1954 code overhaul, and the following decade saw the Ninth Circuit reject the arm’s-length standard in Frank13 on the grounds that it wasn’t even mentioned in other cases and therefore wasn’t the sole criterion in evaluating transfer pricing issues. Shortly thereafter, in Oil Base,14 the Ninth Circuit reversed itself when a multinational oil corporation tried to use Frank to justify commissions sent to its wholly owned Venezuelan distributor that were nearly double the commissions it sent to unaffiliated distributors. The MNC argued that the commission was justified by substantially higher profits received from the subsidiary. The court determined that the commissions lacked fairness and reason and thus had to be reduced to reflect the substance of the transaction. More important, the court acknowledged that the arm’s-length standard applied to these allocations, even though they could not be compared with independent transactions. The Ninth Circuit even went as far as suggesting that the taxpayer hypothesize in the absence of comparables.

The first regulations under section 482 carried over the holding in Oil Base by contemplating the situation in which a taxpayer cannot find comparable transactions to establish a transfer price.15 However, the regulations focused primarily on tangible property transfers and provided guidance on only three allocation methods, all of which required information on comparable uncontrolled transactions. If none of those methods was applicable, the regulations allowed for a facts and circumstances approach as a backstop.

Unsurprisingly, this “fourth method” was frequently applied to unique intangible property. In Lufkin Foundry,16 an oil field machinery manufacturer’s practice of selling machinery to its foreign subsidiary at a 20 percent discount off list price was challenged by the IRS, which allocated 50 percent of the commission back to the parent. In the Tax Court, the taxpayer was only able to offer expert evidence that justified the commissions by reference to the internal structure and characteristics of the company’s overseas operations, yet it was held to have established an arm’s-length exchange. On appeal, the Fifth Circuit refused to uphold the IRS’s reallocation on the grounds that the agency made no showing of similar uncontrolled transactions to rebut the taxpayer’s internal structure argument. In addition to clarifying each party’s burden on a section 482 challenge,17 this case was among the first to grapple with the problem of evaluating the appropriateness of a transfer pricing agreement without evidence of any comparable uncontrolled transactions.

Several years later, the Tax Court seemed to imply that the parties’ bargaining positions are relevant in evaluating whether a transaction meets the arm’s-length standard. In French,18 the petitioner held a patent for instant mashed potatoes, which it had acquired through a license agreement with its British parent that allowed the patent to be marketed domestically. When the license was negotiated, the patent was unproven, so the terms of the agreement were inconsistent with the commercial success that later came from the patent’s exploitation in the United States. The court again sided with the taxpayer, holding that the subsequent profitability of an intangible is irrelevant in establishing the reasonableness of a royalty.19

In an apparent reversal just seven years later, the IRS’s reliance on French was ruled an abuse of discretion in U.S. Steel.20 The parent was using its own prices from small, spontaneous, uncontrolled transactions with third parties to set the prices paid to its foreign subsidiary, with which the parent’s transactions were much larger and ongoing. Unlike in French, the court didn’t note the vast differences in bargaining power in the smaller independent transactions and the larger controlled transactions. Instead, the court held that in evaluating the comparability of independent transactions, it is enough that they are comparable and not identical.

Recognizing a need for guidance, Congress amended section 367(d) under the Deficit Reduction Act of 1984 to require that tax-free transfers of intangibles to controlled foreign corporations be treated as sales requiring annual payments over the life of the asset. In 1986 Congress introduced a similar standard as an addition to section 482, allowing payments for some transfers or licenses to be reallocated to make the payments commensurate with the income attributable to those transactions.21 In a clear departure from French, Congress explicitly indicated that it didn’t intend for the determination of intangibles’ value to be limited to information known at the time of the transfer.22 Implicit in that interpretation was Congress’s apparent desire to have both an arm’s-length standard and a commensurate with income standard apply to intangible property transfers.23

The final relevant historical case is Eli Lilly.24 In an attempt to diversify its manufacturing capabilities and leverage Puerto Rico’s advantageous tax laws, the taxpayer created a Puerto Rican subsidiary to manufacture pharmaceuticals. The IRS challenged the parent’s capitalization of the subsidiary with intangible assets necessary for pharmaceutical manufacturing, in exchange for stock in the subsidiary. The court agreed with the taxpayer’s general argument that the exchange of subsidiary stock for the parent’s intangibles could meet the arm’s-length standard, but it also agreed with the IRS’s contention that in this case, the parent would never have given up the intangibles in an arm’s-length negotiation with an independent enterprise. Deciding not to adopt either allocation proffered by the parties, the court instead imposed a “reasonable profit split” calculated according to the values of each party’s contributions. The decision prompted a flurry of section 482 temporary and proposed regulations in the following years.25 Among them were several important advances in transfer pricing methods,26 including the best method rule.27

Finally, in 2017 the TCJA added the following language to section 482, which appears to mirror Nash bargaining theory’s fixation on each party’s alternatives to transacting:

For purposes of this section, the Secretary shall require the valuation of transfers of intangible property (including intangible property transferred with other property or services) on an aggregate basis or the valuation of such transfer on the basis of the realistic alternatives to such a transfer, if the Secretary determines that such basis is the most reliable means of valuation of such transfers. [Emphasis added.]

The Joint Committee on Taxation’s explanation of these changes acknowledges that the regulations establish a “realistic alternative principle” that applies to all transfer pricing methods.28 The JCT goes on to explain that the effect of a pricing method chosen by the taxpayer must yield economic results consistent with alternative arrangements that were realistically available to the taxpayer.

B. Established Pricing Methods

To appreciate the utility of game theory’s application to transfer pricing, it is critical to understand the methods endorsed by the IRS and the OECD.

1. Comparable uncontrolled price method.

The comparable uncontrolled price method evaluates the merits of a controlled transaction by comparing its terms with those of uncontrolled transactions,29 which are intrinsically assumed to have been negotiated at arm’s length. Whether this method is appropriate is determined by assessing the best method factors, which include reliability, comparability, and the quality of the data used to calculate the transfer price.30 The same basic rules have been adopted by the OECD.31 The CUP method is likely the most accurate and reliable method when the same product or service is sold in the comparable uncontrolled transaction.32 However, this method is rarely applied for intangibles because the standards for comparability are so exacting that unless the intangibles are the same and priced similarly to a commodity, it’s impossible to calculate the transfer price accurately.

2. Comparable profits method.

The comparable profits method evaluates controlled transactions by comparing them with objective measures of profitability derived from uncontrolled taxpayers engaging in similar business activities under similar circumstances.33 The OECD’s transactional net margin method34 similarly looks to net profit indicators in uncontrolled transactions, such as return on assets or operating income from sales, to establish profit allocations in the controlled transaction. Although CPM is less sensitive to minor differences,35 and there is usually no shortage of data on profits from comparable unrelated businesses, it is difficult to check for errors. That problem is compounded by the unique nature of intangible property. Even if comparable unrelated businesses are found, the inherently flexuous nature of the value of intangible property makes it especially hard to determine a reasonable profit indicator.

3. Cost-plus method.

The cost-plus method is a traditional transaction method used primarily for pricing controlled transactions involving unfinished goods. It takes the costs incurred by the supplier in the controlled transaction and adds an appropriate markup consistent with that of other suppliers in comparable uncontrolled transactions.36 The simplicity of the cost-plus method allows it to be easily distorted by the amalgamation of various costs that it can fail to capture. For example, its reliance on cost basis can be distorted if one company owns assets used to manufacture a good or provide a service, and the other company uses leased equipment.37

4. Resale price method.

By taking the difference between the price at which a good is purchased in a controlled transaction and the price at which it is sold to a third party, and isolating the costs related to the good, a gross margin is calculated with the remainder based on the parties’ contributions.38 The resale price method can be accurate for vertically integrated businesses like distributors and resellers, but it is difficult to use in controlled transactions of intangibles because those assets frequently lack reliable comparables.

5. Profit-split method.

Lastly, the profit-split method splits profits from the controlled transaction according to what would have been negotiated if the parties were unrelated.39 This may be accomplished in one of two ways. Under a contribution approach, the combined profits of the associated enterprises are divided based on the approximation of the division of profits that independent enterprises would have expected given the value inputs performed.40 The second residual approach is performed in two steps. First, the non-unique contributions of each party are isolated and typically allocated according to another transfer pricing method. Whatever remains of the combined profits is allocated to each party according to the facts and circumstances and should reflect an outcome that would be reasonable for unrelated parties.41

The profit-split method is readily applied to intangible property primarily because it offers a solution when each party provides unique and valuable contributions but comparable data are lacking.42 It is not without its flaws, however. Perhaps the most dangerous potential side effect of the profit-split method is seen when one entity exports its inefficiencies to the other. For example, if an inefficient and inflated marketing budget for a transferred trademark exists, this might appear to be a contribution when it’s actually the result of mismanagement. Phenomena like this illustrate how the profit-split method can be exceedingly difficult to apply, despite its theoretical functionality.

6. Unspecified methods.

The transfer pricing rules recognize the possibility that no endorsed method provides the direction necessary to calculate transfer price. Accordingly, they leave open to the taxpayer the option of combining methods or using other means to satisfy the arm’s-length requirement.

C. The Best Method Rule

Choosing from among the listed pricing methods is another important element in transfer pricing. Under the best method rule, the taxpayer must determine the method that under its particular facts and circumstances provides the most reliable measure of an arm’s-length result.43 The regulations state that there is no strict hierarchy of methods and that any method may be used to determine an arm’s-length result without establishing the inapplicability of another method, as long as another method is not more reliable.44 If two or more methods are used that yield inconsistent results, a facts and circumstances approach is taken to find the most reliable measure, considering comparability, the quality of data, the reliability of assumptions, the sensitivity of results to deficiencies in the data or assumptions, the functions of the parties, contractual terms, risks, economic conditions, and whether property or services are being evaluated.45

The OECD’s counterpart to the best method rule similarly tries to find the most appropriate method for a particular case and recognizes that no one method is suitable in every situation, so it’s unnecessary to prove a particular method is not suitable under the circumstances.46 In selecting an appropriate transfer pricing method, the OECD rules list four criteria to consider that mirror the direction provided by the regulations, including emphasis on the reliability of information and the comparability of the transactions.47

III. Nash Bargaining Theory

This section introduces the concept of Nash equilibrium and the economic theory underlying the bargaining problem. It explains how Nash’s problem parallels the challenges faced in calculating arm’s-length agreements in the transfer pricing context and argues that Nash bargaining theory may be useful if applied correctly. As illustrated later, Nash bargaining theory could be particularly helpful for transfers of unique intangible property with no reliable comparables and for evaluating the results of prices calculated under other methods.

A. Introduction

Shortly after receiving his Ph.D. from Princeton University in 1950, economist-mathematician John Nash published a series of papers48 on game theory that would eventually develop into a cornerstone of modern economics and win him a Nobel Prize in 1994. His work would be applied well outside academic circles. Governments around the world hired game theorists to provide advice on auctioning public goods such as oil drilling rights and electricity.49 Nash’s discoveries were applied by scholars during the Cold War in an effort to understand and predict the dynamics of the arms race.50 Major League Baseball players used Nash’s teachings during wage negotiations in 1980.51 His work has even made valuable contributions to automobile traffic modeling.52

Before Nash bargaining theory developed, economists had little to no understanding of how their field of study might be applied to predict the results of the bargaining problem, in which two actors haggle over the allocation utility from a particular subject. Instead, the result of a negotiation was generally thought to be an issue governed by psychology.53 Nash ultimately discovered that there is always an equilibrium or steady state of play in strategic games in which each player chooses an action rationally based on complete information of the other player’s behavior.54 In other words, when the mix of potential strategies in a two-player game is simplified, each player will choose a strategy that is best given her beliefs about the other player’s potential move. Of all these possible strategies, at least one of them will maximize the utility for the player regardless of what strategy the other player adopts. This resting point of strategies is known as the Nash equilibrium.55

Perhaps the most elementary example of this equilibrium at work can be seen in a game of “rock, paper, scissors.”56 In this game of chance, players must try to anticipate their opponent’s move by displaying a hand that beats the other’s hand. Both players are disadvantaged by favoring one move more than the other, because the other player will quickly adjust their play to anticipate that tendency. Accordingly, the equilibrium strategy that will give a player the highest chance of winning regardless of her opponent’s actions is one that does not favor rock, paper, or scissors. In other words, the Nash equilibrium is for the player to adopt a strategy of choosing rock, paper, and scissors each 33.33 percent of the time.

In the rock, paper, scissors example, both players are equally situated. Neither has an inherent advantage over the other. Therefore, if both players are seeking to maximize wins, they will both adopt strategies that use each hand 33.33 percent of the time. As illustrated later, Nash proved that even in the haggling context in which both parties assume different bargaining positions (that is, their choice of strategies affects them differently), they still retain a utility-maximizing equilibrium.

B. Nash as a Transfer Pricing Tool

Nash’s discoveries were boundless, yet they have seldom been used in the legal and tax context. Nash bargaining theory’s use as a legal tool has been limited to helping solve patent infringement damages cases, and even then, some courts have dismissed Nash’s theories for evidentiary reasons.57 Conversely, Nash bargaining theory and game theory as a whole have been recognized by economists58 and tax practitioners59 as a potential solution to a diverse array of problems inherent in transfer pricing.

For example, economist Lioubov Pogorelova’s paper “Transfer-Pricing and Game Theory”60 offers a method for incorporating game theory principles into the profit-split method. The framework she proposes looks to the structure of the enterprise and considers the extent to which it is vertically integrated and the extent to which it is diversified. Because both these variables affect the degree to which the business’s subunits depend on one another, they can significantly affect transfer pricing outcomes.61 Based on these variables, Pogorelova optimizes the calculation of transfer price by providing cooperative and noncooperative game theoretic models that are adjusted for those attributes of the organization’s structure.

In anticipation of the OECD’s completion of its base erosion and profit-shifting project,62 transfer pricing specialist Moises Dorey used game theory to evaluate the payoff of a taxpayer’s decision to either engage in an aggressive profit-shifting strategy and risk an audit, or adhere to profit-shifting rules and be content with less profit.63 This was then juxtaposed with a payoff matrix illustrating the tax auditor’s cost and benefit of auditing an enterprise or not. Although the inputs in his calculation were assumed, the result amply showed that an equilibrium strategy between the players existed such that the taxpayer would apply BEPS strategies half the time, while the tax auditor would audit two out of three cases. Like this article, Dorey’s observations about this troublesome competitive dynamic gave rise to a proposal that the OECD engage in efforts that champion cooperation over competition.

Lastly, in a four-part series published in 2008 in BNA’s Tax Planning International Transfer Pricing, game theory’s applicability to the profit-split method was demonstrated by using Shapley value64 to calculate the allocation.65 Similar to this article, it argued that game theory’s ability to explicitly model the economic elements of a controlled transaction made it a suitable tool for analyzing transfer pricing outcomes.

Although these works amply demonstrate game theory’s ability to provide direction on controlled transaction problems associated with enterprise structure, taxpayer-regulator competition, and profit allocation, there has been no attempt to connect game theory to the TCJA. This article builds off those prior publications by providing a framework that integrates the economic fundamentals of the Nash bargaining solution with the TCJA’s amendments to sections 367(d) and 482 governing transfer pricing. I argue that the outcome of applying the Nash bargaining solution to inform the transfer price of a real scenario may be used as an objective measure of profit allocation fairness under the new law.

C. Nash’s Solution to the Bargaining Problem

Nash’s solution makes many assumptions that are critical to understanding its use for modeling negotiations. His model assumed two parties haggling over the allocation of a finite amount of utility when one party’s gain is the other party’s loss, and vice versa. He also assumed that both parties had a fallback or alternative strategy that could be pursued if an agreement wasn’t reached, but that fallback yielded less utility than could be attained from making a deal. Accordingly, any outcome to the bargain that yields a lower amount of utility than what would be realized if the alternative were chosen is a disagreeable outcome, while any outcome yielding utility exceeding the fallback is an agreeable outcome to the bargain.66

Nash’s solution to this problem adjusts for each party’s relative bargaining power, so that both players maximize their surplus utility as adjusted to their respective alternatives. Nash modeled this interaction as follows67:

Equation

U denotes utility; subscript a denotes Player A; subscript b denotes Player B; and V denotes fallback utility. Again, fallback utility is the amount of utility that would be gained if the player chose the second-best option to bargaining. For simplicity, this could be referred to as a reasonable alternative or a fallback threshold. Note that value exceeding V is surplus utility, to which the X is a possible bargaining outcome, and Formula is the maximum of the product of the two players’ surplus utilities as a result of a bargaining outcome. The Nash equilibrium is the value of X that maximizes the product of the two players’ surplus utilities.

D. Similarities to Transfer Pricing Problem

When a controlled transaction is stripped to its basic defining features, it shares many characteristics with the bargaining problem Nash solved. In fact, all the inputs to Nash’s solution are present in controlled (and uncontrolled) transactions. The following sections discuss six key elements and assumptions of Nash’s problem, along with their corresponding roles in transfer pricing.

1. Players and the subject of bargaining.

In the traditional bargaining problem, there are two players bargaining over the allocation of a finite amount of utility, which must be equitably allocated to the parties for both to agree on the transaction. Likewise, the transfer pricing scenario consists of two players, often a parent MNC and a subsidiary, that are required by law to affix price or profit on the same terms as would be negotiated if the two were unrelated.

2. Alternatives and rationality.

As Nash realized in the bargaining problem, it is fair to assume that each player has an alternative to agreeing with the other, and that any agreement yielding more utility than would be gained from the alternative to bargaining is agreeable. One can glean from tax authorities’ insistence on an independent transaction result that there must be an independent transaction alternative that is less appealing than the result of the controlled transaction itself.

As noted, the TCJA, which added to sections 367(d) and 482, has clarified that the value of intangible property transfers must account for either the aggregate basis or realistic alternatives to transfers when the Treasury secretary determines that basis is the most reliable way to value those transfers. The explanation of the law purports to interpret the existing regulations to require all transfers to account for the economic alternatives to the controlled transaction.68

3. Surplus utility maximization.

In addition to each player’s rational objective to reach a deal that distributes more utility than they would gain in its absence, the bargaining problem also assumes that both players seek to maximize the utility received in excess of their alternatives. Naturally, parties to all transfers (controlled and uncontrolled) try to maximize the amount of wealth attainable from the transaction; the seller or transferor seeks to maximize price as much as possible, while the buyer or transferee seeks to minimize it in the same fashion.

4. Competing interests (zero sum).

The bargaining problem Nash solved was a zero-sum game in which the gains of one player result in a loss of equal value for the other player. In the transfer pricing context, every dollar allocated to the parent is a dollar lost by the subsidiary, and vice versa. Perhaps the most troublesome attribute of controlled transactions stems from the fact that the parent and subsidiary are commonly owned. Here, Nash’s model’s dissimilarity with the realities of controlled transactions works in favor of its use in transfer pricing, because it mitigates this dynamic by pitting the financial interests of the parent and the subsidiary against one another in a manner more akin to an uncontrolled transaction.

5. Utility value.

In the bargaining problem, each player is assumed to value utility the same as the other. This is especially important to the benefits of Nash bargaining theory in transfer pricing because the key problem with controlled transactions may be that both parties do not value money the same. When Nash bargaining theory is applied to transfer pricing, it addresses this problem by assuming both the parent and the subsidiary value money equally and seek to maximize it.

6. Allocation.

In Nash’s solution, the amount of utility Player A (Ua) receives from the bargain with Player B must equal some amount that we may denote as t. It follows that the amount Player B receives (Ub) must equal the remainder of Player A’s portion (1 - t). In both controlled and uncontrolled transactions, there is likewise a specific amount of wealth t that is being apportioned between the parties that may be mathematically expressed in the same way.

In the transfer pricing realm, it may be difficult to pinpoint the exact value resulting from the transfer. However, under the profit-split method, which is frequently used for intangible transfers, this value should be calculated anyway. Therefore, so long as each party can quantify alternatives to the bargain, Nash’s solution may be calculated. Concededly, this is the greatest challenge in applying the Nash bargaining solution in the transfer pricing context. However, there are likely many cases, particularly in unique intangible property transfers, in which this input is less difficult to ascertain than those necessary for calculating price under established methods endorsed by the IRS and the OECD.

IV. Nash Applied to Transfer Pricing Problem

This section demonstrates the efficacy of applying the Nash bargaining solution to transfer pricing by using it to determine the allocation of profit between a parent and a subsidiary in two examples. In Example 1, Nash’s model is used to calculate an arm’s-length transfer price. In Example 2, Nash’s model is used to error-check the result of the controlled transaction as calculated by a legally endorsed method.

Example 1: The parent (P) is a large MNC in the online retail business with a global presence. Its European operations are carried out through country-specific subsidiaries, but it is now trying to reorganize into one single subsidiary (S) headquartered in Luxembourg that can manage all its European business. Among the many assets being transferred, the most challenging from a transfer pricing perspective concerns European customer data. For S these data are used to give customers a more personalized e-commerce experience, but S lacks the tools and resources necessary to derive actionable marketing insights from the data. On the other hand, P has analytics resources allowing it to use the data to give managers information that will allow them to better understand their customers and target them more effectively. Thus, S will rely on P to maximize the benefit derived from the data.

Because both P and S own the customer data, which are worth $100 million, no formal transaction is necessary. However, profits generated from the customer data will need to be apportioned according to an arm’s-length exchange in an uncontrolled transaction. An outside firm was asked to estimate what return P and S could expect in the absence of a transaction. It estimates that P would make a 4 percent ($4 million) annual return on the data, while S could make a 2 percent ($2 million) annual return on the data. However, the firm believes that if the transaction is made, a 16 percent annual return ($16 million) could be expected. In sum, the synergies of the controlled transaction would yield $16 million, while P’s and S’s alternatives to the transaction would yield $4 million and $2 million, respectively.

A. The Bargaining Problem

Max(Xp - Vp)(Xs - Vs)

XP represents the utility (X) or profit P stands to gain from the transaction. As explained earlier, P will receive a specific amount (t) from the transaction. Therefore XP = t.

Xs represents the utility (X) or profit S stands to gain from the transaction. Because P will receive an amount (t), it is inferred that the remainder (1 - t) will be allocated to S. Therefore XS = 1 - t.

VP represents the fallback utility (V) or profit P would gain if it chose its next-best alternative to bargaining. The fact pattern indicates that P would gain $4 million out of a possible $16 million if the deal did not manifest.69 Therefore, VP = (1/4).

VS represents the fallback utility (V) or profit S would gain if it chose its next-best alternative to bargaining. The fact pattern indicates that S would gain $2 million out of a possible $16 million if the deal did not manifest. Therefore, VS = (1/8).

B. Solution to the Bargaining Problem

After taking the variables above and inserting the known information from the fact pattern, the following equation appears:

Equation

To solve this, we simply multiply, take the derivative set equal to zero, and then solve for t:

Equations

The $9 million allocated to P and the $7 million allocated to S maximize the product of the surplus profits so that both P and S receive the most profit relative to their fallbacks. Although many factors affect how a price is determined, both parties are ultimately trying to maximize their payoffs. Here, the Nash bargaining solution gives the tax planner a starting point for what the transaction would look like if only the bargaining position of the parties was used to allocate the profit. This is especially beneficial for unique intangibles, like customer data, that have few if any comparables to provide a starting point for transfer pricing analysis.

For this method to produce a workable result, it is critical that the synergistic value of engaging in the transaction and each party’s alternatives to the transaction be determined correctly. Further, inputting the value of each party’s alternative to bargaining will often require a positive or negative adjustment to account for the countless other factors (beyond financial return) that are associated with the fallback option. For example, S’s transfer of the customer data to P could reduce the workload of some employees, making their labor supply less efficient. To account for this factor, the tax planner would be faced with the hard task of building the tangential labor effects of the transaction into the equation. Theoretically, this could be done by valuing S’s $2 million fallback more and reducing the $16 million synergistic effect. However, it is difficult to know how much these inputs should be adjusted. Although MNCs may have the resources to estimate these figures, the accuracy of those valuations are subject to a substantial risk of error that can effectively nullify a result calculated using Nash bargaining theory. Moreover, the inputs to the solution might be gamed to make the result more appealing for the MNC.

Example 2: Assume the same facts as Example 1, except that the transfer is determined using an endorsed method, such as the profit-split method. Assume further that the results of applying this method yielded an even allocation of $8 million for S and $8 million for P. On the surface, a 50-50 split may seem relatively benign, particularly because it is only $1 million off from the result under the Nash bargaining solution. However, if the allocation (t) is plugged into the Nash bargaining solution, and the fallback positions are calculated algebraically, it becomes apparent that the endorsed method might not yield an arm’s-length allocation.

The only way the Nash bargaining solution can allocate an even 50-50 split is if both parties have equal bargaining power. In other words, both parties’ negotiating position must be such that they stand to gain the same amount of surplus utility from the transaction. Accordingly, both parties’ alternatives to bargaining must be equal, which in this case must be $4 million for both P and S. Once this information is consolidated, we can deduce from the application of the Nash bargaining solution that one of the following must be true:

1. the $8 million allocation is not an arm’s-length transfer; or

2. the $8 million allocation is an arm’s-length transfer; but

(a) each party’s fallback to bargaining is $4 million, or

(b) P’s and S’s fallbacks remain $4 million and $2 million, respectively, but there are other factors worth $2 million besides bargaining position that make S’s alternative weigh more.

In this way, the Nash bargaining solution forces tax planners to focus on factors besides bargaining position (regarding direct financial gains from the transaction) that must account for the disparity between results. Those factors could include exchange rate issues, marketing considerations, uncertainty, risks, know-how, timing, tax treatment, and many other variables that affect price. All things being equal, the more a transfer pricing arrangement deviates from the allocation calculated using Nash bargaining theory, the more likely it’s not an arm’s-length transfer.

V. Merits of Integrating Nash in Transfer Pricing

A. Strengths of Nash Bargaining Theory

As suggested earlier, current and historical observers have critiqued authorities and taxpayers alike for the arbitrariness of transfer pricing methods. The subjective nature of some pricing methods, and our growing use of those methods for unique intangible property transfers, have frustrated taxpayers, whose pleas for guidance have been met with equally subjective and vague regulations. Nash bargaining theory, and likely many other foundational tenets of game theory, provides objective, mathematically sound answers to what is perhaps the grayest area of tax law.

Intangible property is especially ripe for evaluation under game theoretical methods such as Nash bargaining theory because they do not depend on the presence of comparables (although comparables may be helpful in assessing the accuracy of inputs to Nash’s bargaining equation). There is clearly a strong need for clarity in this area of the law, and the ability of Nash bargaining theory to contribute depends only on the value of opportunity cost — a variable that, unlike comparables, is present in every transaction. This is implied in the TCJA’s update of sections 367(d) and 482, and its validity is reinforced by its role as a cornerstone of microeconomic understanding. An actor executing a transaction cannot be rational unless the alternatives to it are valued less.

Concededly, it would be rare for a transaction to be governed solely by variables measured by Nash bargaining theory. Accordingly, its use as a primary driver of price is likely limited to only the most complex intangible property transfers. However, its utility in evaluating results calculated under other pricing methods is universal. If the second-best alternative is properly valued, then the more an allocation deviates from Nash’s solution, the more likely the transaction fails the arm’s-length principle.

The reason the agreement point calculated under Nash bargaining theory is such a strong indicator of price stems from a numerical quality that all Nash solutions should have: Pareto optimality. An agreement is Pareto efficient when it could not be improved to either party’s advantage without harming the other party. Because both bargainers are rational, they will not accept a result that makes them worse off than another. The brilliance in Nash’s solution lies in this Pareto stability; it is mathematically impossible for either player to achieve a better result (relative to their alternative) without disadvantaging the other. This is especially useful from a planning perspective in the sense that the solution cannot be wrong; only the inputs can be incorrect. If all the other pricing factors could be measured and accounted for in the alternative cost (VP and VS), the price or allocation reached would always equal the Nash equilibrium.

This unique approach may even have legal importance that is already codified in the IRC. As noted, the TCJA added to sections 367(d) and 482 language indicating that the IRS may evaluate the transfer of intangible property on an aggregate basis or on the basis of the realistic alternatives to that transfer. Regulations have yet to clarify what that means, but a plain reading of the statute indicates that taxpayers must consider the transaction’s opportunity costs. The Nash bargaining solution can objectively quantify this consideration that Congress has clearly indicated is of upmost importance.

B. Limitations of Nash Bargaining Theory

Nash bargaining theory falls far short of solving all problems plaguing transfer pricing. Its theoretical soundness for modeling all transactions is not matched by practical application to most transactions. Further, many of Nash’s assumptions effectively convert an infinitely more complex reality into abstractions that do not illustrate the true interactions between the bargaining parties.

Emphasis on alternatives is perhaps the greatest attribute of Nash bargaining theory, but it is also its Achilles’ heel. This model’s application to transfer pricing assumes that the direct monetary benefits of a transaction (such as return on assets) can be adjusted for factors that are not measured by money. Even if the exact financial effect of the controlled transaction is known, this value may be greatly affected by factors outside the transaction. For example, many assumedly arm’s-length uncontrolled transactions are conducted to be timed with financial quarters. If a similar controlled transaction is rushed, how should the bargaining power of the parties be adjusted for modeling purposes?

A fair critique of using this method would point to the unknowns of pricing the inputs. How does one go about valuing an alternative to a transaction? That question is well beyond the scope of this article and game theory as a whole, but it is highly relevant to Nash bargaining theory because the solution will be only as accurate as the inputs. Fortunately, many consultants can provide an answer to this question. In fact, determining the price of a reasonable alternative may prove easier than calculating the equally challenging inputs necessary for established pricing methods. For example, under the profit-split method, the taxpayer is tasked with placing a dollar amount on both direct and indirect contributions to the transferred asset. Wrangling an MNC’s diverse array of inputs that affect an intangible asset and then valuing them in aggregate is likely to be as challenging as, or more challenging than, simply appraising a reasonable alternative to the controlled transaction.

Lastly, when an agreement is reached in an uncontrolled transaction, the parties usually don’t know how much their trading partner gains or loses as a result of the accord. One of the flaws of controlled transactions is that they involve parties that know exactly how much the other gains or loses, because they are effectively the same entity. Nash’s model fails to mitigate this critical difference in the transaction types because both actors are rational and will adjust price only when it is in their own interest, so they must have the same information. This may also be hard to correct under Nash’s model. It is difficult, if not impossible, to predict the extent to which a transaction is affected by each party knowing how much the other receives.70

C. Practical Application

Despite its theoretical precision, it can be exceptionally difficult to translate the complexities of reality into the few variables the Nash bargaining solution can account for. Admittedly, its utility is limited by the taxpayer’s ability to accurately price a reasonable alternative to the controlled transaction. However, this limitation ultimately gives the taxpayer more freedom and clarity by not requiring a fruitless search for similar uncontrolled intangible property transactions.

The digital era continues to bring increased traffic of unique intangibles like data and intellectual property that are incapable of these comparisons. In the United States, this is compounded by inconsistent case law and a lack of regulatory guidance. At the most, Nash bargaining theory can calculate transfer pricing outcomes for unique intangibles and serve as an evaluation tool for the newfound focus on realistic alternatives. At the very least, Nash bargaining theory is a useful model for practitioners and authorities that provides an unfulfilled need in tax law: an objective measure of a transaction’s validity without the use of comparables.

VI. Conclusion

As technology continues to improve and require more intangible property transfers between parents and subsidiaries, so too should the rules governing these transactions improve. Before the addition of the TCJA’s “realistic alternatives” language in sections 367(d) and 482, the code was plagued by incessant inconsistencies in application, brought on by an untenable mandate that controlled transactions be compared with uncontrolled transactions. The development of transfer pricing methods such as the profit-split method has alleviated some of this uncertainty, but taxpayers still lack a truly predictable measure of a transaction’s compliance, and tax authorities remain unable to police some potentially abusive transfer pricing arrangements. Nash bargaining theory can identify realistic alternatives and reliably score the adequacy of controlled transactions, providing taxpayers much-needed objective clarity.

FOOTNOTES

1 See section 1504 (defining an affiliated group).

2 John McKinley and John Owsley, “Transfer Pricing and Its Effect on Financial Reporting,” J. Acct. (Oct. 1, 2013).

3 8 Mertens Law of Federal Income Taxation, section 33:33 (2019).

5 33A Am. Jur. “Federal Taxation,” para. 6452 (2018) (explaining that section 482 governs not only corporations but also sole proprietorships, partnerships, trusts, and estates).

6 3 Eckstrom’s Licensing in Foreign and Domestic Operations, section 10:15 (2018).

7 OECD model tax treaty, art. 9, para. 1 (2017).

8 Susan Borkowski and Mary Anne Gaffney, “Uncertainty and Transfer Pricing: (Im)Perfect Together?” 21 J. Int’l Acct. Auditing & Tax’n 32 (2012).

9 Revenue Act of 1921.

10 Reuven S. Avi-Yonah, “The Rise and Fall of Arm’s Length: A Study in the Evolution of U.S. International Taxation,” 15 Va. Tax Rev. 89 (1995).

11 Thomas E. Jenks, “Treasury Regulations Under Section 482,” 23 Tax Law. 279 (Winter 1970).

12 Art. 45-1(c) of reg. 86 (1935) (Revenue Act of 1934).

13 See Frank v. International Canadian Corp., 308 F.2d 520 (9th Cir. 1962).

14 Oil Base Inc. v. Commissioner, 362 F.2d 212 (9th Cir. 1966).

15 Reg. section 1.482-2; T.D. 6952.

16 Lufkin Foundry and Machine Co. v. Commissioner, T.C. Memo. 1971-101, rev’d, 468 F.2d 805 (5th Cir. 1972).

17 After establishing the evidentiary burdens for both sides, the Fifth Circuit remanded the case to the Tax Court.

18 R.T. French Co. v. Commissioner, 60 T.C. 836 (1973).

19 Note that field service advice dated November 23, 1992 (1992 WL 1354859) conflicts with this holding by finding “unpersuasive” the taxpayer’s argument that a royalty was arm’s length when entered into (negotiated by unrelated parties) and therefore was currently arm’s length.

20 U.S. Steel Corp. v. Commissioner, 617 F.2d 942 (2d Cir. 1980).

21 Tax Reform Act of 1986, section 1231(e).

22 Joint Committee on Taxation, “General Explanation of the Tax Reform Act of 1986,” JCS-10-87, at 1016 (1987).

23 Eckstrom’s, supra note 6, at section 10:15.

24 Eli Lilly & Co. v. Commissioner, 856 F.2d 855 (7th Cir. 1988).

25 See Notice 88-123, 1988-2 C.B. 458 (white paper); INTL-401-88 (1992 proposed regulations); and T.D. 8470 (1993 temporary regulations). The regulations were eventually finalized in 1994 as T.D. 8552.

26 Other noteworthy additions included the comparable profit interval and the allowance of an acceptable range when computing an estimated transfer price.

27 Aaron M. Rotkowski, “Intangible Property in Transfer Pricing Analyses,” 102 Insights 56 (2015).

28 JCT, “General Explanation of Public Law 115-97,” JCS-1-18, at 387 (2018).

29 Reg. section 1.482-4(c)(1) (“The comparable uncontrolled transaction method evaluates whether the amount charged for a controlled transfer of intangible property was arm’s length by reference to the amount charged in a comparable uncontrolled transaction.”).

31 OECD, “OECD Transfer Pricing Guidelines for Multinational Enterprises and Tax Administrations 2017” (July 10, 2017).

32 OECD, “Transfer Pricing Methods” (July 2010).

34 Transfer pricing guidelines, supra note 31, at para. 2.64 et seq.

35 Id. at para. 2.68.

36 Id. at para. 2.45 et seq.

37 Id. at para. 2.49-2.50 (cautioning against this method when there is a difference in the makeup of the cost basis in the comparable transaction).

38 Id. at para. 2.27 et seq.

39 Reg. section 1.482-6(a); transfer pricing guidelines, supra note 31, at para. 2.114 et seq.

40 Transfer pricing guidelines, supra note 31, at para. 2.125-2.126.

41 Id. at para. 2.127-2.129.

44 Id.

45 Id.

46 Transfer pricing guidelines, supra note 31, at para. 2.1.

47 Id. at para. 2.2.

48 Nash, “Equilibrium Points in N-Person Games,” 36 PNAS 48 (1950); Nash, “The Bargaining Problem,” 18 Econometrica 155 (1950); Nash, “Non-Cooperative Games,” 54 Annals of Mathematics 268 (1951); and Nash, “Two-Person Cooperative Games,” 21 Econometrica 128 (1953).

49 See Harold W. Kuhn and Sylvia Nasar, The Essential John Nash (2002); Prakash P. Shenoy, “A Two-Person Non-Zero-Sum Game Model of the World Oil Market,” 4 Applied Mathematical Modelling 295 (1980); Shenoy, “A Three-Person Cooperative Game Formulation of the World Oil Market,” 4 Applied Mathematical Modelling 301 (1980); Peter C. Fishburn and Gary A. Kochenberger, “Two-Piece Von Neumann-Morgenstern Utility Functions,” 10 Decision Sciences 503 (1979); and Marc S. Robinson, “Collusion and the Choice of Auction,” 16 RAND J. Econ. 141 (1985).

50 Thomas Schelling, The Strategy of Conflict (1960).

51 Daniel R. Marburger, “Bargaining Power and the Structure of Salaries in Major League Baseball,” 15 Managerial & Decision Econ. 433 (1994).

52 Dietrich Braess, “Über ein Paradoxon aus der Verkehrsplanung,” 12 Unternehmensforschung 258 (1969).

53 Mary Ann Dimand and Robert W. Dimand, The History of Game Theory, Volume 1: From the Beginnings to 1945, at 66 (2002).

54 Martin J. Osborne and Ariel Rubinstein, A Course in Game Theory 14 (1994).

55 Avinash K. Dixit and Barry J. Nalebuff, The Art of Strategy 107 (2008).

56 For more easy-to-understand applications of game theory and the Nash equilibrium in particular, see Brian Christian and Tom Griffiths, Algorithms to Live By: The Computer Science of Human Decisions, ch. 11. (2016).

57 Case law is inconsistent on the admissibility of Nash’s theories being applied to patent infringement damage disputes. Ultimately, its admissibility appears to hinge on its relation to the facts of the case, and even then, it seems to vary from judge to judge. Compare Robocast Inc. v. Microsoft Corp., No. 10-1055 (D. Del. 2014) (declining to admit expert testimony using the Nash bargaining solution because it was not sufficiently tied to the facts of the case), with Gen-Probe Inc. v. Becton Dickinson & Co., No. 09-2319 (S.D. Cal. 2012) (allowing testimony based on the Nash bargaining solution because it was sufficiently tied to the facts of the case).

58 Julio B. Clempner and Alexander S. Poznyak, “Negotiating Transfer Pricing Using the Nash Bargaining Solution,” 27 Int’l J. Applied Mathematics & Comput. Sci. 853 (2017); Mingming Leng and Mahmut Parlar, “Transfer Pricing in a Multidivisional Firm: A Cooperative Game Analysis,” 40 Operational Res. Letters 364 (Sept. 2012); Edward C. Rosenthal, “A Game-Theoretic Approach to Transfer Pricing in a Vertically Integrated Supply Chain,” 115 Int’l J. Production Econ. 542 (Oct. 2008); Ramy Elitzur and Jack Mintz, “Transfer Pricing Rules and Corporate Tax Competition,” 60 J. Pub. Econ. 401 (1996).

59 Lioubov Pogorelova, “Transfer-Pricing and Game Theory,” 43 Intertax 395 (2015); Moises Dorey, “To Audit or Not to Audit: Applying Game Theory to a Post-BEPS World,” 24 Transfer Pricing Rep. 404 (Aug. 6, 2015); Jeremy Y. Zhou, “Using a Bargaining Model for Arm’s-Length Allocations,” Transfer Pricing Rep. (2009); Alexander Voegele, Sébastien Gonnet, and Bastian Gottschling, “Transfer Prices Determined by Game Theory,” Tax Planning Int’l Transfer Pricing (Oct.-Dec. 2008) (four-part series).

60 Pogorelova, supra note 59.

61 All things being equal, a vertically integrated company’s business units will be more interdependent, because the success of this type of business rests on cooperation-borne synergies. Similarly, vertically integrated companies tend to be less diverse, because more diversity correlates with subunits’ interests being more conflicting.

62 The BEPS project (2012-2016) was an OECD effort to curtail multinational profit shifting from higher- to lower-taxed jurisdictions. This culminated with the BEPS multilateral instrument, which has since been signed by 88 different countries. The United States is not a signatory of the agreement.

63 Dorey, supra note 59.

64 Shapley value is a game theory solution that looks to the varying contributions of actors to a common whole and then spreads the marginal costs among those actors equally.

65 Voegele, Gonnet, and Gottschling, supra note 59.

66 See the Nash publications listed supra note 48.

67 For simplification purposes, I have made adjustments to the letters and symbols such that they differ from those used in Nash’s original paper. These adjustments are not substantively significant.

68 JCS-1-18, supra note 28, at 387.

69 For a party to a controlled transaction, there are two situations that could constitute a fallback: (1) transacting with a third party in an uncontrolled transaction, or (2) not engaging in any transaction at all. If neither of those fallbacks are dwarfed by the potential gains of the controlled transaction, there cannot be an arm’s-length transfer. This is because the opportunity cost of the independent transaction, or not transacting at all, brings about more utility to both parties than engaging in the controlled transaction (effectively making the controlled transaction the realistic alternative, or V).

70 For example, a company selling a good with an elastic demand curve might be harmed if its consumers knew that the product cost only a penny to make but was sold to them for $10.

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