# A Comparison of Game-Theoretic Models for Parallel Trade

04 Feb 2018-International Game Theory Review (World Scientific Publishing Company)-Vol. 20, Iss: 03, pp 1850003

TL;DR: This paper investigates the efficiency (expressed in terms of the price of anarchy) of the subgame-perfect Nash equilibria associated with five dynamic noncooperative game-theoretic models for the parallel trade of pharmaceuticals and compares such models with regard to the manufacturer’s incentive to invest in R & D.

Abstract: Within the EU Single Market for medicines, differences in drug prices, regulations, and transaction costs may create, under suitable conditions, arbitrage opportunities well before patent expiratio

## Summary (2 min read)

Jump to: [1 Introduction] – [2 Related Literature] – [GW (B)] – [5 A Decision Theoretic Model, and Five Game-Theoretic Models for Parallel Trade] and [8 Conclusions]

### 1 Introduction

- Section 2 describes works in the literature related to parallel trade.
- Section 3 describes the adopted two-country model for the trade of pharmaceuticals.
- In Section 4, the authors express in closed form the optimal value of the global welfare of the two countries, when parallel trade is permitted/forbidden.
- The two dynamic noncooperative games proposed in [36] to model no parallel trade threat/parallel trade threat are shortly summarized in Section 5, together with the third one proposed in [31] to model the occurrence of parallel trade at equilibrium.

### GW (B)

- In the following, the authors find the optimal value of the Bentham global welfare function for a global planner who maximizes it under suitable assumptions.
- In the next analysis, the authors consider two situations: one is when the manufacturer enters the market, and the other one is when the manufacturer does not enter the market.
- Of the two situations, of course, the global planner prefers the one with the largest value of the global welfare (or is indifferent, when they produce the same value).
- Again, when the manufacturer does not enter the market and parallel trade is forbidden, there is actually nothing to optimize, and the optimal value of GW EQUATION ).

### 5 A Decision Theoretic Model, and Five Game-Theoretic Models for Parallel Trade

- (vi) in general, among all the models, the equilibria associated with the "pure" models of parallel trade (see Remark 5.7) have the smallest efficiencies. .
- It is worth also comparing that model with its two modifications.
- To generate the figure, the parameters have been chosen likewise for Figure 4 .
- Compared with these two models, larger incentives are obtained by considering the two models of parallel trade that include the transfer payment as a "corrective action", since in those cases the manufacturer is able to take over (part of) the distributor's surplus.

### 8 Conclusions

- The results of such a comparison would be useful to measure the efficiency of the proposed solutions, and to detect when policymakers should change the rules of each game in order to increase the value of the global welfare significantly.
- Similarly, one could compare the manufacturers' incentive to invest in R & D for the various cases.

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A Comparison of Game-Theoretic Models for Parallel Trade

Giorgio Gnecco - IMT School for Advanced Studies, Lucca, Italy

e-mail: giorgio.gnecco@imtlucca.it

Berna Tuncay - Koc University, Istanbul, Turkey

e-mail: betuncay@ku.edu.tr

Fabio Pammolli - Polytechnic University of Milan, Department of

Management Engineering, and CADS, Human Technopole, Milan

e-mail: fabio.pammolli@polimi.it

Abstract Within the EU Single Market for medicines, dierences in drug prices, regulations, and transaction costs

may create, under suitable conditions, arbitrage opportunities well before patent expiration, giving an incentive to

the occurrence of parallel trade. When this is permitted, parallel traders may obtain a prot from buying drugs in

a country where prices are lower, then re-selling them in a country where prices are higher. This phenomenon may

cause ineciencies from a global welfare perspective, and reduce the manufacturers’ incentive to invest in Research and

Development (R & D). Given this framework, in this paper, we investigate the eciency (expressed in terms of the price

of anarchy) of the subgame-perfect Nash equilibria associated with ve dynamic noncooperative game-theoretic models

for the parallel trade of pharmaceuticals. We also compare such models with regard to the manufacturer’s incentive to

invest in R & D. More specically, rst we nd in closed form the optimal value of the global welfare of two countries,

which is obtained by solving a suitable quadratic optimization problem modeling the decision-making process of a

global planner. Then, we use such a result to evaluate and compare the prices of anarchy of ve games modeling the

interaction between a manufacturer in the rst country and a potential parallel trader in the second country. The

rst three games refer, respectively, to the cases of no parallel trade threat, parallel trade threat, and parallel trade

occurrence at equilibrium. Then, we investigate two modications of the third game, in which its transfer payment

from the potential parallel trader to the manufacturer is, respectively, removed/determined by Nash bargaining. For

completeness, we also consider a decision-theoretic model of no parallel trade threat. For what concerns the incentive for

the manufacturer to invest in R & D, the results of our numerical comparison show that the decision-theoretic model of

no parallel trade threat is always the one with the highest incentive, whereas the two game-theoretic models of parallel

trade threat/occurrence that do not include the transfer payment provide typically the smallest incentives. Moreover,

the latter two models have the largest prices of anarchy (i.e., their equilibria have the smallest eciencies). From a

policy-making perspective, improvements are obtained if suitable countermeasures are taken to help the manufacturer

recover from the costs of R & D, such as the inclusion of a transfer payment in the model.

Keywords Economic applications of operations research · global welfare optimization · noncooperative game theory ·

subgame-perfect Nash equilibrium · numerical comparison of eciency · incentive to invest in Research and

Development

The authors acknowledge support from the Italian National Interest Project “Crisis Lab” (MIUR, PNR 2011-2013). G. G. is a member

of GNAMPA-INdAM (Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni - Istituto Nazionale di Alta

Matematica).

2

1 Introduction

Drug prices, regulations, and transaction costs usually vary across countries. Under suitable conditions, dierences in

such factors may create an arbitrage opportunity well before patent expiration (i.e., before competition with generic

drugs takes place), giving an incentive to the occurrence of a phenomenon known as parallel trade. When parallel

trade is allowed by policymakers, parallel traders (e.g., distributors or agents trading with authorized distributors)

may buy drugs in a country where prices are lower, then re-sell them in a country where prices are higher, and obtain

a prot. As locally sourced and parallel traded drugs are produced by the same manufacturer, they are exactly the

same (apart from dierent labeling/packaging), which creates opportunities for potential parallel traders. Parallel

trade tends to increase prices in lower price countries, and to reduce them in higher price countries, decreasing also

the revenues earned by manufacturers. This could make it dicult for the manufacturers to recover their past costs

of Research and Development (R & D), discouraging their future eorts in R & D of new drugs. It is also worth

mentioning that negative eects of parallel trade on the manufacturers’ incentive to do R & D and on other issues

were already highlighted in several theoretical and empirical works (see, e.g., [9–11, 14,23,28,32, 45], and Section 2 for

their discussion, and more generally for a literature review). This is particularly relevant, since endogenous sunk costs,

such as those associated with R & D, can improve the product quality, raising its demand [43].

Relevance of the topic for trade in the European Union. In order to grasp the practical importance of the topic,

we recall that in Europe the phenomenon of parallel trade is made possible by free movement of goods [24], which is

one of its fundamental principles, as being supported by European Union Treaty resolutions. As an example, parallel

trade of pharmaceuticals in Europe is based on the concept of “community exhaustion” of intellectual property rights

(IPRs) [47]. Once a patented drug has been sold in a country inside the European Union, the IPR holder has no longer

the right to restrict selling that drug in other countries still inside the European Union (however, this does not exhaust

such a restriction right outside the European Union). In Europe, free movement of goods is practically unlimited,

with some exceptions in case of its negative inuence on some selected markets. In particular, free trade in Europe is

allowed for pharmaceutical products, whenever they are available on the market in at least one of its member states.

As discussed in [9], parallel trade of pharmaceuticals within the European Union determines a conict among dierent

principles. On the one hand, countries generally dier in their health policies, which leads to dierences in their prices,

even when the marketed drug is identical. On the other hand, free movement of goods inside Europe makes it possible

for parallel traders to obtain a prot from the possible arbitrage opportunity due to such price dierences. In more

quantitative terms, according to the recent study [23] made for the European Parliament, with reference to the main

importing countries of the European Union, the market share of parallel-traded medicines has been reported between

1.7 % (Finland) and 16.5 % (Denmark). The phenomenon is particularly relevant since, according to the same study,

medicines constitute the third largest cost component in the health care budgets of European countries, which spend

more than 26 billion Euros per year on R & D. However, as reviewed by the European Court of Justice, such an

expenditure in R & D may not be incentivated by parallel trade.

Relevance of the topic for Operations Research. It is worth mentioning that the study of manufacturer’s strategies to

deal with potential competition from parallel trade has recently attracted interest also in Operations Research journals.

Indeed, since parallel traders and manufacturers can be modeled as dierent agents with their own objectives, it is

natural to investigate parallel trade using noncooperative game-theoretic models. For example, the paper [48] presents

consumer rebates (i.e., payments from the manufacturer to the consumer, e.g., in the form of coupons [1, 7, 12]) as a

possible tool to bypass competition from parallel trade, whereas [21] employs techniques from Operations Research to

study the eect of investments in demand-enhancing activities to boost authorized channel demand as a mechanism

to lower the pressure from parallel trade. Finally, [25] analyses the eects on pricing of centralization/decentralization

of a multinational rm in the presence of competition from parallel traders.

Contributions of the work. Within this game-theoretic framework, in the paper we adopt the concept of price

of anarchy [27] as a means to investigate the eciency of equilibria to noncooperative game-theoretic models of

parallel trade (and in one case, of the optimal solution to a related decision-theoretic model). Loosely speaking, for a

A Comparison of Game-Theoretic Models for Parallel Trade 3

noncooperative game, the price of anarchy measures the “worst-case” loss of eciency of an equilibrium, which is due

to the selsh behavior of its players. When the price of anarchy is “large”, the rules of the game should be modied to

achieve a much more ecient worst-case equilibrium. On the other hand, when it is “small”, no change in the model is

really needed. In the present context, the price of anarchy is the ratio between the optimal value of the global welfare

(i.e., the one obtained by a hypothetical global planner, by solving a suitable optimization problem) and its value

obtained in correspondence of the “worst” equilibrium of the game. A similar denition holds for a decision-theoretic

model, with the equilibrium replaced by an optimal solution to the associated optimization problem.

In summary, the aim of the paper consists in comparing the eects of dierent levels of parallel trade freedom

on the price of anarchy, considering various models (four from the literature, and two original modications of an

existing model). Our investigation takes also into account the total xed cost of R & D (and, more generally, the

total xed cost of market entry). This makes it possible to compare, for the various models, the decision by the

manufacturer whether to invest or not to invest in R & D. In order to compute the price of anarchy, we adopt the

Bentham model for the global welfare function, formulating and solving in closed form suitable quadratic optimization

problems modeling the decision-making process of the global planner (see Propositions 4.1 and 4.2), after expressing

in closed form the surpluses of all the entities involved in the model. Then, we compare the expressions of the price

of anarchy (and of the incentive for the manufacturer to invest in R & D) obtained for three noncooperative games

corresponding to dierent levels of parallel trade freedom: two dynamic noncooperative games proposed in [36] to model

the interaction between a manufacturer and a distributor, which assume, respectively, no parallel trade threat from the

distributor, and parallel trade threat from the distributor (but no occurrence of parallel trade at equilibrium), and a

third dynamic noncooperative game proposed in [31], for which the manufacturer is able to take over the distributor’s

surplus through a transfer payment, and there is occurrence of parallel trade at equilibrium (see Propositions 5.2, 5.3,

and 5.4). We also introduce and investigate two modications of this third model. In the rst modication, the transfer

payment is removed. In the second modication, it is still present, but it is determined by Nash bargaining between

the manufacturer and the distributor. In this way, the manufacturer is able to take over only part of the distributor’s

surplus. For completeness, we include in the comparison also a decision-theoretic model of no parallel trade threat

from [34], in which the manufacturer is the only decision maker. For all the models, we nd closed-form expressions

for the price of anarchy, and we also prove that this is nondecreasing with respect to the total xed cost of R & D

when the global planner decides to invest in R & D (see Proposition 6.2 (i), (ii)).

Our main ndings in the successive numerical comparison are summarized as follows. We show that, in the ranges

considered for the parameters, the game-theoretic models of parallel trade threat/occurrence that do not include the

transfer payment provide the largest prices of anarchy, hence their equilibria have the smallest eciencies. Instead,

the decision-theoretic model of no parallel trade threat and the game-theoretic model of parallel trade occurrence with

Nash bargaining have typically the smallest prices of anarchy. For what concerns the incentive for the manufacturer

to invest in R & D, we show numerically that the decision-theoretic model of no parallel trade threat is always the

one with the largest incentive, whereas the two game-theoretic models of parallel trade threat/occurrence that do

not include the transfer payment provide typically the smallest incentives. This is reasonable, since in those cases,

the manufacturer is unable to take over (part of) the distributor’s prot through the transfer payment. However, a

larger incentive (still smaller than the one provided by the decision-theoretic model of no parallel trade threat) is

obtained when one introduces, as a countermeasure, the transfer payment in the model. The results are in agreement

with several studies (see, e.g., [10, 11, 45]), which highlight the negative eects of parallel trade, and the need to take

suitable countermeasures to help the manufacturer recover from R & D costs.

Structure of the paper. The paper is organized as follows. Section 2 describes works in the literature related to paral-

lel trade. Section 3 describes the adopted two-country model for the trade of pharmaceuticals. In Section 4, we express

in closed form the optimal value of the global welfare of the two countries, when parallel trade is permitted/forbidden.

The two dynamic noncooperative games proposed in [36] to model no parallel trade threat/parallel trade threat are

shortly summarized in Section 5, together with the third one proposed in [31] to model the occurrence of parallel

trade at equilibrium. The section summarizes also a decision-theoretic model of no parallel trade threat from [34],

4

and presents two original modications of the game-theoretic model from [31]. Then, in Section 6, we evaluate the

prices of anarchy associated with all the models above, and highlight their dependence on the relative market size of

the two countries, the parallel trade cost per-unit, and the total xed cost of R & D. Section 7 presents numerical

results. Finally, Section 8 discusses the results and mentions possible extensions of the methodology to other models

for parallel trade investigated in the literature. All the proofs are reported in the appendix.

2 Related Literature

According to [33], the literature about the determinants of parallel trade can be divided into three streams. On one

hand, [30,31] focus on the diculties encountered by multinational companies in prohibiting sales outside the authorized

distribution chains. One the other hand, [6,16] focus on international price dierences due to price regulation by national

governments, which are typical, e.g., of the pharmaceutical industry. Finally, according to [30], a third determinant of

parallel trade is the incentive to parallel traders of free-riding on investments in marketing.

In the literature, there is a strong debate about the consequences of parallel trade on global welfare, and about

the opportunity or not of permitting parallel trade [9, 20, 24, 40]. For instance, according to the analysis presented

in [9], trade usually increases global welfare, by making consumers in higher price countries benet from lower prices

in other countries, when these lower prices are motivated by a more ecient or lower cost technology. Nevertheless,

still according to [9], in the case of pharmaceuticals parallel trade may reduce global welfare, as an eect of a more

intensive regulation. Moreover, the presence of parallel trade often lowers the incentive of the manufacturer for product

innovation [28]. In [14], this has been conrmed empirically (referring to the case of the German market of oral

anti-diabetics) through a structural approach, by comparing a counterfactual scenario with the status quo market.

Additionally, according to [23], most of the revenues originated by parallel trade are accrued not to the consumers,

but to the parallel traders themselves. Another negative aspect of parallel trade of pharmaceuticals has to do with

its increase in the risk of drug shortage, for both higher and lower price countries

1

[38]. In lower price countries,

indeed, parallel trade may cause drug shortage, when one cannot foresee the extent of drug exports. In higher price

countries, when imported drugs are sold at a lower price than locally sourced ones, sales of the same drugs produced

by national suppliers may be discouraged, possibly causing drug shortage also in this case. Additionally, parallel trade

may increase prices in lower price countries [32]. It is worth mentioning that, according to [22], parallel trade may

even have a positive eect on global welfare, e.g., when it implies a re-allocation of consumption from individuals with

relatively less drug needs to individuals with relatively more drug needs. Nevertheless, according to the same reference,

parallel trade reduces global welfare when it implies, instead, a re-allocation of consumption from individuals with

relatively more drug needs to individuals with relatively less drug needs, and also in case one market is not served

as a consequence of parallel trade. More generally, the eect of parallel trade on global welfare is considered in [22]

as ambiguous, in the sense that the positive/negative inuence of parallel trade on global welfare depends on which

aspects are taken into account in the model (e.g., the need for the manufacturer to recover from the R & D costs). A

two-country model of the eects of parallel trade on R & D is investigated in [2], where the dependence on the size of

the two countries is also taken into account. In case the negative eects of parallel trade dominate, the following are

some ways to still prevent its occurrence:

(i) a uniform pricing scheme could be adopted in all the countries potentially involved in parallel trade: in such

a case, potential parallel traders would have no incentive to do parallel trade, due to the presence of positive

parallel trade costs (associated, e.g., with transportation/repackaging). Although such a uniform pricing scheme

has global welfare losses, there are some situations in which it has good global welfare properties [46]. An extreme

case of uniform pricing is represented by the so-called “external reference pricing” scheme, which consists in setting

the price of a specic drug (or its reimbursement from the government) to the smallest price of the same drug

1

It is worth mentioning that, when patents expire, competition from generics makes the price dierences tend to vanish, eliminating the

possible arbitrage opportunity for parallel trade, which is its main prot motivation for parallel importers.

A Comparison of Game-Theoretic Models for Parallel Trade 5

(or of a group of similar drugs) among countries otherwise potentially involved in parallel trade (hence, referring

to the smallest “external” reference price);

(ii) parallel trade may simply be forbidden

2

: however, this would require the intervention of policymakers. In such a

case, if also external reference pricing does not occur, the so-called “dierential pricing” or “price discrimination”

scheme (in which possibly dierent prices are used in dierent countries) is considered in [10] as a good way to

minimize global welfare losses, when such prices are set according to the so-called Ramsey pricing model [39].

For the pharmaceutical sector, price discrimination is considered in [11] as global welfare-superior to uniform

pricing schemes, when both static and dynamic eciency (related, respectively, to the optimal use of existing

products, and to the optimal investment in R & D) are taken into account, as price discrimination can increase

the manufacturer’s incentive to invest in R & D

3

. As an example, according to [45], price discrimination could

be implemented in European Union:

(a) either by a Treaty change or a voluntary agreement to power centralization;

(b) or through the creation of dierent blocks of high-income/low-income countries, with parallel trade permitted

only in the same block;

(c) or under discounts/voluntary contractual agreements implemented condentially.

Parallel trade and its consequences on the global welfare of the involved countries are also investigated in the literature

through various noncooperative game-theoretic models [8, 20, 31, 33, 36]. For instance, according to the two-country

model developed in [31], restricting parallel trade is always advantageous for the manufacturer, but it may either

increase or decrease the global welfare of the two countries. However, a dierent model is used in [20], showing that

parallel trade may even increase the prot of a pharmaceutical rm, depending on its bargaining power and on the

relative market size of the exporting country with respect to the importing one. In [33], two dynamic noncooperative

games are proposed to investigate the equilibrium behavior of a manufacturer located in a country and a distributor

belonging to a second country, when parallel trade from the distributor is, respectively, permitted/forbidden. In the

rst case, it is shown that parallel trade actually does not even occur at equilibrium (i.e., the quantity of the re-

imported product from the parallel trader is zero), but the threat of potential parallel trade (or parallel trade freedom)

inuences the equilibrium behavior of both players, changing the equilibrium prices and quantities of the product

sold by each of them. Instead, in the noncooperative game-theoretic model examined by [31], parallel trade actually

occurs at equilibrium, when parallel trade is permitted. For other noncooperative games modeling parallel trade, we

refer the reader to the monograph [36]. Finally, decision-theoretic models for parallel trade (in which there is only the

manufacturer as the decision maker) are considered in [34].

3 A Two-Country Model of Trade

In this section, we summarize (and extend through the possible insertion of a total xed cost of market entry, which

can be interpreted, e.g., as the total xed cost of R & D) the model for the trade of pharmaceuticals considered

in [31] and [36], involving two countries, which are characterized by dierent demand functions of one specic product

possibly subject to parallel trade. The model includes both cases in which there is parallel trade freedom/banning, and

applies also to parallel trade of other typologies of products. More precisely, the following is assumed in the model.

The rst country (named “country A” in the following) is the one in which a drug is produced by a manufacturer with

a marginal cost of production equal to 0 (e.g., because it is negligible, or because the most relevant costs are the ones

of R & D). Since the drug can be also sold in a second country (named “country B” in the following), the country A is

2

To this aim, various alternatives to “community exhaustion” of IPRs, mentioned in Section 1, exist [31]. For instance, according to

“national exhaustion”, IPRs of a product are exhausted inside a country after its rst sale within that country, but parallel trade is still

forbidden from abroad. According to “regional exhaustion”, IPRs are exhausted inside a group of countries after the rst sale within one

of them (hence, allowing for parallel trade among such countries), but parallel trade is still not permitted from the outside.

3

It is worth remarking that, in the context of the paper, the piecewise-linearity of the demand functions considered later in formulas (1)

and (2) precludes the application of the analysis made in [41], which provides conditions under which uniform pricing with linear demand

functions is, instead, global welfare-superior.

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TL;DR: In this paper, the authors consider the problem of adjusting the marginal utility of money to different people in a purely competitive system with no foreign trade and assume that private and social net products are always equal or have been made so by State interference not included in the taxation.

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1,582 citations

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TL;DR: In this paper, the authors propose the price of anarchy, which is the ratio between the worst possible Nash equilibrium and the social optimum, as a measure of the effectiveness of the system.

1,346 citations

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TL;DR: In this article, the authors focus on the output and welfare implications of monopolistic third-degree price discrimination, and propose a solution to maximize profits by charging different prices to different markets or classes for customers; Maldistribution of resources for different uses.

Abstract: Focuses on output and welfare implications of monopolistic third-degree price discrimination Maximization of profits by charging different prices to different markets or classes for customers; Maldistribution of resources for different uses (From Ebsco)

511 citations

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TL;DR: A situational analysis was performed to aid the Medical Department of Kamuzu Central Hospital in Malawi to define and prioritize its quality improvement activities, finding human resource shortages, staff attitudes and shortage of equipment were identified as major constraints to patient care, and the running of the Medical department.

Abstract: Background
Knowledge regarding the best approaches to improving the quality of healthcare and their implementation is lacking in many resource-limited settings. The Medical Department of Kamuzu Central Hospital in Malawi set out to improve the quality of care provided to its patients and establish itself as a recognized centre in teaching, operations research and supervision of district hospitals. Efforts in the past to achieve these objectives were short-lived, and largely unsuccessful. Against this background, a situational analysis was performed to aid the Medical Department to define and prioritize its quality improvement activities.

278 citations