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Journal ArticleDOI

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)

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, dierences 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 prot 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 ineciencies 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 eciency (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 specically, 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 modications 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 eciencies). 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 eciency · 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, dierences 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 prot. As locally sourced and parallel traded drugs are produced by the same manufacturer, they are exactly the
same (apart from dierent 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 dicult for the manufacturers to recover their past costs
of Research and Development (R & D), discouraging their future eorts in R & D of new drugs. It is also worth
mentioning that negative eects 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 inuence 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 conict among dierent
principles. On the one hand, countries generally dier in their health policies, which leads to dierences 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 prot from the possible arbitrage opportunity due to such price dierences. 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 dierent 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 eect 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 eects 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 eciency 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 eciency of an equilibrium, which is due
to the selsh behavior of its players. When the price of anarchy is “large”, the rules of the game should be modied to
achieve a much more ecient 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 denition 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 eects of dierent levels of parallel trade freedom
on the price of anarchy, considering various models (four from the literature, and two original modications 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 dierent 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 modications of this third model. In the rst modication, the transfer
payment is removed. In the second modication, 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 eciencies. 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 prot 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 eects 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 modications 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 diculties encountered by multinational companies in prohibiting sales outside the authorized
distribution chains. One the other hand, [6,16] focus on international price dierences 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 benet from lower prices
in other countries, when these lower prices are motivated by a more ecient or lower cost technology. Nevertheless,
still according to [9], in the case of pharmaceuticals parallel trade may reduce global welfare, as an eect 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 conrmed 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 eect 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 eect of parallel trade on global welfare is considered in [22]
as ambiguous, in the sense that the positive/negative inuence 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 eects 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 eects 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 specic 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 dierences tend to vanish, eliminating the
possible arbitrage opportunity for parallel trade, which is its main prot 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 “dierential pricing” or “price discrimination”
scheme (in which possibly dierent prices are used in dierent 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 eciency (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 dierent blocks of high-income/low-income countries, with parallel trade permitted
only in the same block;
(c) or under discounts/voluntary contractual agreements implemented condentially.
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 dierent model is used in [20], showing that
parallel trade may even increase the prot 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)
inuences 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 dierent demand functions of one specic 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.

Citations
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TL;DR: In a system where noncooperative agents share a common resource, the price of anarchy is proposed, which is the ratio between the worst possible Nash equilibrium and the social optimum, as a measure of the effectiveness of the system.
Abstract: In a system in which noncooperative agents share a common resource, we propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model in which several agents share a very simple network leads to some interesting mathematics, results, and open problems.

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TL;DR: In this paper, a comparison of the optimal solutions to the optimization problems modeling the three pricing schemes is performed, and conditions are found under which the two differential pricing schemes are more desirable from several points of view (e.g., incentive for the manufacturer to do Research and Development, product accessibility, global welfare) than the uniform pricing scheme.
Abstract: This paper is about the application of optimization methods to the analysis of three pricing schemes adopted by one manufacturer in a two-country model of production and trade. The analysis focuses on pricing schemes—one uniform pricing scheme, and two differential pricing schemes—for which there is no competition coming from the so-called parallel trade. This term denotes the practice of buying a patented product like a medicine in one market at one price, then re-selling it in a second so-called gray market at a higher price, on a parallel distribution chain where it competes with the official distribution chain. The adoption of pricing schemes under which parallel trade does not arise can prevent the occurrence of its well-documented negative effects. In the work, a comparison of the optimal solutions to the optimization problems modeling the three pricing schemes is performed. More specifically, conditions are found under which the two differential pricing schemes are more desirable from several points of view (e.g., incentive for the manufacturer to do Research and Development, product accessibility, global welfare) than the uniform pricing scheme. In particular, we prove that, compared to the uniform pricing scheme, the two differential pricing schemes increase the incentive for the manufacturer to invest in Research and Development. We also prove that they serve both countries under a larger range of values for the relative market size, making the product more accessible to consumers in the lower price country. Moreover, we provide a sufficient condition under which price discrimination is more efficient from a global welfare perspective than uniform pricing. The analysis applies in particular to the case of the European Single Market for medicines. Compared to other studies, our work takes into account also the possible presence in all the optimization problems of a positive constant marginal cost of production, showing that it can have non-negligible effects on the results of the analysis. As an important contribution, indeed, our analysis clarifies the conditions—which have been overlooked in the literature about the mechanisms adopted to prevent parallel trade occurrence—that allow/do not allow one to neglect the presence of this factor. Such conditions are related, e.g., to the comparison between the positive constant marginal cost of production, the parallel trade cost per-unit, and the maximal price that can be effectively charged to the consumers in the lower price country.

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01 Dec 2022
TL;DR: In this paper , an agent-based model for the parallel trade of pharmaceuticals was developed and elaborated for the pharmaceutical trade market and employed it to run multiple scenarios that are impossible to analyze through game-theoretic models.
Abstract: Pharmaceutical parallel trade is a legal trade in European countries, where traders can buy medicinal products in one country and sell them in other countries to make a profit. In the pharmaceutical parallel trade market, players such as manufacturers, wholesalers, parallel traders, pharmacies, and hospitals are involved. Studying and analyzing this market is of significant interest to economists and players involved. Agent-based modeling offers a robust algorithmic framework to analyze macroeconomic phenomena through micro-founded models. As an initial step in using agent-based modeling for the parallel trade of pharmaceuticals, we consider a simplified pharmaceutical trading market inspired by available game theory models. In this paper, we developed and elaborated the implementation of an agent-based model for the pharmaceutical trade market and employed it to run multiple scenarios that are impossible to analyze through game-theoretic models. Subsequently, we demonstrated how an agent-based model could be utilized to analyze the market from an economic perspective and how players in this market can recruit this model in their business decisions.

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Proceedings ArticleDOI
01 Dec 2022
TL;DR: In this article , an agent-based model for the parallel trade of pharmaceuticals was developed and elaborated for the pharmaceutical trade market and employed it to run multiple scenarios that are impossible to analyze through game-theoretic models.
Abstract: Pharmaceutical parallel trade is a legal trade in European countries, where traders can buy medicinal products in one country and sell them in other countries to make a profit. In the pharmaceutical parallel trade market, players such as manufacturers, wholesalers, parallel traders, pharmacies, and hospitals are involved. Studying and analyzing this market is of significant interest to economists and players involved. Agent-based modeling offers a robust algorithmic framework to analyze macroeconomic phenomena through micro-founded models. As an initial step in using agent-based modeling for the parallel trade of pharmaceuticals, we consider a simplified pharmaceutical trading market inspired by available game theory models. In this paper, we developed and elaborated the implementation of an agent-based model for the pharmaceutical trade market and employed it to run multiple scenarios that are impossible to analyze through game-theoretic models. Subsequently, we demonstrated how an agent-based model could be utilized to analyze the market from an economic perspective and how players in this market can recruit this model in their business decisions.
References
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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.
Abstract: TILE problem I propose to tackle is this: a given revenue is to be raised by proportionate taxes on some or all uses of income, the taxes on different uses being possibly at different rates; how should these rates be adjusted in order that the decrement of utility may be a minimum? I propose to neglect altogether questions of distribution and considerations arising from the differences in the marginal utility of money to different people; and I shall deal only with a purely competitive system with no foreign trade. Further I shall suppose that, in Professor Pigou's terminology, private and social net products are always equal or have been made so by State interference not included in the taxation we are considering. I thus exclude the case discussed in Marshall's Principles in which a bounty on increasing-return commodities is advisable. Nevertheless we shall find that the obvious solution that there should be no differentiation is entirely erroneous. The effect of taxation is to transfer income in the first place from individuals to the State and then, in part, back again to rentiers and pensioners. These transfers will slightly alter the demand schedules in a way depending on the incidence of the taxes and the manner of their expenditure. I neglect these alterations; 1 and I also suppose that \" a given revenue \" means a given money revenue, \" money \" being so adjusted that its marginal utility is constant. This problem was suggested to me by Professor Pigou, to whom I am also indebted for help and encouragement in its solution. In the first part I deal with the perfectly general utility function and establish a result which is valid for a sufficiently small revenue, and takes a peculiarly simple form if we can treat the revenue as an infinitesimal. I prove, in fact, that in raising an infinitesimal revenue by proportionate taxes on given commodities the taxes should be such as to diminish in the same proportion the production of each commodity taxed. In the second part I assume that the utility function is quadratic, which means roughly that the supply and demand

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Book
01 Jan 1992
TL;DR: Gibbons as discussed by the authors introduces the economic applications of game theory at least as much as the pure theory itself; formal arguments about abstract games play a minor role; the applications illustrate the process of model building, of translating an informal description of a multi-person decision situation into a formal game-theoretic problem to be analyzed.
Abstract: This book introduces one of the most powerful tools of modern economics to a wide audience: those who will later construct or consume game-theoretic models. Robert Gibbons addresses scholars in applied fields within economics who want a serious and thorough discussion of game theory but who may have found other works overly abstract. Gibbons emphasizes the economic applications of the theory at least as much as the pure theory itself; formal arguments about abstract games play a minor role. The applications illustrate the process of model building--of translating an informal description of a multi-person decision situation into a formal game-theoretic problem to be analyzed. Also, the variety of applications shows that similar issues arise in different areas of economics, and that the same game-theoretic tools can be applied in each setting. In order to emphasize the broad potential scope of the theory, conventional applications from industrial organization have been largely replaced by applications from labor, macro, and other applied fields in economics. The book covers four classes of games, and four corresponding notions of equilibrium: static games of complete information and Nash equilibrium, dynamic games of complete information and subgame-perfect Nash equilibrium, static games of incomplete information and Bayesian Nash equilibrium, and dynamic games of incomplete information and perfect Bayesian equilibrium.

1,582 citations

Journal ArticleDOI
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

Posted Content
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

Journal ArticleDOI
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

Frequently Asked Questions (1)
Q1. What are the contributions mentioned in the paper "A comparison of game-theoretic models for parallel trade" ?

This phenomenon may cause inefficiencies from a global welfare perspective, and reduce the manufacturers ’ incentive to invest in Research and Development ( R & D ). Given this framework, in this paper, the authors investigate 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. Then, the authors investigate two modifications 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, the authors 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 their 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. Then, the authors use such a result to evaluate and compare the prices of anarchy of five games modeling the interaction between a manufacturer in the first country and a potential parallel trader in the second country.