nep-gth New Economics Papers
on Game Theory
Issue of 2019‒11‒11
twenty papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Efficient Partnership Formation In Networks By Francis Bloch; Bhaskar Dutta; Mihai Manea
  2. Coalition Formation and History Dependence By Bhaskar Dutta; Hannu Vartiainen
  3. Axiomatizations of the proportional division value By Zhengxing Zou; Rene van den Brink; Youngsub Chun; Yukihiko Funaki
  4. Best-Response Dynamics in Directed Network Games By Péter Bayer; György Kozics; Nóra Szőke
  5. Outside options and confidence in Zeuthen-Hicks bargaining By Luis Miguel Cândido Dias; Rudolf Vetschera
  6. Necessary conditions on the existence of pure Nash equilibrium in concave games and Cournot oligopoly games By Forgó, Ferenc
  7. Winning Coalitions in Plurality Voting Democracies By René van den Brink; Dinko Dimitrov; Agnieszka Rusinowska
  8. Optimal dynamic antitrust fines By Merino Troncoso, Carlos
  9. Explaining black box decisions by Shapley cohort refinement By Masayoshi Mase; Art B. Owen; Benjamin Seiler
  10. An experimental study of partnership formation in social networks By Francis Bloch; Bhaskar Dutta; Stéphane Robin; Min Zhu
  11. Persuasion Bias in Science: An Experiment on Strategic Sample Selection By Arianna Degan; Ming Li; Huan Xie
  12. Heterogeneity and the Provision of a Public Good in Leading and Lagging Regions By Batabyal, Amitrajeet; Yoo, Seung Jick
  13. Market collusion with joint harm and liability sharing By Andreea Cosnita-Langlais; Maxime Charreire; Florian Baumann
  14. Forward Guidance: Communication, Commitment, or Both? By Bassetto, Marco
  15. Tying in evolving industries, when future entry cannot be deterred By Chiara Fumagalli; Massimo Motta
  16. Indeterminacy and Imperfect Information By Lubik, Thomas A.; Matthes, Christian; Mertens, Elmar
  17. Breaking Up: Experimental Insights into Economic (Dis)Integration By Gabriele Camera; Lukas Hohl; Rolf Weder
  18. Why do cloud providers prefer renting to selling? A supply side perspective By Fujisawa, Chieko; Kasuga, Norihiro
  19. Diffusion in countably infinite networks By Michel Grabisch; Agnieszka Rusinowska; Xavier Venel
  20. Slavery, corruption, and institutions By Rauscher, Michael; Willert, Bianca

  1. By: Francis Bloch (Université Paris 1 and Paris School of Economics); Bhaskar Dutta (University of Warwick and Ashoka University); Mihai Manea (Stony Brook University)
    Abstract: We analyze the formation of partnerships in social networks. Players need favors at random times and ask their neighbors in the network to form exclusive long-term partnerships that guarantee reciprocal favor exchange. Refusing to provide a favor results in the automatic removal of the underlying link. Players agree to provide the ï¬ rst favor in a partnership only if they otherwise face the risk of eventual isolation. In equilibrium, players essential for realizing every maximum matching can avoid this risk and enjoy higher payoffsthaninessentialplayers.Althoughthesearchforpartnersisdecentralizedandreflects local partnership opportunities, the strength of essential players drives efficient partnership formation in every network. Equilibrium behavior is determined by the classiï¬ cation of nodes in the Gallai-Edmonds decomposition of the underlying network.
    Keywords: networks, efficiency, decentralized markets, partnerships, favor exchange, maximum matchings, Gallai-Edmonds decomposition, under-demanded.
    Date: 2019–02
  2. By: Bhaskar Dutta (University of Warwick and Ashoka University); Hannu Vartiainen (University of Helsinki and Helsinki Graduate School of Economics)
    Abstract: Farsighted formulations of coalitional formation, for instance by Harsanyi (1974) and Ray and Vohra(2015), have typically been based on the von NeumannMorgenstern (1944) stable set. These farsighted stable sets use a notion of indirect dominance in which an outcome can be dominated by a chain of coalitional 'moves' in which each coalition that is involved in the sequence eventually stands to gain. Dutta and Vohra(2016) point out that these solution concepts do not require coalitions to make optimal moves. Hence, these solution concepts can yield unreasonable predictions. Dutta and Vohra (2016) restricted coalitions to hold common, history independent expectations that incorporate optimality regarding the continuation path. This paper extends the Dutta-Vohra analysis by allowing for history dependent expectations. The paper provides characterization results for two solution concepts corresponding to two versions of optimality. It demonstrates the power of history dependence by establishing nonemptyness results for all ï¬ nite games as well as transferable utility partition function games. The paper also provides partial comparisons of the solution concepts to other solutions.
    Keywords: Coalition
    Date: 2018–07
  3. By: Zhengxing Zou (Vrije Universiteit Amsterdam); Rene van den Brink (Vrije Universiteit Amsterdam); Youngsub Chun (National University, Seoul); Yukihiko Funaki (Waseda University, Tokyo)
    Abstract: We present axiomatic characterizations of the proportional division value for TU-games, a value that distributes the worth of the grand coalition in proportion to the stand-alone worths of its members. First, a new proportionality principle, called balanced treatment, is introduced by strengthening Shapley's symmetry axiom, which states that if two players make the same contribution to any nonempty coalition, then they receive the amounts in proportion to their stand-alone worths.We characterize the family of values satisfying efficiency, weak linearty, and balanced treatment. We also show that this family is incompatible with the dummy player property. However, we show that the proportional division value is the unique value in this family that satisfies the dummifying player property. Second, we propose three appropriate monotonicity axioms by considering two games in which the stand-alone worths of all players are equal or in the same proportion to each other, and obtain three axiomatizations of the proportional division value without both weak linearity and the dummifying player property. Third, from the perspective of a variable player set, we show that the proportional division value is the only one that satisfies proportional standardness and projection consistency. Finally, we provide characterizations of proportional standardness.
    Keywords: Cooperative game, proportional division value, monotonicity, consistency
    JEL: C71
    Date: 2019–11–01
  4. By: Péter Bayer; György Kozics; Nóra Szőke
    Abstract: We study public goods games played on networks with possibly non-reciprocal relationships between players. Examples for this type of interactions include one-sided relationships, mutual but unequal relationships, and parasitism. Directed cycles and parasitic relations lead to the emergence of best-response cycles, leading to non-convergence to the game's Nash equilibrium under best-response dynamics. It is well known that, in reciprocal interaction networks, best-response dynamics converge to a Nash equilibrium. We show that a class of non-reciprocal networks, characterized by transitive relative importance of players also features this property, as by a rescaling of the action space the interaction becomes reciprocal. Additionally, we show that networks rescalable to exhibit weak externalities always have a single Nash equilibrium, and by the theory of best-response potential games we show convergence for this class as well. Finally, we show that this class includes directed acyclic networks.
    Date: 2019–11–06
  5. By: Luis Miguel Cândido Dias (CeBER and Faculty of Economics, University of Coimbra); Rudolf Vetschera (Faculty of Business, Economics and Statistics, University of Vienna)
    Abstract: The Zeuthen-Hicks bargaining model connects strategic and axiomatic bargaining models by providing a description of the behavior of each party,and showing that the entire process leads to the axiomatically founded Nash bargaining solution. In its original formulation, the model treats parties asymmetrically by considering different decision alternatives of the focal party (who can either accept the opponent's offer or make a counteroffer, but not quit the negotiation) and the opponent (who can accept the focal party's offer or quit the negotiation, but not make a counteroffer). We extend the model to consider the full set of possible actions from both sides, which requires explicit modeling of the expectations of the parties concerning outcomes and outside options that become available during the process. We show analytically that under the assumption of concave utilities of both parties, the bargaining process converges to the nonsymmetric Nash bargaining solution. This result provides a new interpretation of the parameters of the nonsymmetric Nash bargaining solution, linking them to behavior in the bargaining process. Furthermore,we perform a simulation study to analyze the outcomes for non-concave utilities.
    Keywords: Zeuthen-Hicks bargaining, Nonsymmetric Nash bargaining solution, negotiator confidence.
    JEL: C72 C78 C44 C63
    Date: 2019–10
  6. By: Forgó, Ferenc
    Abstract: Necessary conditions for the existence of pure Nash equilibria introduced by Joó (A note on minimax theorems, Annales Univ. Sci. Budapest, 39(1996) 175-179) for concave non-cooperative games are generalized and then applied to Cournot oligopoly games. If for a specified class of games there always exists a pure Nash equilibrium, then cost functions of the firms must be convex. Analogously, if for another specified class of games there always exists a pure Nash equilibrium, then revenue functions of the firms must be concave in their respective variables.
    Keywords: Nash equilibrium, Cournot oligopoly
    JEL: L13
    Date: 2019–11
  7. By: René van den Brink (VU University Amsterdam); Dinko Dimitrov (Saarland University [Saarbrücken]); Agnieszka Rusinowska (CNRS - Centre National de la Recherche Scientifique, CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics)
    Abstract: We study the issue of assigning weights to players that identify winning coalitions in plurality voting democracies. For this, we consider plurality games which are simple games in partition function form such that in every partition there is at least one winning coalition. Such a game is said to be precisely supportive if it possible to assign weights to players in such a way that a coalition being winning in a partition implies that the combined weight of its members is maximal over all coalitions in the partition. A plurality game is decisive if in every partition there is exactly one winning coalition. We show that decisive plurality games with at most four players, majority games with an arbitrary number of players, and almost symmetric decisive plurality games with an arbitrary number of players are precisely supportive. Complete characterizations of a partition's winning coalitions are provided as well.
    Abstract: Nous étudions la question de l'attribution de pondérations aux acteurs qui identifient les coalitions gagnantes dans les démocraties à la pluralité des suffrages. Pour cela, nous considérons les jeux à la pluralité qui sont de simples jeux sous forme de partition, de telle sorte que dans chaque partition, il existe au moins une coalition gagnante. On dit qu'un tel jeu est justement favorable s'il est possible d'attribuer des pondérations aux joueurs de telle sorte qu'une coalition gagnante dans une partition implique que le poids combiné de ses membres est maximal par rapport à toutes les coalitions de la partition. Un jeu à la pluralité est décisif si dans chaque partition il y a exactement une coalition gagnante. Nous montrons que les jeux à la pluralité décisive avec au plus quatre joueurs, les jeux à la majorité avec un nombre arbitraire de joueurs et les jeux à la pluralité décisive presque symétriques avec un nombre de joueurs arbitraire sont précisément favorables. Des caractérisations complètes des coalitions gagnantes d'une partition sont également fournies.
    Keywords: plurality game,plurality voting,precise support,simple game in partition function form,winning coalition,jeu à la pluralité,vote à la pluralité,soutien précis,jeu simple sous forme de partition,coalition gagnante
    Date: 2019–07
  8. By: Merino Troncoso, Carlos
    Abstract: Standard antitrust optimal fines rely on a microeconomic static model. Motchenkova describes optimal antitrust dynamic sanctions and their application for EU and US methodology. For the EU fine, and based on this methodology, we find an equilibrium point for a high level of offense (2 times normal profits ) and a high detection probability (0.6).
    Keywords: antitrust,cartel,differential games
    JEL: K21 L4
    Date: 2019–11–01
  9. By: Masayoshi Mase; Art B. Owen; Benjamin Seiler
    Abstract: We introduce a variable importance measure to explain the importance of individual variables to a decision made by a black box function. Our measure is based on the Shapley value from cooperative game theory. Measures of variable importance usually work by changing the value of one or more variables with the others held fixed and then recomputing the function of interest. That approach is problematic because it can create very unrealistic combinations of predictors that never appear in practice or that were never present when the prediction function was being created. Our cohort refinement Shapley approach measures variable importance without using any data points that were not actually observed.
    Date: 2019–11
  10. By: Francis Bloch (Université Paris 1 and Paris School of Economics); Bhaskar Dutta (University of Warwick and Ashoka University); Stéphane Robin (Université de Lyon); Min Zhu (Beijing Normal University)
    Abstract: This paper reports on laboratory experiments on the formation of partnerships in social networks. Agents randomly request favors and turn to their neighbors to form a partnership where they commit to provide the favor when requested. The formation of a partnership is modeled as a sequential game, which admits a unique subgame perfect equilibrium resulting in the formation of the maximum number of partnerships. Experimental results show that a large fraction of the subjects (75%) play according to their subgame perfect equilibrium strategy and reveals that the efficient maximum matching is formed over 78% of the times. When subjects deviate from their best responses, they accept to form partnerships too early. The incentive to accept when it is optimal to reject is positively correlated with subjects’ risk aversion, and players employ simple heuristics – like the presence of a captive partner – to decide whether they should accept or reject the formation of a partnership.
    Keywords: social networks, partnerships, matchings in networks, non-stationary networks, laboratory experiments
    Date: 2018–08
  11. By: Arianna Degan; Ming Li; Huan Xie
    Abstract: We experimentally test a game theoretical model of researcher-evaluator interaction à la Di Tillio, Ottaviani, and Sørensen (2017a). Researcher may strategically manipulate sample selection using his private information in order to achieve favourable research outcomes and thereby obtain approval from Evaluator. Our experimental results confirm the theoretical predictions for Researcher’s behaviour but find significant deviations from them about Evaluator’s behaviour. However, comparative statics are mostly consistent with the theoretical predictions. In the welfare analysis, we find that Researcher always benefits from the possibility of manipulation, in contrast to the theoretical prediction that he sometimes is hurt by it. Consistent with theoretical predictions, Evaluator benefits from the possibility of Researcher’s manipulation when she leans towards approval or is approximately neutral but is hurt by that possibility when she leans against approval.
    Keywords: Persuasion Bias,Research Conduct,Manipulation,Sample Selection,Randomized Controlled Trials,
    JEL: C72 C92 D83
    Date: 2019–10–28
  12. By: Batabyal, Amitrajeet; Yoo, Seung Jick
    Abstract: The literature on leading and lagging regions has paid scant attention to how heterogeneity between the two regions impacts the provision of a public good. Given this lacuna, our contribution is to construct a game-theoretic model of an aggregate economy consisting of a leading and a lagging region and to then analyze this model. We show how two kinds of heterogeneity affect the provision of a public good such as higher education. In addition, we focus on decentralized and centralized public good provision and comment on the resulting welfare implications. We obtain two key conclusions. First, under decentralization, there exist several situations in which it is optimal for only one region to provide the public good. Second, under centralization, this exclusive provision is not optimal but the amount of the public good provided can be larger or smaller than the amount provided under decentralization. Our research tells policymakers that population size and values differences between the two regions and the use of majority voting are key factors to consider when pondering the optimal provision of a public good.
    Keywords: Centralization, Decentralization, Lagging Region, Leading Region, Public Good
    JEL: H41 R11 R13
    Date: 2019–06–09
  13. By: Andreea Cosnita-Langlais; Maxime Charreire; Florian Baumann
    Abstract: When it is impossible to identify ex post the producer of a product causing harm or the damage caused is indivisible although caused by multiple injurers, courts must apportion the total damage among tortfeasors. In this model we examine how such liability sharing rules affect the likelhood of tacit collusion. For this we use a standard Cournot oligopoly model where firms are collectively held liable for joint harm inflicted on third parties. The damage caused may be either linear or cumulative in total industry output. With repeated market interaction and grim strategies, we investigate the sustainability of collusion to derive some policy implications.
    Keywords: Cournot oligopoly, liability sharing rules, market collusion
    JEL: L41 L13 K13
    Date: 2019
  14. By: Bassetto, Marco (Federal Reserve Bank of Chicago)
    Abstract: A policy of forward guidance has been suggested either as a form of commitment ("Odyssean") or as a way of conveying information to the public ("Delphic"). I analyze the strategic interaction between households and the central bank as a game in which the central bank can send messages to the public independently of its actions. In the absence of private information, the set of equilibrium payoffs is independent of the announcements of the central bank: forward guidance as a pure commitment mechanism is a redundant policy instrument. When private information is present, central bank communication can instead have social value. Forward guidance emerges as a natural communication strategy when the private information in the hands of the central bank concerns its own preferences or beliefs: while forward guidance per se is not a substitute for the central bank's commitment or credibility, it is an instrument that allows policymakers to leverage their credibility to convey valuable information about their future policy plans. It is in this context that "Odyssean forward guidance" can be understood.
    Keywords: Forward guidance; monetary policy; interest rates
    JEL: C5 E4 E5
    Date: 2019–07–25
  15. By: Chiara Fumagalli; Massimo Motta
    Abstract: We show that the incentive to engage in exclusionary tying (of two complementary products) may arise even when tying cannot be used as a defensive strategy to protect the incumbent's dominant position in the primary market. By engaging in tying, an incumbent firm sacrifices current profits but can exclude a more efficient rival from a complementary market by depriving it of the critical scale it needs to be successful. In turn, exclusion in the complementary market allows the incumbent to be in a favorable position when a more efficient rival will enter the primary market, and to appropriate some of the rival's efficiency rents. The paper also shows that tying is a more profitable exclusionary strategy than pure bundling, and that exclusion is the less likely the higher the proportion of consumers who multi-home.
    Keywords: Inefficient foreclosure, Tying, Scale economies, Network Externalities
    JEL: K21 L41
    Date: 2019
  16. By: Lubik, Thomas A. (Federal Reserve Bank of Richmond); Matthes, Christian (Federal Reserve Bank of Richmond); Mertens, Elmar (Deutsche Bundesbank)
    Abstract: We study equilibrium determination in an environment where two kinds of agents have different information sets: The fully informed agents know the structure of the model and observe histories of all exogenous and endogenous variables. The less informed agents observe only a strict subset of the full information set. All types of agents form expectations rationally, but agents with limited information need to solve a dynamic signal extraction problem to gather information about the variables they do not observe. We show that for parameter values that imply a unique equilibrium under full information, the limited information rational expectations equilibrium can be indeterminate. We illustrate our framework with a monetary policy problem where an imperfectly informed central bank follows an interest rate rule.
    Keywords: Limited information; rational expectations; Kalman filter; belief shocks
    JEL: C11 C32 E52
    Date: 2019–10–08
  17. By: Gabriele Camera (Economic Science Institute, Chapman University and University of Bologna); Lukas Hohl (University of Basel); Rolf Weder (University of Basel)
    Abstract: Standard international economic theory suggests that people should embrace economic integration because it promises large gains. But recent events such as Brexit indicate a desire for economic disintegration. Here we report results of an experiment, based on a strategic analytical framework, of how size and distribution of potential gains from integration in?uence outcomes and individuals’ inclination to embrace integration. We ?nd that cross-country inequality in potential gains acts as a friction to realize those gains. This suggests that to better understand recent phenomena, international economic theory should account for distributional considerations and behavioral aspects it currently ignores.
    Keywords: Endogenous institutions; Globalization; Indefinitely repeated games; Social dilemmas
    JEL: C70 C90 F02
    Date: 2019
  18. By: Fujisawa, Chieko; Kasuga, Norihiro
    Abstract: Expansion of the cloud computing market, a major reform in information and communication technology (ICT), has attracted wide attention. From the perspective of companies that need cloud services, if access to cloud spreads is available on rent instead of sales, initial investment cost will decline and the number of companies currently adopting the cloud system in the form of renting servers will increase. From the supply side perspective, what are the advantages of renting cloud services? To analyze this question, we consider a duopoly cloud market under licensing and examine the optimal strategy for providers. We find that in a two-part licensing contract, which includes high royalty and fixed fee charged upfront, when the cost-saving effect is high, both firms prefer renting to increase their revenue, but when the effect is low, each firm makes a different choice.
    Keywords: Durable goods,Licensing contract,Selling,Renting,Cloud market
    JEL: D43 L13 L68
    Date: 2019
  19. By: Michel Grabisch (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics, UP1 - Université Panthéon-Sorbonne); Agnieszka Rusinowska (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics, CNRS - Centre National de la Recherche Scientifique); Xavier Venel (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics, UP1 - Université Panthéon-Sorbonne)
    Abstract: We investigate the phenomenon of diffusion in a countably infinite society of individuals interacting with their neighbors. At a given time, each individual is either active (i.e., has the status or opinion 1) or inactive (i.e., has the status or opinion 0). The configuration of the society describes active and inactive individuals. The diffusion mechanism is based on an aggregation function, which leads to a Markov process with an uncountable set of states, requiring the involvement of σ-fields. We focus on two types of aggregation functions - strict, and Boolean. We determine absorbing, transient and irreducible sets under strict aggregation functions. We show that segregation of the society cannot happen and its state evolves towards a mixture of infinitely many active and infinitely many inactive agents. In our analysis, we mainly focus on the network structure. We distinguish networks with a blinker (periodic class of period 2) and those without. ø-irreducibility is obtained at the price of a richness assumption of the network, meaning that it should contain infinitely many complex stars and have enough space for storing local configurations. When considering Boolean aggregation functions, the diffusion process becomes deterministic and the contagion model of Morris (2000) can be seen as a particular case of our framework with aggregation functions. In this case, consensus and non trivial absorbing states as well as cycles can exist.
    Abstract: Nous étudions le phénomène de diffusion dans une société infinie dénombrable d'individus en interaction avec leurs voisins. A un moment donné, chaque individu est soit actif (c'est-à-dire a le statut ou l'opinion 1), soit inactif (c'est-à-dire a le statut ou l'opinion 0). La configuration de la société décrit les individus actifs et inactifs. Le mécanisme de diffusion est basé sur une fonction d'agrégation, qui conduit à un processus de Markov avec un ensemble indénombrable d'états nécessitant l'implication de σ-algèbres. Nous nous concentrons sur deux types de fonctions d'agrégation : stricte et booléenne. Nous déterminons des ensembles absorbants, transitoires et irréductibles dans le cadre de fonctions d'agrégation strictes. Nous montrons que la ségrégation de la société ne peut pas se produire et que son état évolue vers un mélange d'un nombre infini d'agents actifs et d'un nombre infini d'agents inactifs. Dans notre analyse, nous nous concentrons principalement sur la structure du réseau. Nous distinguons les réseaux avec un clignotant (classe périodique de période 2) et ceux sans clignotant. La ø-irréductibilité est obtenue au prix d'une hypothèse de richesse du réseau, ce qui signifie qu'il devrait contenir un nombre infini d'étoiles complexes et disposer de suffisamment d'espace pour stocker les configurations locales. Lorsque l'on considère les fonctions d'agrégation booléennes, le processus de diffusion devient déterministe et le modèle de contagion de Morris (2000) peut être considéré comme un cas particulier de notre cadre avec des fonctions d'agrégation. Dans ce cas, des états absorbants consensuels et non triviaux ainsi que des cycles peuvent exister.
    Keywords: Networks/graphs,Probability: diffusion,Markov processes,Réseaux/graphes,Probabilité : diffusion,Processus de Markov
    Date: 2019–07
  20. By: Rauscher, Michael; Willert, Bianca
    Abstract: We develop a model where firms profit from coercing workers into employment under conditions violating national law and international conventions and where bureaucrats benefit from accepting bribes from detected perpetrators. Firms and bureaucrats are hetero-geneous. Employers differ in their unscrupulousness regarding the use of slave labour whereas bureaucrats have differing intrinsic motivations to behave honestly. Moreover, there is a socially determined warm-glow effect: honest bureaucrats feel better if their colleagues are honest too. The determination of bribes is modelled via Nash bargaining between the firm and the corrupt civil servant. It is shown that multiple equilibria and hysteresis are possible. Depending on history, an economy may be trapped in a locally stable high-corruption, high-slavery equilibrium and major changes in government policies may be necessary to move the economy out of this equilibrium. Moreover, we show that trade bans that are effective in reducing slavery in the export industry tend to raise slavery in the remainder of the economy. It is possible that this leakage effect dominates the reduction of slavery in the export sector.
    Keywords: Coerced Labour,Modern Slavery,Corruption,Social Norms,Trade-Related Process Standards
    JEL: D73 F16 J47
    Date: 2019

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