nep-gth New Economics Papers
on Game Theory
Issue of 2021‒08‒09
twenty-one papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. A Local Variation Method for Bilevel Nash Equilibrium Problems By Francesco Caruso; Maria Carmela Ceparano; Jacqueline Morgan
  2. Sampling Dynamics and Stable Mixing in Hawk–Dove Games By Arigapudi, Srinivas; Heller, Yuval; Schreiber, Amnon
  4. English Versus Vickrey Auctions With Loss-Averse Bidders By Jonas von Wangenheim
  5. Plea Bargaining and Investigation Effort: Inquisitorial Criminal Procedure as a Three-Player Game By Christmann, Robin
  6. Dutch vs. First-Price Auctions With Expectations-Based Loss-Averse Bidders By Benjamin Balzer; Antonio Rosato; Jonas von Wangenheim
  7. Personal norms in the online public good game By Marco Catola; Simone D'Alessandro; Pietro Guarnieri; Veronica Pizziol
  8. Delaying and Motivating Decisions in the (Bully) Dictator Game By Ennio Bilancini; Leonardo Boncinelli; Pietro Guarnieri; Lorenzo Spadoni
  9. Our product is unique: A note on a delegation game with differentiated products By Clemens Buchen; Sven A. Hartmann; Alberto Palermo
  10. The R&D investment decision game with product differentiation By Domenico Buccella; Luciano Fanti; Luca Gori
  11. Empowerment of social norms on water consumption By Pedehour, Pauline; Richefort, Lionel
  12. Parochial cooperation and the emergence of signalling norms By Przepiorka, Wojtek; Andreas, Diekmann
  13. Voluntary Partnerships For Equally Sharing Contribution Costs - Theoretical Aspects and Experimental Evidence - By Irene Maria Buso; Daniela Di Cagno; Werner Güth; Lorenzo Spadoni
  14. Revealing Private Information in a Patent Race By Pavel Kocourek
  15. Selling Impressions: Efficiency vs. Competition By Dirk Bergemann; Tibor Heumann; Stephen Morris
  16. Structure and oddness theorems for pairwise stable networks By Philippe Bich; Julien Fixary
  17. Why Minimum Corporate Income Taxation Can Make the High-Tax Countries Worse off: the Compliance Dilemma By Yukihiro NISHIMURA; Jean HINDRIKS
  18. Laws of Divine Power in the Greek Pantheon By Laurent Gauthier
  19. Stressed but not Helpless: Strategic Behaviour of Banks Under Adverse Market Conditions By Grzegorz Halaj; Sofia Priazhkina
  20. Renegotiation and discrimination in symmetric procurement auctions By Leandro Arozamena; Juan José Ganuza; Federico Weinschelbaum
  21. "Mixed oligopoly and predatory public firms". By Joan-Ramon Borrell; Carlos Suarez

  1. By: Francesco Caruso (Università di Napoli Federico II); Maria Carmela Ceparano (Università di Napoli Federico II); Jacqueline Morgan (Università di Napoli Federico II and CSEF)
    Abstract: We address the numerical approximation of bilevel problems consisting of one Nash equilibrium problem in the upper level and another Nash equilibrium problem in the lower level. These problems, widely employed in engineering and economic applications, are a generalization of the well-known Stackelberg (or bilevel optimization) problem. In this paper, we define a numerical method for bilevel Nash equilibrium problems where in the lower level there is a ratio-bounded game (introduced in Caruso, Ceparano, Morgan [CSEF Working Papers, 593 (2020)]) and in the upper level there is a potential game (introduced in Monderer, Shapley [Games Econ. Behav., 14 (1996)]). The method, relying on a derivative-free unconstrained optimization technique called local variation method, is shown to globally converge towards a solution of the problem and also allows to obtain error estimations.
    Keywords: Bilevel Nash equilibrium problem, Stackelberg problem, multi-leader-follower game, ratio-bounded game, potential game, Nash equilibrium, existence and uniqueness, local variation method, global convergence, error estimation.
    Date: 2021–07–30
  2. By: Arigapudi, Srinivas; Heller, Yuval; Schreiber, Amnon
    Abstract: The hawk–dove game admits two types of equilibria: an asymmetric pure equilibrium in which players in one population play “hawk” and players in the other population play “dove,” and a symmetric mixed equilibrium. The existing literature on dynamic evolutionary models shows that populations will converge to playing one of the asymmetric pure equilibria from any initial state. By contrast, we show that plausible sampling dynamics, in which agents occasionally revise their actions by observing either opponents’ behavior or payoffs in a few past interactions, can induce the opposite result: global convergence to a symmetric mixed equilibrium.
    Keywords: Chicken game, learning, evolutionary stability, bounded rationality, payoff sampling dynamics, action sampling dynamics.
    JEL: C72 C73
    Date: 2021–07–15
    Abstract: Abstract. This paper examines the Big Push industrialization model due to [Murphy et al., 1989] by featuring a game where public and private agents must coordinate their complementary investment decisions and the outcome where all agents invest dominates in payoffs the no-investment alternative.Two different paths of analysis are pursued. If the coordination game has complete information, the selection of the “right” equilibrium appears to be easier if the initial level of total factor productivity (TFP) is not too low. The comparison of the “payoff dominance” and the “risk dominance” criteria due to [Harsanyi and Selten, 1988]shows that the ability to plan jointly different kinds of investment relaxes the constraint on initial TFP. Industrialization can be alternatively modelled as an incomplete information game. In this case,underdevelopment follows from a coordination break, where typically the Government supplies infrastructures which remain underused because the private sector fails to modernize. We find out that such a coordination break is likelier in economies where the starting level of TFP is low. Consequently, a low initial TFP level tends to create a “Poverty Trap”, which however can be overcome by enhancing the ability to coordinate different kinds of investment, namely public and private.
    JEL: O10 O14 C71 C72 C73
    Date: 2021–07
  4. By: Jonas von Wangenheim
    Abstract: Evidence suggests that people evaluate outcomes relative to expectations. I analyze this expectations-based loss aversion à la Köszegi and Rabin in the context of dynamic and static auctions, where the reference point is given by the (endogenous) equilibrium outcome. If agents update their reference point during the auction, the arrival of information crucially affects equilibrium behavior. Consequently, I show that - even with independent private values - the Vickrey auction yields strictly higher revenue than the (ascending clock) English auction, violating the well-known revenue equivalence.
    Keywords: Vickrey auction, English auction, Japanese auction, expectationsbased loss aversion, revenue equivalence, dynamic loss aversion, personal equilibrium
    JEL: D03 D44
    Date: 2021–07
  5. By: Christmann, Robin
    Abstract: We study the impact of plea bargaining on decision errors and operating costs of the inquisitorial justice system. Scholars and legal professionals are divided over whether such plea deals are compatible with the inquisitorial tradition. In this paper, we stylize inquisitorial criminal procedure as a sequential game with two benevolent investigators, judge and prosecutor. Both agents are subject to private investigation costs and seek a correct decision over a defendant of uncertain guilt. Our analysis shows that the introduction of plea deals in courtroom helps to overcome the problem of effort coordination between the two investigating agents. All equilibria that involve a conviction also adhere to the ‘beyond reasonable doubt’-conviction threshold. Moreover, we demonstrate that plea bargaining reduces the frequency of wrongful convictions (type I errors) in inquisitorial procedures.
    Keywords: screening, free-riding, litigation, court errors
    JEL: D82 K14 K41
    Date: 2021–07–30
  6. By: Benjamin Balzer; Antonio Rosato; Jonas von Wangenheim
    Abstract: We study Dutch and fi rst-price auctions with expectations-based loss-averse bidders and show that the strategic equivalence between these formats no longer holds. Intuitively, as the Dutch auction unfolds, a bidder becomes more optimistic about her chances of winning; this stronger "attachment" effect pushes her to bid more aggressively than in the first-price auction. Thus, Dutch auctions raise more revenue than first-price ones. Indeed, the Dutch auction raises the most revenue among standard auction formats. Our results imply that dynamic mechanisms that make bidders more optimistic raise more revenue, thereby ratio- nalizing the use of descending-price mechanisms by sellers in this field.
    Keywords: Loss Aversion, Dutch Auctions, Revenue Equivalence, Personal Equilibrium
    JEL: D44 D81 D82
    Date: 2021–07
  7. By: Marco Catola; Simone D'Alessandro; Pietro Guarnieri; Veronica Pizziol
    Abstract: This paper shows that personal norms have a prominent role in explaining prosocial contributions in an online public good game. This finding suggests that the role of social norms might be loosened when subjects are distanced, and interaction occurs online and in complete anonymity. Through cluster analysis, we show that a) subjects who contributed more hold both high expectations about the social norms followed by others and a high personal normative commitment; b) subjects who contributed less hold both low expectations and have low personal commitment. However, for both clusters the personal norm is the main driver of decisions. Moreover, we elicited personal and social norms in a group of subjects not performing the contribution task, thus obtaining a measure of norms not affected by self-justification and ruling out a potential endogeneity issue.
    Keywords: Public good game, online experiment, personal norms, social norms, belief elicitation, social dilemma
    JEL: C90 D71 H41
    Date: 2021–07–01
  8. By: Ennio Bilancini; Leonardo Boncinelli; Pietro Guarnieri; Lorenzo Spadoni
    Abstract: We investigate experimentally how decisions in the Dictator Game are affected by cognitive manipulations aimed at promoting greater reliance on deliberation. Specifically, we run an online experiment where we have 6 distinct experimental conditions resulting from the combination of 2 conditions for the Dictator Game (non-bully: the dictator is initially endowed with all the money; bully: the initial endowment is equally split), and 3 conditions for the cognitive manipulations (time delay: decisions are delayed; motivated delay: decisions are delayed and a written motivation is required; control: no manipulation). We find that the equal initial endowment leads the dictator to keep less for himself, confirming in the online setting previous evidence from the lab. Further, our findings suggest that the request to write a motivation makes subjects take less for themselves with respect to the mere request to wait some time before choosing.
    Keywords: dual process, motivation, deliberation, intuition, Dictator Game, bully, social norms
    JEL: D01 D81
    Date: 2021–07–01
  9. By: Clemens Buchen (WHU – Otto Beisheim School of Management); Sven A. Hartmann (Institute for Labour Law and Industrial Relations in the European Union (IAAEU), Trier University); Alberto Palermo (Institute for Labour Law and Industrial Relations in the European Union (IAAEU), Trier University)
    Abstract: We analyze a Cournot duopoly market with differentiated goods and the separation between ownership and control. We consider a delegation game, for which the owner of a firm hires a manager who acts as if the good has a lower degree of substitutability than it really has. This is so either because managers are biased and perceive the good in this way, or because firms design an incentive scheme accordingly, which leads the manager to act in this way. Both firms rely on delegation. We discuss conditions, which lead one firm to increase its profit implying that the usual result of a prisoners’ dilemma is avoided.
    Keywords: Strategic Delegation, Managerial Incentives, Oligopoly
    JEL: D21 D62 L13
    Date: 2021–02
  10. By: Domenico Buccella; Luciano Fanti; Luca Gori
    Abstract: This article extends the classical d'Aspremont and Jacquemin's (1988, 1990) cost-reducing R&D model with spill-overs to allow quantity-setting firms (Cournot rivalry) to play the non-cooperative R&D investment decision game with horizontal product differentiation. Unlike Bacchiega et al. (2010), who identify a parametric region – defined by the extent of technological spill-overs and the efficiency of R&D activity – in which the game is a prisoner's dilemma (self-interest and mutual benefit of cost-reducing innovation conflict), this work shows that product differentiation changes the game into a deadlock (self-interest and mutual benefit do not conflict), irrespective of the parameter scale (thus, holding also in the absence of spill-over effects). The social welfare when the degree of product differentiation is high enough and a deadlock characterises investing in cost-reducing R&D is larger than when firms do not invest in R&D, irrespective of the technological spillovers extent and the R&D activity's efficiency. These findings suggest that investing in R&D challenges the improvement of interventions aimed at favouring product differentiation. These results also hold for pricesetting firms (Bertrand rivalry).
    Keywords: Process innovation, Nash equilibrium, Social welfare
    JEL: D43 L13 O31
    Date: 2021–07–01
  11. By: Pedehour, Pauline; Richefort, Lionel
    Abstract: This study develops a model of water extraction with endogenous social norms. Many users are connected by a unique shared resource that can become scarce in case of over-exploitation. Preferences of individuals are guided by their extraction values and their taste for conformity to social norms which provide incentives to follow others. As the main result of this study, the uniqueness of the Nash equilibrium is established under a sufficient condition. Afterward, some comparative statics analysis shows the effects of change in individual heterogeneous parameters, conformism, and density of the network on the global quantity extracted. Welfare and social optimum properties are established to avoid the tragedy of the commons and sub-optimal consumptions of water. Lastly, this theoretical framework is completed by extensions to highlight levers of water preservation, including the calibration of social norm incentives.
    Keywords: Resource /Energy Economics and Policy
    Date: 2021–07–29
  12. By: Przepiorka, Wojtek; Andreas, Diekmann
    Abstract: Why do people adorn themselves with elaborate body piercings or tattoos, wear obstructing garbs, engage in life-threatening competitions and other wasteful and harmful but socially stipulated practices? Norms of cooperation and coordination, which promote the efficient attainment of collective benefits, can be explained by theories of collective action. However, social norms prescribing wasteful and harmful behaviours have eluded such explanations. We argue that signalling theory constitutes the basis for the understanding of the emergence of such norms, which we call signalling norms. Signalling norms emerge as a result of the uncertainty about who is friend and who is foe. The need to overcoming this uncertainty arises when different groups compete for scarce resources and individuals must be able to identify, trust and cooperate with their fellow group members. After reviewing the mechanisms that explain the emergence of cooperation and coordination norms, we introduce the notion of signalling norms as markers of group distinction. We argue that adherence to signalling norms constitutes a commitment promoting parochial cooperation rather than a quality-revealing signal facilitating partner choice. We formalize our argument in a game-theoretic model that allows us to specify the boundary conditions for the emergence of signalling norms. Our paper concludes with a discussion of potential applications of our model and a comparison of signalling norms with related concepts.
    Date: 2021–07–24
  13. By: Irene Maria Buso; Daniela Di Cagno; Werner Güth; Lorenzo Spadoni
    Abstract: Contributors to public goods with individual commitment power decide before voluntarily contributing, whether and when to join the (sub)group whose partners equally share the cost of their contributions. We analyse the voluntary formation of the cost sharing partnership, when it is internally (no partner wants to opt out) and externally (no outsider wants to opt in) stable, and how (un)stable partnerships affect contribution behaviour. All contributors decide between joining and not joining for all possible conditions before learning in which random sequence individual contributors successively enter or not the partnership. After being informed about whether there is no partnership and, when there is one, how many belong to it, and whether one is partner or outsider, all group members independently contribute. So participants can freeride not only by abstaining from voluntary contributions, but also by not joining the partnership. Theoretically participants would form a stable cost sharing partnership whose partners (outsiders) contribute maximally (minimally); experimental evidece shows that hardly any such benchmark behavior exists. Instead we confirm a strong inclination to join the partnership to avoid or at least weaken freeridng incentives.
    Keywords: Endogenous Public Good, Group Formation, Group Size.
    JEL: C92 H41 D85
    Date: 2021
  14. By: Pavel Kocourek
    Abstract: In this paper I investigate the role of private information in a patent race. Since firms often do their research in secrecy, the common assumption in patent race literature that firms know each other’s position in the race is questionable. I analyze how the dynamics of the game changes when a firm’s progress is its private information, and I address the question whether revealing it might be to a firm’s advantage. I find that a firm has an incentive to reveal its breakthrough only if its rival has not done so, and only if the research is costly.
    Keywords: : Patent Race; R&D Investment; Race; Optimal Effort; Revealing Private Information;
    Date: 2021–07
  15. By: Dirk Bergemann (Cowles Foundation, Yale University); Tibor Heumann (Pontificia Universidad Católica de Chile); Stephen Morris (Dept. of Economics, MIT)
    Abstract: In digital advertising, a publisher selling impressions faces a trade-off in deciding how precisely to match advertisers with viewers. A more precise match generates efficiency gains that the publisher can hope to exploit. A coarser match will generate a thicker market and thus more competition. The publisher can control the precision of the match by controlling the amount of information that advertisers have about viewers. We characterize the optimal trade-off when impressions are sold by auction. The publisher pools premium matches for advertisers (when there will be less competition on average) but gives advertisers full information about lower quality matches.
    Keywords: Second Price Auction, Conflation, Digital Advertising, Impressions, Bayesian Persuasion, Information Design
    JEL: D44 D47 D83 D84
    Date: 2021–07
  16. By: Philippe Bich (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, UP1 - Université Paris 1 Panthéon-Sorbonne, PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Julien Fixary (UP1 - Université Paris 1 Panthéon-Sorbonne, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)
    Abstract: We determine the topological structure of the graph of pairwise stable weighted networks. As an application, we obtain that for large classes of polynomial payoff functions, there exists generically an odd number of pairwise stable networks. This improves the results in Bich and Morhaim ([5]) or in Herings and Zhan ([14]), and can be applied to many existing models, as for example to the public good provision model of Bramoullé and Kranton ([8]), the information transmission model of Calvó-Armengol ([9]), the two-way flow model of Bala and Goyal ([2]), or Zenou-Ballester's key-player model ([3]).
    Keywords: Weighted Networks,Pairwise Stable Networks Correspondence,Generic oddness
    Date: 2021–06
  17. By: Yukihiro NISHIMURA (Graduate School of Economics, Osaka University); Jean HINDRIKS
    Abstract: Minimum taxation means that if a multinational enterprise (MNE) declares its operations in a jurisdiction taxing less than the minimum tax, the countries where the real economic activity takes place would have the right to tax the difference. There is a revival of the minimum tax standard for two reasons. First, there is concern about the complexity of assigning taxing rights and the effectiveness of profit-splitting rules in eliminating profit shifting. Second, the minimum tax standard has the merit of tackling multinational tax avoidance at its root. However, this argument ignores the strategic interaction between minimum taxation and tax compliance. Building upon Hindriks and Nishimura (2021), we develop a framework in which effective international tax compliance requires enforcement coordination between countries (e.g. exchange of information). We show that under sufficient market asymmetry (translating into the tax differential), minimum taxation may induce the low-tax countries to withdraw from international tax compliance agreements. We then show that such a breakdown of cooperation can make the high-tax country worse off compared to the absence of minimum taxation.
    Keywords: Profit shifting; Tax competition; Tax enforcement;
    JEL: C72 F23 F68 H25 H87
    Date: 2021–07
  18. By: Laurent Gauthier (LED - Laboratoire d'Economie Dionysien - UP8 - Université Paris 8 Vincennes-Saint-Denis)
    Abstract: In ancient Greek polytheism, worshippers could choose which gods they would address, and in doing so they expected some form of benefit in a quid pro quo relationship. We look into the optimal choice of which god to worship as a function of the presumed strategy of the gods for returning favors to the worshippers, and relate it to a form of divine efficiency measure. At the equilibrium the model also shows that the least-worshipped god receives at least a certain volume of devotion. We propose two different approaches that may account for the assumed divine efficiency measure, one based on projecting characteristics of human performance onto the gods, and the other based on a random growth model for the benefits of addressing each god. Both approaches imply that observed acts of worship would follow a type of power law. We gathered data from a large volume of epigraphic and literary sources on actual acts of worships from the ancient Greeks, and it allows us to show that the distributions of these acts at the polis level effectively follow power laws with a particularly high degree of regularity. The number of votive acts towards the least-worshipped gods also match the model's prediction. We test the extent to which the known characteristics of the poleis affect the shape of these distributions, and find little explanatory power. The shape of the distribution of votive acts across gods hence appears to have followed a general law for the Ancient Greeks.
    Keywords: Ancient Greek polytheism,religious studies,theory of religious economy,game theory,random growth models,power laws,human performance modeling
    Date: 2021–07–17
  19. By: Grzegorz Halaj; Sofia Priazhkina
    Abstract: We model bank management actions in severe stress test conditions using a game-theoretical framework. Banks update their balance sheets to strategically maximize risk-adjusted returns to shareholders given three regulatory constraints and feedback effects related to fire sales, interactions of loan supply and demand, and deteriorating funding conditions. The framework allows us to study the role of strategic behaviors in amplifying or mitigating adverse macrofinancial shocks in a banking system and the role of macroprudential policies in the mitigation of systemic risk. In a macro-consistent stress testing application, we show that a trade-off can arise between banking stability (solvency) and macroeconomic stability (lending) and test whether the release of a countercyclical capital buffer can reduce systemic risk.
    Keywords: Central bank research; Economic models; Financial institutions; Financial stability; Financial system regulation and policies
    JEL: C72 G21
    Date: 2021–07
  20. By: Leandro Arozamena; Juan José Ganuza; Federico Weinschelbaum
    Abstract: In order to make competition open, fair and transparent, procurement regulations often require equal treatment for all bidders. This paper shows how a favorite supplier can be treated preferentially (opening the door to home bias and corruption) even when explicit discrimination is not allowed. We analyze a procurement setting in which the optimal design of the project to be contracted is unknown. The sponsor has to invest in specifying the project. The larger the investment, the higher the probability that the initial design is optimal. When it is not, a bargaining process between the winning firm and the sponsor takes place. Profits from bargaining are larger for the favorite supplier than for its rivals. Given this comparative advantage, the favored firm bids more aggressively and then, it wins more often than standard firms. Finally, we show that the sponsor invests less in specifying the initial design, when favoritism is stronger. Underinvestment in design specification is a tool for providing a comparative advantage to the favored firm.
    Keywords: auctions, favoritism, auction design, renegotiation, corruption
    JEL: I12 J13 H31 H24
    Date: 2021–07
  21. By: Joan-Ramon Borrell (Universitat de Barcelona.); Carlos Suarez (Universidad Jorge Tadeo Lozano, Universitat Barcelona.)
    Abstract: In this paper, we propose a mixed duopoly model in which the public company aims to maximize a weighted function of profits and a function of its production scale. We found that if the weight to the scale of production is high the public firms may exclude its rivals from the market (exercising predatory prices). We also find that the profit sacrifice by the public firm to get this exclusion is higher if there are marked differences between the cost efficiency of private and public firms.
    Keywords: Mixed Oligopoly, Predatory prices, Public firm. JEL classification: L13, L94, C10.
    Date: 2021–07

This nep-gth issue is ©2021 by Sylvain Béal. It is provided as is without any express or implied warranty. It may be freely redistributed in whole or in part for any purpose. If distributed in part, please include this notice.
General information on the NEP project can be found at For comments please write to the director of NEP, Marco Novarese at <>. Put “NEP” in the subject, otherwise your mail may be rejected.
NEP’s infrastructure is sponsored by the School of Economics and Finance of Massey University in New Zealand.