nep-gth New Economics Papers
on Game Theory
Issue of 2021‒02‒08
nineteen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Stable Coalition Structures and Power Indices for Majority Voting By Takaaki Abe
  2. The computation of pairwise stable networks By Herings, P. Jean-Jacques; Zhan, Yang
  3. Implementation with farsighted agents By Ville Korpela; Michele Lombardi; Hannu Vartiainen
  4. Best-response dynamics in directed network games By P\'eter Bayer; Gy\"orgy Kozics; N\'ora Gabriella Sz\H{o}ke
  5. Robust communication on networks By Marie Laclau; Ludovic Renou; Xavier Venel
  6. Equilibrium Player Choices in Team Contests with Multiple Pairwise Battles By Hideo Konishi; Chen-Yu Pan; Dimitar Simeonov
  7. The General Graph Matching Game: Approximate Core By Vijay V. Vazirani
  8. Copositive Duality for Discrete Markets and Games By Cheng Guo; Merve Bodur; Joshua A. Taylor
  9. Predicting Efficiency in Threshold Public Good Games: A Learning Direction Theory Approach By Federica Alberti; Anna Cartwright; Edward Cartwright
  10. Testing Models of Strategic Uncertainty: Equilibrium Selection in Repeated Games By Emanuel Vespa; Taylor Weidman; Alistair J. Wilson
  11. Market power in California's water market By Françeska Tomori; Erik Ansink; Harold Houba; Nick Hagerty; Charles Bos
  12. Trapped by the Prisoner’s Dilemma, the United States Presidential Election Needs a Coordination Device By Héloïse Cloléry; Yukio Koriyama
  13. Self-Enforcing Peace Agreements that Preserve the Status Quo By Michelle R. Garfinkel; Constantinos Syropoulos
  14. Fungicide Resistance and Misinformation: A Game Theoretic Approach By Chelsea, Chelsea; Espinola-Arredondo, Ana
  15. Regulators and Environmental Groups: Substitutes or Complements? By Espinola-Arredondo, Ana; Stathopoulou, Eleni; Munoz, Felix
  16. Competitive Strategy : a multifaceted Strategy ? By Jules-Alain Ngan
  17. Pricing the COVID-19 Vaccine: A Mathematical Approach By Susan Martonosi; Banafsheh Behzad; Kayla Cummings
  18. Competition and private R&D investment By Thomas Grebel; Lionel Nesta
  19. One-dimensional game-theoretic differential equations By Rafa{\l} M. {\L}ochowski; Nicolas Perkowski; David J. Pr\"omel

  1. By: Takaaki Abe (School of Political Science and Economics, Waseda University)
    Abstract: An (n,k)-game is a voting game in which each player has exactly one vote, and decisions are made by at least k affirmative votes of the n players. A power index is a measure of the a priori power of the n voters. The purpose of this paper is to show what axioms of power indices generate stable coalition structures for each (n,k)-game. Using the stability notion of the core, we show that a coalition structure containing a minimal winning coalition is stable for a wide range of general power indices satisfying a set of axioms, such as the Shapley-Shubik, Banzhaf, normalized Banzhaf, and Deegan-Packel power indices. Moreover, we also show that a coalition structure that represents a two-party system can be stable if the two large parties are close enough in size. Some unstable coalition structures are also analyzed.
    Keywords: coalition structure; core; majority voting; power index
    JEL: C71
    Date: 2020–10
  2. By: Herings, P. Jean-Jacques (RS: GSBE Theme Data-Driven Decision-Making, RS: GSBE Theme Conflict & Cooperation, Microeconomics & Public Economics); Zhan, Yang
    Abstract: One of the most important stability concepts for network formation is pairwise stability. We develop a homotopy algorithm that is effective in computing pairwise stable networks for a generic network formation problem. To do so, we reformulate the concept of pairwise stability as a Nash equilibrium of a non-cooperative game played by the links in the network and adapt the linear tracing procedure for non-cooperative games to the network formation problem. As a by-product of our main result, we obtain that the number of pairwise stable networks is generically odd. We apply the algorithm to the connections model.
    Date: 2021–01–26
  3. By: Ville Korpela (Turku School of Economics, University of Turku FI-20014, Finland); Michele Lombardi (Adam Smith Business School, University of Glasgow; Department of Economics and Statistics, University of Naples); Hannu Vartiainen (University of Helsinki and Helsinki Graduate School of Economics, Finland)
    Abstract: Agents are farsighted when they consider the ultimate consequences of their actions. We re-examine the classical questions of implementation theory under complete information in a setting with transfers, where farsighted coalitions are considered fundamental behavioral units, and the equilibrium outcomes of their interactions are predicted via the stability notion of the largest consistent set. The designer’s exercise consists of designing a rights structure that formalizes the idea of power distribution in society. The designer’s challenge lies in forming a rights structure in which the equilibrium behavior of agents always coincides with the recommendation given by a social choice rule. We show that (Maskin) monotonicity fully identifies the class of implementable single-valued social choice rules. Even though, monotonicity is not necessary for implementation in general, we show that every monotonic social choice rule can be implemented. These findings imply that the class of implementable social choice rules in core equilibria is unaltered by farsighted reasoning.
    Keywords: Implementation, rights structures, largest consistent set, core, (Maskin) monotonicity
    JEL: C72 C78 D71
    Date: 2021–01
  4. By: P\'eter Bayer; Gy\"orgy Kozics; N\'ora Gabriella Sz\H{o}ke
    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. It is well known that many simple learning processes converge to a Nash equilibrium if interactions are reciprocal, but this is not true in general for directed networks. However, by a simple tool of rescaling the strategy space, we generalize the convergence result for a class of directed networks and show that it is characterized by transitive weight matrices. Additionally, we show convergence in a second class of networks; those rescalable into networks with weak externalities. We characterize the latter class by the spectral properties of the absolute value of the network's weight matrix and show that it includes all directed acyclic networks.
    Date: 2021–01
  5. By: Marie Laclau (CNRS - Centre National de la Recherche Scientifique, GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique, HEC Paris - Ecole des Hautes Etudes Commerciales); Ludovic Renou (QMUL - Queen Mary University of London, University of Adelaide); Xavier Venel (LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma])
    Abstract: We consider sender-receiver games, where the sender and the receiver are two distinct nodes in a communication network. Communication between the sender and the receiver is thus indirect. We ask when it is possible to robustly implement the equilibrium outcomes of the direct communication game as equilibrium outcomes of indirect communication games on the network. Robust implementation requires that: (i) the implementation is independent of the preferences of the intermediaries and (ii) the implementation is guaranteed at all histories consistent with unilateral deviations by the intermediaries. We show that robust implementation of direct communication is possible if and only if either the sender and receiver are directly connected or there exist two disjoint paths between the sender and the receiver. We also show that having two disjoint paths between the sender and the receiver guarantees the robust implementation of all communication equilibria of the direct game. We use our results to reflect on organizational arrangements.
    Keywords: Cheap talk,direct,mediated,communication,protocol,network. JEL CLASSIFICATION: C72,D82
    Date: 2021–01–06
  6. By: Hideo Konishi (Boston College); Chen-Yu Pan (Wuhan University); Dimitar Simeonov (Boston College)
    Abstract: We consider games in which team leaders strategically choose the order of players sent to the battlefield in majoritarian team contests with multiple pairwise battles as in Fu, Lu, and Pan (2015 American Economic Review). We consider one-shot order choice games and battle-by-battle sequential player choice games. We show that as long as the number of players on each team is the same as the number of battles, the equilibrium winning probability of a team and the ex ante expected effort of each player in a multi-battle contest are independent of whether players' assignments are one-shot or battle-by-battle sequential. This equilibrium winning probability and ex ante expected total effort coincide with those where the player matching is chosen totally randomly with an equal probability lottery by the contest organizer. Finally, we show how player choices add subtleties to the equivalence result by examples.
    Keywords: group contest, team contest, multi-battle contest, sports economics
    JEL: C72 D72 D74 D82
    Date: 2021–01–22
  7. By: Vijay V. Vazirani
    Abstract: The classic paper of Shapley and Shubik \cite{Shapley1971assignment} characterized the core of the assignment game using powerful ideas from matching theory and LP-duality theory and their highly non-trivial interplay. Whereas the core of the assignment game is always non-empty, that of the general graph matching game the core can be empty. This paper salvages the situation by giving an imputation in the $2/3$-approximate core for the latter. We show that this bound is best possible -- it is the integrality gap of the natural underlying LP. Our profit allocation method goes further: the multiplier on the profit of an agent lies in the interval $[{2 \over 3}, 1]$, depending on how severely constrained the agent is. The core is a quintessential solution concept in cooperative game theory. It contains ways of distributing the total worth of a game among agents in such a way that no sub-coalition has incentive to secede from the grand coalition. Our $2/3$-approximate imputation implies that a sub-coalition will be able to gain at most a $3/2$ factor by seceding, and less in typical cases.
    Date: 2021–01
  8. By: Cheng Guo; Merve Bodur; Joshua A. Taylor
    Abstract: Optimization problems with discrete decisions are nonconvex and thus lack strong duality, which limits the usefulness of tools such as shadow prices and the KKT conditions. It was shown in Burer(2009) that mixed-binary quadratic programs can be written as completely positive programs, which are convex. Completely positive reformulations of discrete optimization problems therefore have strong duality if a constraint qualification is satisfied. We apply this perspective in two ways. First, we write unit commitment in power systems as a completely positive program, and use the dual copositive program to design a new pricing mechanism. Second, we reformulate integer programming games in terms of completely positive programming, and use the KKT conditions to solve for pure strategy Nash equilibria. To facilitate implementation, we also design a cutting plane algorithm for solving copositive programs exactly.
    Date: 2021–01
  9. By: Federica Alberti (University of Portsmouth); Anna Cartwright (Coventry University); Edward Cartwright (De Montfort University)
    Abstract: In this paper we propose a tractable model of behavior in threshold public good games. The model is based on learning direction theory. We find that individual behavior is consistent with the predictions of the model. Moreover, the model is able to accurately predict the success rate of groups in providing the public good. We apply this to give novel insight on the assurance problem by showing that the problem (of coordinating on the inefficient equilibrium of no contributions) is only likely with a relatively low endowment. In developing the model we compare and contrast best reply learning and impulse balance theory. Our results suggest that best reply learning provides a marginally better fit with the data.
    Keywords: public good, threshold, learning direction theory, impulse balance theory, counterfactual thinking
    JEL: C72 H41 C92
    Date: 2021–01–27
  10. By: Emanuel Vespa; Taylor Weidman; Alistair J. Wilson
    Abstract: In repeated-game applications where both the collusive and non-collusive outcomes can be supported as equilibria, researchers must resolve underlying selection questions if theory will be used to understand counterfactual policies. One guide to selection, based on clear theoretical underpinnings, has shown promise in predicting when collusive outcomes will emerge in controlled repeated-game experiments. In this paper we both expand upon and experimentally test this model of selection, and its underlying mechanism: strategic uncertainty. Adding an additional source of strategic uncertainty (the number of players) to the more-standard payoff sources, we stress test the model. Our results affirm the model as a tool for predicting when tacit collusion is likely/unlikely to be successful. Extending the analysis, we corroborate the mechanism of the model. When we remove strategic uncertainty through an explicit coordination device, the model no longer predicts the selected equilibrium.
    Date: 2021–01
  11. By: Françeska Tomori (Universitat Rovira i Virgili); Erik Ansink (Vrije Universiteit Amsterdam); Harold Houba (Vrije Universiteit Amsterdam); Nick Hagerty (Montana State University); Charles Bos (Vrije Universiteit Amsterdam)
    Abstract: We estimate market power in California's thin water market. Market frictions may distort the potential welfare gains from water marketing. We use a Nash-Cournot model and derive a closed-form solution for the extent of market power in a typical water market setting. We then use this solution to estimate market power in a newly assembled dataset on California's water economy. We show that, under the assumptions of the Cournot model, market power in this thin market is limited.
    Keywords: Water markets, Market power, California, Cournot-Nash
    JEL: C72 D43 Q25
    Date: 2021–01–24
  12. By: Héloïse Cloléry; Yukio Koriyama (X - École polytechnique)
    Abstract: Summary: The system according to which the President of the United States of America is elected, the Electoral College, has often raised concerns. Among those, the winner-take-all rule is often criticized for potentially – and in recent years effectively – bringing to power a president who has not obtained the majority of the popular vote. This note shows that most of the reform proposals have failed due to the structure of the problem: the US Presidential Election is trapped by the Prisoner's Dilemma. Each state would rationally choose the winner-take-all rule in order to best reflect its citizens' preferences on the federal decision. However, the outcome of such a choice, if adopted by all states, would not be desirable for the nation as a whole, because it prevents the optimal aggregation of all citizens' preferences. A weighted proportional rule, if used by all states, would make all citizens better off by reflecting their preferences on the final decision more accurately. However, since each state has an incentive to adopt the winner-take-all rule regardless of the choice of the other states, it is impossible for all the states to adopt such a rule without a coordination device. We therefore analyze interesting attempts to escape from this dilemma, such as the National Popular Vote Interstate Compact, and how our framework applies to representative democracy. Key points: The winner-take-all rule has been used almost exclusively in the US presidential elections since the 1830s, but has been criticized for various reasons. One of these is the occasional discrepancy between the election winner and the national popular vote results (e.g. George W. Bush vs. Al Gore in 2000, and Donald Trump vs. Hilary Clinton in 2016). The structure of the problem can be described with a game-theoretic analysis, at least partially: the Electoral College system is trapped by the Prisoner's Dilemma. States could benefit from cooperating, but they do not achieve this because each state does not have any guarantee that the other states would join a cooperative action. A coordination device is necessary in order to escape from the dilemma. Some interesting attempts, such as the National Popular Vote Interstate Compact, are underway. The same structure of the dilemma appears in representative democracy. Party discipline may induce distortion of the preference aggregation and thus may be welfare-detrimental for the society.
    Date: 2020–10
  13. By: Michelle R. Garfinkel; Constantinos Syropoulos
    Abstract: On the basis of a single-period, guns-versus-butter, complete-information model in which two agents dispute control over an insecure portion of their combined output, we study the choice between a peace agreement that maintains the status quo without arming (or unarmed peace) and open conflict (or war) that is possibly destructive. With a focus on outcomes that are immune to both unilateral deviations and coalitional deviations, we find that, depending on war’s destructive effects, the degree of output security and the initial distribution of resources, peace can, but need not necessarily, emerge in equilibrium. We also find that, ex ante resource transfers without commitments can improve the prospects for peace, but only when the configuration of parameters describing the degree of output security and the degree of war’s destruction ensure the possibility of peace without such transfers at least for some sufficiently even initial resource distributions.
    Keywords: disputes, output insecurity, destructive wars, peaceful settlement, unarmed peace
    JEL: D30 D74 F51
    Date: 2021
  14. By: Chelsea, Chelsea (Washington State University); Espinola-Arredondo, Ana (Washington State University)
    Abstract: Fungicide resistance developed by pathogens that grapes are susceptible to is problematic for the industry today. We provide further insight into the strategic behavior of grape growers when their choices of fungicide levels generate a negative intertemporal production externality in the form of fungicide resistance. We find that when growers encounter this type of externality, the noncooperative fungicide level is higher than the socially optimal level. We examine a compensation mechanism designed to ameliorate fungicide resistance and find that it induces the socially optimal level; however, misinformation about the severity of the fungicide resistance generates distortions. The results suggest that the information available to growers about fungicide resistance is essential for its mitigation with the proposed compensation mechanism. In particular, we find that if the misinformed grower considers fungicide resistance to be relatively mild, then it is preferable that the misinformed grower has the compensating role.
    Keywords: Fungicide resistance; game theory; compensation mechanism; intertemporal externality; misinformation
    JEL: C73 D21 H23 Q16
    Date: 2022–10–20
  15. By: Espinola-Arredondo, Ana (Washington State University); Stathopoulou, Eleni (University of Leicester); Munoz, Felix (Washington State University)
    Abstract: This paper examines green alliances between environmental groups and polluting firms, which have become more common in the last decades, and analyzes how they a¤ect policy design. We first show that the activities of regulators and environmental groups are strategic substitutes, giving rise to free-riding incentives on both agents. Nonetheless, we find that the presence of the environmental group alone yields no welfare bene?t, as firms have no incentives to alter their abatement decisions when they do not face regulation. Therefore, the introduction of environmental groups yields a welfare gain when firms are already subject to regulation, suggesting that the former cannot completely replace environmental policy.
    Keywords: Abatement; Emission fees; R&D disruptive e¤ects; Equilibrium pro?les; Spillovers
    JEL: H23 L12 Q58
    Date: 2019–03–12
  16. By: Jules-Alain Ngan (UNISTRA - Université de Strasbourg)
    Abstract: This Summary Note focuses on the Analysis of competitive Strategy studied in managerial Economics. This seems to be relevant as a Synthesis of the Strategies drawn from Game Theory and Management. To the substantive Rationality or perfect Rationality highlighted in economic Theory — which consists in referring to the optimal Result to define a Strategy — we prefer the limited Rationality or procedural Rationality according to which Individual uses the Possibilities available to solve the Problems, the Process being as satisfactory and important as the optimal Result which could be obtained in a complex economic Environment.
    Abstract: Cette note de synthèse porte sur l'analyse de la stratégie compétitive étudiée en économie managériale. Celle-ci semble pertinente en tant que synthèse des stratégies tirées de la théorie des jeux et du management. À la rationalité substantive ou rationalité parfaite mise en évidence en théorie économique — qui consiste à se référer au résultat optimal pour définir une stratégie — nous préférons la rationalité limitée ou rationalité procédurale selon laquelle on se sert des possibilités dont on dispose pour résoudre les problèmes auxquels on est confronté, le processus dans lequel on est engagé étant aussi satisfaisant et important que le résultat optimal qu'on pourrait éventuellement obtenir dans un environnement économique complexe.
    Keywords: Strategy,Game Theory,Management,managerial Economics.,stratégie,théorie des jeux,management,économie managériale.
    Date: 2020–01–23
  17. By: Susan Martonosi; Banafsheh Behzad; Kayla Cummings
    Abstract: According to the World Health Organization, development of the COVID-19 vaccine is occurring in record time. Administration of the vaccine has started the same year as the declaration of the COVID-19 pandemic. The United Nations emphasized the importance of providing COVID-19 vaccines as "a global public good", which is accessible and affordable world-wide. Pricing the COVID-19 vaccines is a controversial topic. We use optimization and game theoretic approaches to model the COVID-19 U.S. vaccine market as a duopoly with two manufacturers Pfizer-BioNTech and Moderna. The results suggest that even in the context of very high production and distribution costs, the government can negotiate prices with the manufacturers to keep public sector prices as low as possible while meeting demand and ensuring each manufacturer earns a target profit. Furthermore, these prices are consistent with those currently predicted in the media.
    Date: 2020–12
  18. By: Thomas Grebel; Lionel Nesta (Université Côte d'Azur, CNRS, GREDEG (France))
    Abstract: We investigate the determinants of the sign of Research and Development reaction functions of rival firms. Using a two-stage n-firm Cournot competition game, we show that this sign depends on four types of environments in terms of product rivalry and technology spillovers. We test the predictions of the model on the world's largest manufacturing corporations. Assuming that firms make R&D investments based on the R&D effort of the representative rival company, we develop a dynamic panel data model that accounts for the endogeneity of the decision of the rival firm. Empirical results thoroughly corroborate the validity of the theoretical model.
    Date: 2020–05–27
  19. By: Rafa{\l} M. {\L}ochowski; Nicolas Perkowski; David J. Pr\"omel
    Abstract: We provide a very brief introduction to typical paths and the corresponding It\^o type integration. Relying on this robust It\^o integration, we prove an existence and uniqueness result for one-dimensional differential equations driven by typical paths with non-Lipschitz continuous coefficients in the spirit of Yamada--Watanabe as well as an approximation result in the spirit of Doss--Sussmann.
    Date: 2021–01

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