
on Game Theory 
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 ShapleyShubik, Banzhaf, normalized Banzhaf, and DeeganPackel power indices. Moreover, we also show that a coalition structure that represents a twoparty 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 
URL:  http://d.repec.org/n?u=RePEc:wap:wpaper:2015&r=all 
By:  Herings, P. JeanJacques (RS: GSBE Theme DataDriven DecisionMaking, 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 noncooperative game played by the links in the network and adapt the linear tracing procedure for noncooperative games to the network formation problem. As a byproduct 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 
URL:  http://d.repec.org/n?u=RePEc:unm:umagsb:2021004&r=all 
By:  Ville Korpela (Turku School of Economics, University of Turku FI20014, 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 reexamine 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 singlevalued 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 
URL:  http://d.repec.org/n?u=RePEc:tkk:dpaper:dp140&r=all 
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 nonreciprocal relationships between players. Examples for this type of interactions include onesided 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 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2101.03863&r=all 
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 senderreceiver 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 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal03099678&r=all 
By:  Hideo Konishi (Boston College); ChenYu 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 oneshot order choice games and battlebybattle 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 multibattle contest are independent of whether players' assignments are oneshot or battlebybattle 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, multibattle contest, sports economics 
JEL:  C72 D72 D74 D82 
Date:  2021–01–22 
URL:  http://d.repec.org/n?u=RePEc:boc:bocoec:1025&r=all 
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 LPduality theory and their highly nontrivial interplay. Whereas the core of the assignment game is always nonempty, 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 subcoalition has incentive to secede from the grand coalition. Our $2/3$approximate imputation implies that a subcoalition will be able to gain at most a $3/2$ factor by seceding, and less in typical cases. 
Date:  2021–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2101.07390&r=all 
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 mixedbinary 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 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2101.05379&r=all 
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 
URL:  http://d.repec.org/n?u=RePEc:pbs:ecofin:202101&r=all 
By:  Emanuel Vespa; Taylor Weidman; Alistair J. Wilson 
Abstract:  In repeatedgame applications where both the collusive and noncollusive 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 repeatedgame 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 morestandard 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 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2101.05900&r=all 
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 NashCournot model and derive a closedform 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, CournotNash 
JEL:  C72 D43 Q25 
Date:  2021–01–24 
URL:  http://d.repec.org/n?u=RePEc:tin:wpaper:20210011&r=all 
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 winnertakeall 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 winnertakeall 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 winnertakeall 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 winnertakeall 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 gametheoretic 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 welfaredetrimental for the society. 
Date:  2020–10 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs03019446&r=all 
By:  Michelle R. Garfinkel; Constantinos Syropoulos 
Abstract:  On the basis of a singleperiod, gunsversusbutter, completeinformation 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 
URL:  http://d.repec.org/n?u=RePEc:ces:ceswps:_8858&r=all 
By:  Chelsea, Chelsea (Washington State University); EspinolaArredondo, 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 
URL:  http://d.repec.org/n?u=RePEc:ris:wsuwpa:2020_004&r=all 
By:  EspinolaArredondo, 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 freeriding 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 
URL:  http://d.repec.org/n?u=RePEc:ris:wsuwpa:2019_001&r=all 
By:  JulesAlain 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. Celleci 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 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal03112080&r=all 
By:  Susan Martonosi; Banafsheh Behzad; Kayla Cummings 
Abstract:  According to the World Health Organization, development of the COVID19 vaccine is occurring in record time. Administration of the vaccine has started the same year as the declaration of the COVID19 pandemic. The United Nations emphasized the importance of providing COVID19 vaccines as "a global public good", which is accessible and affordable worldwide. Pricing the COVID19 vaccines is a controversial topic. We use optimization and game theoretic approaches to model the COVID19 U.S. vaccine market as a duopoly with two manufacturers PfizerBioNTech 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 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2101.03234&r=all 
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 twostage nfirm 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 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal03042941&r=all 
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 onedimensional differential equations driven by typical paths with nonLipschitz continuous coefficients in the spirit of YamadaWatanabe as well as an approximation result in the spirit of DossSussmann. 
Date:  2021–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2101.08041&r=all 