
on Game Theory 
By:  Frédéric Koessler (PJSE  Paris Jourdan Sciences Economiques  UP1  Université PanthéonSorbonne  ENS Paris  École normale supérieure  Paris  INRA  Institut National de la Recherche Agronomique  EHESS  École des hautes études en sciences sociales  ENPC  École des Ponts ParisTech  CNRS  Centre National de la Recherche Scientifique, PSE  Paris School of Economics); Marie Laclau (PJSE  Paris Jourdan Sciences Economiques  UP1  Université PanthéonSorbonne  ENS Paris  École normale supérieure  Paris  INRA  Institut National de la Recherche Agronomique  EHESS  École des hautes études en sciences sociales  ENPC  École des Ponts ParisTech  CNRS  Centre National de la Recherche Scientifique, PSE  Paris School of Economics); Tristan Tomala (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) 
Abstract:  We study the interaction between multiple information designers who try to influence the behavior of a set of agents. When the set of messages available to each designer is finite, such games always admit subgame perfect equilibria. When designers produce public information about independent pieces of information, every equilibrium of the direct game (in which the set of messages coincides with the set of states) is an equilibrium with larger (possibly infinite) message sets. The converse is true for a class of Markovian equilibria only. When designers produce information for their own corporation of agents, pure strategy equilibria exist and are characterized via an auxiliary normal form game. In an infinitehorizon multiperiod extension of information design games, a feasible outcome which Pareto dominates a more informative equilibrium of the oneperiod game is supported by an equilibrium of the multiperiod game. 
Keywords:  statistical experiments,splitting games,sharing rules,information design,Bayesian persuasion 
Date:  2018–05 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:halshs01791918&r=gth 
By:  Shubhayan Sarkar; Colin Benjamin 
Abstract:  The quantum Nash equilibrium in the thermodynamic limit is studied for games like quantum Prisoner's dilemma and the quantum game of chicken. A phase transition is seen in both games as a function of the entanglement in the game. We observe that for maximal entanglement irrespective of the classical payoffs, a majority of players choose Quantum strategy over Defect in the thermodynamic limit. 
Date:  2018–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1806.07343&r=gth 
By:  Miltiadis Makris (Department of Economics, University of Southampton); Ludovic Renou (Queen Mary University of London) 
Abstract:  We consider multistage games, where at each stage, players receive private signals about past and current states, past actions and past signals, and choose actions. We fully characterize the distributions over actions, states, and signals that obtain in any (sequential) communication equilibrium of any expansion of multistage games, i.e., when players can receive additional signals about past and current states, past actions, and past and current signals (including the additional past signals). We interpret our results as revelation principles for information design problems. We apply our characterization to bilateral bargaining problems. 
Keywords:  multistage games, information design, communication equilibrium, sequential communication equilibrium, information structures, Bayes correlated equilibrium, revelation principle 
JEL:  C73 D82 
Date:  2018–06–25 
URL:  http://d.repec.org/n?u=RePEc:qmw:qmwecw:861&r=gth 
By:  David K Levine 
Date:  2018–07–10 
URL:  http://d.repec.org/n?u=RePEc:cla:levarc:786969000000001474&r=gth 
By:  Hélène Le Cadre (EnergyVille); Bernardo Pagnoncelli (Santiago  University Adolfo Ibanez); Tito HomemDeMello (Santiago  University Adolfo Ibanez); Olivier Beaude 
Abstract:  We model the relation between an aggregator and consumers joining a coalition to reduce the risk resulting from the unpredictability of their base load demand, as a Stackelberg game formulated as a mathematical bilevel program with private information on the consumers' reservation prices. At the upperlevel of the Stackelberg game, the aggregator optimizes his daily price profile so as to reach a net targeted profit which is the maximum value guaranteeing that no consumer will leave the coalition  to contract with a conventional retailer considered here as a fixed alternative  while meeting fairness criterion imposed by the costsharing mechanism. At the lowerlevel, the consumers are asked to provide in day ahead an estimate of their base load hourly demand profile and to schedule their shiftable loads depending on the price signal sent by the aggregator. We provide algorithms that determine the unique price profile and consumer shiftable load schedules as functions of the reservation price estimates. The Stackelberg game between the aggregator and the consumers being repeated for a period of time, the aggregator has the possibility to update his estimates of the reservation prices relying on a feedback function which depends on the percentage of activated loads. A randomized algorithm for consumers' reservation price learning based on regret minimization is provided. For four costsharing mechanisms such as uniform allocation, standalone cost, Shapley value, separable and nonseparable costs, we determine the closed form of the aggregator's optimal net targeted profit guaranteeing the stability of the coalition. We also determine conditions guaranteeing the core nonemptiness and prove that for a profitmaximizing aggregator, the standalone cost is always preferable to the Shapley value, which coincides with the uniform allocation. Furthermore, the optimal size of the coalition  in terms of the aggregator's profit  can be determined analytically when the Shapley value is implemented as costsharing mechanism. The results are illustrated on a case study where we show that there exists an optimal net targeted profit below which the consumers energy bill is lower when joining the aggregator than with the conventional retailer. Coalition dynamics is also analyzed numerically depending on the consumer inertia in their energy supplier choice process, for each costsharing mechanism. 
Keywords:  Forecast Algorithm,Load Scheduling,Coalition Formation,Game Theory,OR in Energy 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal01353763&r=gth 
By:  Kenju Kamei (Durham University Business School) 
Abstract:  One of the important topics in public choice is how people’s freeriding behavior could differ by group size in collective action dilemmas. This paper experimentally studies how the strength of third party punishment in a prisoner’s dilemma could differ by the number of third parties in a group. Our data indicate that as the number of third party punishers increases in a group, the average punishment intensity per third party punisher decreases. However, the decrease rate is very mild and therefore the size of total punishment in a group substantially increases with an increase in group size. As a result, third party punishment becomes a sufficient deterrent against a player selecting defection in the prisoner’s dilemma when the number of third party punishers is sufficiently large. Nevertheless, when there are too many third party punishers in a group, a defector’s expected payoff is far lower than that of a cooperator due to strong aggregate punishment, while some cooperators are even hurt through punishment. Therefore, the group incurs a huge efficiency loss. Such overpunishment results from third party punishers’ conditional punishment behaviors: their punishment intensity is positively correlated with their beliefs on the peers’ punitive actions. Some possible ways to coordinate punishment among peers even when group size is very large, thus enabling the efficiency loss to be mitigated, are also discussed in the paper. 
Keywords:  experiment, cooperation, third party punishment, dilemma, group size effect 
JEL:  C92 D72 D78 H41 
Date:  2018–04 
URL:  http://d.repec.org/n?u=RePEc:dur:durham:2018_04&r=gth 
By:  Joseph Abdou (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique); Hans Keiding (KU  University of Copenhagen) 
Abstract:  We view political activity as an interaction between forces seeking to achieve a political agenda. The viability of a situation depends on the compatibility of such agendas. However even in a conflictual situation a compromise may be possible. Mathematically a political structure is modeled as a simplicial complex and a viable configuration as a simplex. A represented compromise is a viable configuration obtained by the withdrawal of some agents in favor of some friendly representatives. A delegated compromise is a sophisticated version of a compromise obtained by the iteration of the withdrawal process. Existence of such solutions depends on the discrete topology of the simplicial complex. In particular we prove that the existence of a delegated compromise is equivalent to the strong contractibility of the simplicial complex. 
Keywords:  Delegation, compromise, simplicial complex, contiguity,strong homotopy 
Date:  2018–05–19 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal01796062&r=gth 
By:  Robin Lindsey (University of Alberta [Edmonton]); André De Palma (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique); Hugo Silva (Instituto Superior Técnico  Technical University of Lisbon) 
Abstract:  Individual users often control a significant share of total traffic flows. Examples include airlines, rail and maritime freight shippers, urban goods delivery companies and passenger transportation network companies. These users have an incentive to internalize the congestion delays their own vehicles impose on each other by adjusting the timing of their trips. We investigate simultaneous triptiming decisions by large users and small users in a dynamic model of congestion. Unlike previous work, we allow for heterogeneity of triptiming preferences and for the presence of small users such as individual commuters and fringe airlines. We derive the optimal fleet departure schedule for a large user as a bestresponse to the aggregate departure rate of other users. We show that when the vehicles in a large user's fleet have a sufficiently dispersed distribution of desired arrival times, there may exist a purestrategy Nashequilibrium (PSNE) in which the large user schedules vehicles when there is a queue. This resolves the problem of nonexistence of a PSNE identified in Silva et al. (2017) for the case of symmetric large users. We also develop some examples to identify under what conditions a PSNE exists. The examples illustrate how selfinternalization of congestion by a large user can affect the nature of equilibrium and the travel costs that it and other users incur. 
Keywords:  departuretime decisions,bottleneck model,congestion,schedule delay costs,large users,user heterogeneity,existence of Nash equilibrium $ 
Date:  2018–04–06 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal01760135&r=gth 
By:  Atsuhiro Satoh; Yasuhito Tanaka 
Abstract:  We consider the relation between Sion's minimax theorem for a continuous function and a Nash equilibrium in an asymmetric multiplayers zerosum game in which only one player is different from other players, and the game is symmetric for the other players. Then, 1. The existence of a Nash equilibrium, which is symmetric for players other than one player, implies Sion's minimax theorem for pairs of this player and one of other players with symmetry for the other players. 2. Sion's minimax theorem for pairs of one player and one of other players with symmetry for the other players implies the existence of a Nash equilibrium which is symmetric for the other players. Thus, they are equivalent. 
Date:  2018–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1806.07253&r=gth 
By:  Mustapha Ridaoui (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique, PSE  Paris School of Economics); Michel Grabisch (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique, PSE  Paris School of Economics); Christophe Labreuche (Thales Research and Technology [Palaiseau]  THALES) 
Abstract:  We provide an axiomatisation of the Banzhaf value (or power index) and the Banzhaf interaction index for multichoice games, which are generalisation of cooperative games with several levels of participation. Multichoice games can model any aggregation model in multicriteria decision making, provided the attributes take a finite number of values. Our axiomatisation uses standard axioms of the Banzhaf value for classical games (linearity, null axiom, symmetry), an invariance axiom specific to the multichoice context, and a generalisation of the 2efficiency axiom, characteristic of the Banzhaf value. 
Abstract:  Nous donnons une axiomatisation de la valeur de Banzhaf (ou indice de pouvoir) et de l'indice d'interaction de Banzhaf pour les jeux multichoix, qui sont une généralisation des jeux coopératifs avec plusieurs niveaux de participation. Les jeux multichoix peuvent modéliser tout modèle d'agrégation en décision multicritère quand les attributs prennent un nombre fini de valeurs. Notre axiomatisation utilise les axiomes standard de la valeur de Banzhaf pour les jeux classiques (linéarité, axiome nul, symétrie), un axiome d'invariance spécifique au contexte multichoix et une généralisation de l'axiome de 2efficience, caractéristique de la valeur de Banzhaf. 
Keywords:  Banzhaf value,multicriteria decision aid,multichoice games,interaction,jeu multichoix,valeur de Banzhaf,décision multicritère 
Date:  2018–03 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs01814977&r=gth 
By:  Michel Grabisch (Centre d'Economie de la Sorbonne  Paris School of Economics); Tomáš Kroupa (Czech Academy of Sciences, Prague) 
Abstract:  In this article, we study supermodular functions on finite distributive lattices. Relaxing the assumption that the domain is a powerset of a finite set, we focus on geometrical properties of the polyhedral cone of such functions. Specifically, we generalize the criterion for extremal rays and study the face lattice of the supermodular cone. An explicit description of facets by the corresponding tight linear inequalities is provided 
Keywords:  supermodular/submodular function; core; coalitional game; polyhedral cone 
JEL:  C71 
Date:  2018–03 
URL:  http://d.repec.org/n?u=RePEc:mse:cesdoc:18010&r=gth 
By:  Masahiko Hattori; Atsuhiro Satoh; Yasuhito Tanaka 
Abstract:  We consider a symmetric multiplayers zerosum game with two strategic variables. There are $n$ players, $n\geq 3$. Each player is denoted by $i$. Two strategic variables are $t_i$ and $s_i$, $i\in \{1, \dots, n\}$. They are related by invertible functions. Using the minimax theorem by \cite{sion} we will show that Nash equilibria in the following states are equivalent. 1. All players choose $t_i,\ i\in \{1, \dots, n\}$, (as their strategic variables). 2. Some players choose $t_i$'s and the other players choose $s_i$'s. 3. All players choose $s_i,\ i\in \{1, \dots, n\}$. 
Date:  2018–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1806.07203&r=gth 
By:  Christophe Labreuche (Thales Research and Technology [Palaiseau]  THALES); Michel Grabisch (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique, PSE  Paris School of Economics) 
Abstract:  In many MultiCriteria Decision problems, one can construct with the decision maker several reference levels on the attributes such that some decision strategies are conditional on the comparison with these reference levels. The classical models (such as the Choquet integral) cannot represent these preferences. We are then interested in two models. The first one is the Choquet with respect to a pary capacity combined with utility functions, where the pary capacity is obtained from the reference levels. The second one is a specialization of the GeneralizedAdditive Independence (GAI) model, which is discretized to fit with the presence of reference levels. These two models share common properties (monotonicity, continuity, properly weighted, …), but differ on the interpolation means (Lovász extension for the Choquet integral, and multilinear extension for the GAI model). A drawback of the use of the Choquet integral with respect to a pary capacity is that it cannot satisfy decision strategies in each domain bounded by two successive reference levels that are completely independent of one another. We show that this is not the case with the GAI model. 
Abstract:  Dans beaucoup de problème de décision multicritère, on peut construire avec le décideur plusieurs niveaux de référence sur les attributs de telle sorte que des stratégies de décision soient conditionnelles sur la comparaison avec les niveaux de référence. Les modèles classiques (Choquet) ne peuvent représenter ces préférences. Nous nous intéressons à deux modèles, le premier étant Choquet vs. une pcapacité qui est obtenue à partir des niveaux de référence. Le second est une spécialisation du modèle GAI (GeneralizedAdditive Independence). Ces deux modèles ont en commun des propriétés (monotonie, continuité), mais diffèrent sur le type d'interpolation (Lovász, multilinéaire). Un défaut de l'intégrale de Choquet est qu'elle ne satisfait pas les stratégies de décision dans chaque domaine borné par deux niveaux de références indépendants l'un de l'autre. Nous montrons que cela ne peut arriver avec le modèle GAI. 
Keywords:  multiple criteria analysis,Generalized Additive Independence,Choquet integral,reference levels,intégrale de Choquet,niveau de références,interpolation,GAI,analyse multicritère 
Date:  2018–03 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs01815028&r=gth 
By:  Kwiek, Maksymilian (University of Southampton); Marreiros, Helia (Universidade Catolica Portuguesa, Porto); Vlassopoulos, Michael (University of Southampton) 
Abstract:  We study communication in committees selecting one of two alternatives when consensus is required and agents have private information about their preferences. Delaying the decision is costly, so a form of multiplayer war of attrition emerges. Waiting allows voters to express the intensity of their preferences and may help to select the alternative correctly more often than simple majority. In a series of laboratory experiments, we investigate how various rules affect the outcome reached. We vary the amount of feedback and the communication protocol available to voters: complete secrecy about the pattern of support; feedback about this support; public communication; and withingroup communication. The feedback nocommunication mechanism is worse than no feedback benchmark in all measures of welfare  the efficient alternative is chosen less often, waiting cost is higher, and thus net welfare is lower. Our headline result is that adding communication restores net efficiency, but in different ways. Public communication does poorly in terms of selecting the correct alternative, but limits the cost of delay, while group communication improves allocative efficiency, but has at best a moderate effect on delay. 
Keywords:  voting, intensity of preferences, supermajority, conclave, war of attrition, communication 
JEL:  C78 C92 D72 D74 
Date:  2018–06 
URL:  http://d.repec.org/n?u=RePEc:iza:izadps:dp11595&r=gth 
By:  Garcia, Arturo; Leal, Mariel; Lee, SangHo 
Abstract:  This note examines social responsibility in a linear bilateral monopoly by incorporating a costreducing R&D investment and investigates an endogenous timing game. We find that in the presence of R&D, the retailer always adopts social responsibility irrespective of the timing of the game, but the manufacturer adopts only with its leadership in a sequential game where it can take the firstmover advantage. We also show that two sequential choices will be subgame perfect equilibria, but the commitment to the social responsibility by manufacturer is a payoff dominance outcome. 
Keywords:  social responsibility; R&D investment; fixedtiming game; endogenoustiming game 
JEL:  D21 L13 L22 M14 
Date:  2018–05 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:87200&r=gth 
By:  Michel Grabisch (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique, PSE  Paris School of Economics); Christophe Labreuche (Thales Research and Technology [Palaiseau]  THALES); Mustapha Ridaoui (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique, PSE  Paris School of Economics) 
Abstract:  We address in this paper the problem of how to define an importance index in multicriteria decision problems, when a numerical representation of preference is given. We make no restrictive assumption on the model, which could have discrete or continuous attributes, and in particular, it is not assumed that the model is monotonically increasing or decreasing with respect to (w.r.t.) the attributes. Our analysis first considers discrete models, which are seen to be equivalent to multichoice games. We propose essentially two importance indices, namely the signed importance index and the absolute importance index, both based on the average variation of the value of the model induced by a given attribute. We provide several axiomatizations for these importance indices, extend them to the continuous case, and finally illustrate them with examples (classical simple models and a example of discomfort evaluation based on real data). 
Abstract:  Dans ce papier, on s'intéresse au problème de définir un indice d'importance dans un problème de décision multicritère, en supposant une représentation numérique de celuici. Nous ne faisons aucune hypothèse restrictive sur le modèle qui peut avoir des attributs discrets ou continus, et en particulier, on ne suppose pas que le modèle est monotone croissant ou décroissant selon les attributs. Notre analyse considère d'abord des modèles discrets qui sont équivalents à des jeux multichoix. Nous proposons essentiellement deux indices d'importance, à savoir l'indice d'importance signé et l'indice d'importance absolu, tous deux basés sur la variation moyenne de la valeur du modèle induite par un attribut donné. Nous donnons plusieurs axiomatisations de ces indices d'importance, les étendons au cas continu et finalement les illustrons sur des exemples (modèles classiques simples et un exemple d'évaluation d'inconfort sur des données réelles). 
Keywords:  Multiple criteria analysis,Multichoice game,Shapley value,Choquet integral,Décision multicritère,jeu multichoix,valeur de Shapley,intégral de Choquet 
Date:  2018–03 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs01815012&r=gth 
By:  Haraguchi, Junichi; Hirose, Kosuke 
Abstract:  We investigate the endogenous order of moves in a pricesetting mixed oligopoly model, comprising two private firms and a public firm. We show that sequential moves emerge as the equilibrium in the observable delay game. Specifically, one of the private firms and the public firm set their prices in period 1, and the other private firm does so in period 2, in equilibrium, if their goods are not significantly differentiated. This is a clear contrast to a mixed duopoly where a simultaneous move game is a unique equilibrium. We also discuss a number of extensions and the robustness of our result. 
Keywords:  Mixed Markets; Endogenous Timing; Stackelberg 
JEL:  H44 L13 
Date:  2018–06–12 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:87285&r=gth 
By:  Sakshi Gupta (Department of Economics, Columbia University, New York); Ram Singh (Department of Economics, Delhi School of Economics) 
Abstract:  The use of ‘ratio form’ probability of success function dominates the existing literature on contests. Very few works have focused on the ’difference form’functions, notwithstanding their robust theoretical foundations and intuitive appeal in several contexts. Assuming the cost of efforts to be linear, Hirshleifer (1989) and Baik (1998) have argued that under the difference form contests, there is no interior pure strategy Nash equilibrium. In contrast, existence of interior pure strategy Nash equilibrium is well known for the ratio form contest functions. In this paper we use strictly convex cost functions and demonstrate existence of pure strategy Nash equilibrium for the difference form. Moreover, we show that several properties of equilibria and the comparative statics for the difference form closely resemble those for the ratio form. However, unlike the ratio form, under a difference form contest the existence of pure strategy Nash equilibrium is sensitive to the value of the prize. 
Date:  2018–05 
URL:  http://d.repec.org/n?u=RePEc:cde:cdewps:288&r=gth 
By:  Patrice CASSAGNARD; Pierre REGIBEAU 
Abstract:  We propose a simple twostages duopoly game where two firms produce an homogeneous good to satisfy the demand in a foreign market. First they decide whether to serve this market with exports or with foreign direct investments and then they play a oneshot CournotNash game. This game has been made even more complex by the fact that foreign direct investments induce technological spillovers which imply the possible entry of a third firm. From the complete characterization of the equilibria we show that a small disadvantage of one of the both firms can conduce this firm to invest alone in the foreign country rather than export. In this case, the investment is motivated by the fact that the dissipation risk of both firmspecific assets to a local potential entrant triopoly payoffs is beared by the two firms whereas the gain increased market share in duopoly is captured by the firm which chooses to invest abroad. We have in mind the competition between Airbus and Boeing in China. 
Keywords:  Entry Deterrence ; FDI ; Export ; Cournot duopoly ; Spillovers ; Airbus and Boeing 
Date:  2018–07 
URL:  http://d.repec.org/n?u=RePEc:tac:wpaper:20172018_11&r=gth 