
on Game Theory 
By:  Dmitry Levando (National Research University Higher School of Economics [Moscow], CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique) 
Abstract:  Traditionally social sciences are interested in structuring people in multiple groups based on their individual preferences. This paper suggests an approach to this problem in the framework of a noncooperative game theory. Definition of a suggested finite game includes a family of nested simultaneous noncooperative finite games with intra and intercoalition externalities. In this family, games differ by the size of maximum coalition, partitions and by coalition structure formation rules. A result of every game consists of partition of players into coalitions and a payoff profile for every player. Every game in the family has an equilibrium in mixed strategies with possibly more than one coalition. The results of the game differ from those conventionally discussed in cooperative game theory, e.g. the Shapley value, strong Nash, coalitionproof equilibrium, core, kernel, nucleolus. We discuss the following applications of the new game: cooperation as an allocation in one coalition, Bayesian games, stochastic games and construction of a noncooperative criterion of coalition structure stability for studying focal points. 
Keywords:  Noncooperative games,Nash equilibrium,Shapley value,strong equilibrium,core 
Date:  2017–05 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs01491935&r=gth 
By:  Besner, Manfred 
Abstract:  Shapley (1953a) introduced the weighted Shapley values as a family of values, also known as Shapley set. For each exogenously given weight system exists a seperate TUvalue. Shapley (1981) and Dehez (2011), in the context of cost allocation, and Radzik (2012), in general, presented a value for weighted TUgames that covers the hole family of weighted Shapley values all at once. To distinguish this value from a weighted Shapley value in TUgames we call it Shapley set value. This value coincides with a weighted Shapley value only on a subdomain and allows weights which can depend on coalition functions. Hammer (1977) and Vasil’ev (1978) introduced independently the Harsanyi set, also known as selectope (Derks, Haller and Peters, 2000), containing TUvalues which are referred to as Harsanyipayoffs. These values are obtained by distributing the dividends from all coalitions by a sharing system that is independent from the coalition function. In this paper we introduce the Harsanyi set value that, similar to the Shapley set value, covers the hole family of Harsanyi payoffs at once, allows not exogenously given share systems and coincides thus also with non linear values on some subdomains. We present some new axiomatizations of the Shapley set value and the Harsanyi set value containing a player splitting or a players merging property respectively as a main characterizing element that recommend these values for profit distribution and cost allocation. 
Keywords:  Cost allocation · Profit distribution · Player splitting · Players merging · Shapley set value · Harsanyi set value 
JEL:  C70 C71 
Date:  2018–06–01 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:87125&r=gth 
By:  Tomala, Tristan; Koessler, Frederic; Laclau, Marie 
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:  Bayesian persuasion; information design; sharing rules; splitting games; statistical experiments. 
JEL:  C72 D82 
Date:  2018–04–25 
URL:  http://d.repec.org/n?u=RePEc:ebg:heccah:1260&r=gth 
By:  Besner, Manfred 
Abstract:  The proportional Shapley value (Besner 2016; Béal et al. 2017; Gangolly 1981) is an proportional counterpart to the Shapley value (Shapley 1953b) in cooperative games. As shown in Besner (2017a), the proportional Shapley value is a convincing nonlinear alternative, especially in cost allocation, if the stand alone worths of the players are plausible weights. To enable similar properties for cooperative games with a level structure, we generalize this value. Therefore we adapt the proceeding applied to the weighted Shapley values in Besner (2017b). We present, analogous to the four classes of weighted Shapley levels values in Besner (2017b), four different values, the proportional Shapley hierarchy levels value, the proportional Shapley support levels value, the proportional Shapley alliance levels value and the proportional Shapley collaboration levels value, respectively. 
Keywords:  Cooperative game · Level structure · (Proportional) Shapley (levels) value · Proportionality · Component substitution · Dividends 
JEL:  C70 C71 
Date:  2018–06–01 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:87120&r=gth 
By:  Tomohiko Konno; Yannis M. Ioannides 
Abstract:  This paper proposes a logit response game with a spatial social structure and solves it exactly. We derive closedform solutions for the strategy choice probabilities, the spatial correlation function of strategies of distant players, and the expected utility. We study how the prob ability of adopting a cooperative strategy in a prisoner's dilemma game and the probability of adopting Pareto efficient strategies in a cooperation game are affected by changes in the parameter that expresses payoffresponsiveness. 
Keywords:  Spatial Logit Game, Exact solution, Network,Logit Local Interaction, Competi tion with Spatial Structure, Spatial coordination game 
JEL:  R00 R30 R32 R39 D21 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:tuf:tuftec:0827&r=gth 
By:  Satoh, Atsuhiro; Tanaka, Yasuhito 
Abstract:  We consider the relation between Sion's minimax theorem for a continuous function and a Nash equilibrium in an asymmetric threeplayers zerosum game with two groups. Two players are in Group A, and they have the same payoff function and strategy space. One player, Player C, is in Group C. Then, 1. The existence of a Nash equilibrium, which is symmetric in Group A, implies Sion's minimax theorem for pairs of a player in Group A and Player C with symmetry in Group A. 2. Sion's minimax theorem for pairs of a player in Group A and Player C with symmetry in Group A implies the existence of a Nash equilibrium which is symmetric in Group A. Thus, they are equivalent. 
Keywords:  threeplayers zerosum game, two groups, Nash equilibrium, Sion's minimax theorem 
JEL:  C72 
Date:  2018–06–09 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:87249&r=gth 
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:  Regarding the approximation of Nash equilibria in games where the players have a continuum of strategies, there exist various algorithms based on adjustment processes: from one step to the next, one player updates his strategy solving an optimization problem where the strategies of the other players come from the previous steps. These iterative schemes generate sequences of strategy profiles which are constructed by using continuous optimization techniques and which converge to a Nash equilibrium of the game. In this paper, we propose an adjustment process based on continuous optimization which guarantee the convergence to a Nash equilibrium in twoplayer non zerosum games when the best response functions are not linear, both compositions of the best response functions are not contractions, and the strategy sets are Hilbert spaces. Firstly, we address the issue of uniqueness of the Nash equilibrium extending to a more general class the result obtained in F. Caruso, M.C. Ceparano, and J. Morgan (J Math Anal Appl 2018) for weighted potential games. Secondly, we describe a theoretical adjustment process involving the best response functions which converges to the unique Nash equilibrium of the game. Finally, in order to ap proximate the unique Nash equilibrium of the game, we present a discretization scheme and a numerical adjustment process based on continuous optimization, and we compute error bounds. 
Keywords:  Noncooperative game; Approximation of Nash equilibrium; Uniqueness of Nash equilibrium; Fixed point; Adjustment process; Best response; Error bound. 
Date:  2018–06–25 
URL:  http://d.repec.org/n?u=RePEc:sef:csefwp:502&r=gth 
By:  Alexandre Skoda (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique) 
Abstract:  We consider restricted games on weighted graphs associated with minimum partitions. We replace in the classical definition of Myerson restricted game the connected components of any subgraph by the subcomponents corresponding to a minimum partition. This minimum partition Pmin is induced by the deletion of the minimum weight edges. We provide five necessary conditions on the graph edgeweights to have inheritance of convexity from the underlying game to the restricted game associated with Pmin. Then, we establish that these conditions are also sufficient for a weaker condition, called Fconvexity, obtained by restriction of convexity to connected subsets. Moreover, we prove that inheritance of convexity for Myerson restricted game associated with a given graph G is equivalent to inheritance of Fconvexity for the Pminrestricted game associated with a particular weighted graph G' built from G by adding a dominating vertex, and with only two different edgeweights. Then, we prove that G is cyclecomplete if and only if a specific condition on adjacent cycles is satisfied on G'. 
Keywords:  partitions,restricted game,convex game,communication networks,cooperative game 
Date:  2017–08 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs01659804&r=gth 
By:  Marcel Nutz; Jaime San Martin; Xiaowei Tan 
Abstract:  We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of $n$player equilibria converges to it as $n\to\infty$. However, both the finite and infinite player versions of the game often admit multiple equilibria. We show that mean field equilibria satisfying a transversality condition are limit points of $n$player equilibria, but we also exhibit a remarkable class of mean field equilibria that are not limits, thus questioning their interpretation as "large $n$" equilibria. 
Date:  2018–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1806.00817&r=gth 
By:  Effrosyni Diamantoudi (Department of Economics, Concordia University); Eftichios Sartzetakis (Department of Economics, University of Macedonia); Stefania Strantza (Department of Economics, Concordia University) 
Abstract:  The present paper examines the stability of selfenforcing International Environmental Agreements (IEAs) among heterogeneous countries in a twostage emission game. In the first stage each country decides whether or not to join the agreement, while in the second stage the quantity of emissions is chosen simultaneously by all countries. We use quadratic benefit and environmental damage functions and assume k types of countries that differ in their sensitivity to the global pollutant. We find that the introduction of heterogeneity does not yield larger stable coalitions. In particular, we show that, in the case of two types, when stable coalitions exist their size is very small, and, if the asymmetry is strong enough, they include only one type of countries. Moreover, heterogeneity can reduce the scope of cooperation relative to the homogeneous case. We demonstrated that introducing asymmetry into a stable, under symmetry, agreement can disturb stability. 
Keywords:  Environmental Agreements 
JEL:  D6 Q5 C7 
Date:  2018–07 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2018.22&r=gth 
By:  Marta Leniec (Uppsala University); Kristoffer Glover (Finance Discipline Group, University of Technology Sydney); Erik Ekström (Uppsala University) 
Abstract:  We study zerosum optimal stopping games (Dynkin games) between two players who disagree about the underlying model. In a Markovian setting, a verification result is established showing that if a pair of functions can be found that satisfies some natural conditions then a Nash equilibrium of stopping times is obtained, with the given functions as the corresponding value functions. In general, however, there is no uniqueness of Nash equilibria, and different equilibria give rise to different value functions. As an example, we provide a thorough study of the game version of the American call option under heterogeneous beliefs. Finally, we also study equilibria in randomized stopping times. 
Keywords:  Dynkin game; heterogeneous belief; multiple Nash equilibria; optimal stopping theory 
Date:  2017–01–01 
URL:  http://d.repec.org/n?u=RePEc:uts:ppaper:20172&r=gth 
By:  Simon Schopohl (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique, EDEEM  Université Paris 1  EDEEM  European Doctorate in Economics Erasmus Mundus, Universität Bielefeld (GERMANY), UCL  Université Catholique de Louvain) 
Abstract:  We analyze a game in which players with unique information are arranged in a hierarchy. In the lowest layer each player can decide in each of several rounds either to pass the information to his successor or to hold. While passing generates an immediate payoff according to the value of information, the player can also get an additional reward if he is the last player to pass. Facing this problem while discounting over time determines the player's behavior. Once a successor has collected all information from his workers he starts to play the same game with his successor. We state conditions for different Subgame Perfect Nash Equilibria and analyse the time it takes each hierarchy to centralize the information. This allows us to compare different structures and state which structure centralizes fastest depending on the information distribution and other parameters. We show that the time the centralization takes is mostly affected by the least informed players. 
Keywords:  communication network,dynamic network game,hierarchical structure,information transmission 
Date:  2017–02 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs01491930&r=gth 
By:  Guilhem Lecouteux (Université Côte d'Azur; GREDEG CNRS) 
Abstract:  This editorial presents the main contributions of the theory of team reasoning in game theory, and the issues that remain to be solved before this theory could become a credible alternative to 'orthodox' game theory. I argue in particular that an approach based on collective agency rather than rational choice theory and social preferences offer a scientifically preferable theory of unselfish behaviours, both in terms of parsimony and empirical validation. I review the economic literature on team reasoning, and highlight the contributions of the papers of the present volume to tackle the open issues of the theory of team reasoning. 
Keywords:  team reasoning, preferences, rationality, cooperation, coordination 
JEL:  B41 C72 D70 
Date:  2018–07 
URL:  http://d.repec.org/n?u=RePEc:gre:wpaper:201817&r=gth 
By:  A Skoda (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique) 
Abstract:  We consider restricted games on weighted graphs associated with minimum partitions. We replace in the classical definition of Myerson restricted game the connected components of any subgraph by the subcomponents corresponding to a minimum partition. This minimum partition Pmin is induced by the deletion of the minimum weight edges. We provide a characterization of the graphs satisfying inheritance of convexity from the underlying game to the restricted game associated with P min. 
Keywords:  partitions ,cooperative game,convex game,restricted game 
Date:  2017–10 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs01660670&r=gth 
By:  Lily Ling Yang 
Abstract:  In this paper, we employ a novel approach to study the value of information in games. A decision problem is relevant to another if the optimal decision rule of the former, when applied to the latter, is better than making a decision without any information in the latter. In a game, if the problem originally faced by a player is relevant to the problem induced by a change of the situation, the player benefits more from her own information after the change. Using the notion of relevance, we study the value of information in various games, even when a closed form solution is not available. 
Keywords:  Value of information, Quadratic game, Global game, Persuasion game 
JEL:  D81 D83 
Date:  2018–06 
URL:  http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_025_2018&r=gth 
By:  Antoine Mandel (PSE  Paris School of Economics, CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique); Xavier Venel (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique, PSE  Paris School of Economics) 
Abstract:  We provide an analytical approach to the problem of influence maximization in a social network when two players compete by means of dynamic targeting strategies. We formulate the problem as a twoplayer zerosum stochastic game. We prove the existence of the uniform value: if the players are sufficiently patient, both players can guarantee the same meanaverage opinion without knowing the exact discount factor. Further, we put forward some elements for the characterization of equilibrium strategies. In general, players must implement a tradeoff between a forwardlooking perspective, according to which they shall aim at maximizing the future spread of their opinion in the network, and a backwardlooking perspective, according to which they shall aim at counteracting their opponent's previous actions. When the influence potential of players is small, an equilibrium strategy is to systematically target the agent with the largest eigenvector centrality. 
Abstract:  Nous proposons une approche analytique au problème de maximisation de l'influence dans un réseau social entre deux joueurs utilisant des stratégies dynamiques. Le problème est formulé comme un jeu stochastique à somme nulle. Nous prouvons l'existence de la valeur uniforme et donnons une caractérisation partielle des stratégies d'équilibre. Nous montrons notamment que lorsque l'influence exercée par les agents est faible, ces derniers doivent systématiquement cibler l'agent avec la centralité "vecteur propre" la plus élevée. 
Keywords:  Stochastic games,Social network,Dynamic games,Targeting,Jeux stochastiques,Jeux dynamiques,Réseaux sociaux 
Date:  2017–04 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs01524453&r=gth 
By:  Alexandre Skoda (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique) 
Abstract:  Let G = (N,E,w ) be a weighted communication graph (with weight function w on E ). For every subset A ⊆ N, we delete in the subset E (A ) of edges with ends in A, all edges of minimum weight in E (A ). Then the connected components of the corresponding induced subgraph constitue a partition of A that we Pmin(A ). For every game (N , v ), we define the Pminrestricted game (N , v ) by v (A = ∑F∈ Pmin (A) v(F ) for all A ⊆ N. We prove that we can decide in polynomial time if there is inheritance of Fconvexity from N , v ) to the Pminrestricted game (N , v ) where Fconvexity is obtained by restricting convexity to connected subsets 
Keywords:  restricted game, convex game, cooperative game,communication networks, partitions, supermodularity, complexity, graph 
Date:  2016–07 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs01382502&r=gth 
By:  JørgenVitting Andersen (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique); Philippe De Peretti (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique) 
Abstract:  We introduce a new methodology that enables the detection onset of convergence towards Nash equilibria, in simple market games with infinite larges strategy spaces. The method works by constraining on a special and finite subset of strategies. We illustrate how the method can be used to … in a series of experiments. 
Keywords:  convergence,multiperiod games,experiments,decoupling 
Date:  2017–12 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs01673331&r=gth 
By:  Takayuki Oishi; Gerard van der Laan (VU University Amsterdam); René van den Brink (VU University Amsterdam) 
Abstract:  We analyze a legal compensation scheme axiomatically under the situation where causation of the cumulative injury appears in multiple sequences of wrongful acts caused by tortfeasors. This situation is a generalization of joint liability problems on tort law, and it is described by a rootedtree graph. We show that there is a unique compensation scheme that satisfies three axioms, one about lower bounds of individual compensations, one about upper bounds of individual compensations, and one about casesystem consistency. These axioms are derived from legal observations on tort law. The unique compensation scheme satisfying the three axioms yields the Nucleolus of an associated liability game. 
Keywords:  Tort law; Rootedtree graph; Axiomatization; Nucleolus 
JEL:  C71 D63 K13 K49 
Date:  2018–03 
URL:  http://d.repec.org/n?u=RePEc:mei:wpaper:37&r=gth 
By:  Andersson , Tommy (Department of Economics, Lund University); Ehlers , Lars (Département de sciences économiques, Université de Montréal); Svensson , LarsGunnar (Department of Economics, Lund University); Tierney , Ryan (Institute of Business and Economics, University of Southern Denmark) 
Abstract:  We consider the taxation of exchanges among a set of agents where each agent owns one object. Agents may have different valuations for the objects and they need to pay taxes for exchanges. Using basic properties, we show that if pairwise (or some) exchanges of objects are allowed, then all exchanges (in any possible manner) must be feasible. Furthermore, whenever any agent exchanges his object, he pays the same fixed tax (a lump sum payment which is identical for all agents) independently of which object he consumes. Gale's top trading cycles algorithm finds the final allocation using the agents' valuations adjusted with the fixed tax. Our mechanisms are in stark contrast to ClarkeGroves taxation schemes or the maxmed schemes proposed by Sprumont (2013). 
Keywords:  Fixed Tax; Exchanges; Top Trading 
JEL:  C71 C78 D63 D71 D78 
Date:  2018–06–20 
URL:  http://d.repec.org/n?u=RePEc:hhs:lunewp:2018_017&r=gth 
By:  Urbinati, Niccolò 
Abstract:  On a Boolean algebra we consider the topology $u$ induced by a finitely additive measure $\mu$ with values in a locally convex space and formulate a condition on $u$ that is sufficient to guarantee the convexity and weak compactness of the range of $\mu$. This result à la Lyapunov extends those obtained in (Khan, Sagara 2013) to the finitely additive setting through a more direct and less involved proof. We will then give an economical interpretation of the topology $u$ in the framework of coalitional large economies to tackle the problem of measuring the bargaining power of coalitions when the commodity space is infinite dimensional and locally convex. We will show that our condition on $u$ plays the role of the "many more agents than commodities" condition introduced by Rustichini and Yannelis in (1991). As a consequence of the convexity theorem, we will obtain two straight generalizations of Schmeidler's and Vind's Theorems on the veto power of coalitions of arbitrary economic weight. 
Keywords:  Lyapunov's Theorem; finitely additive measures; correspondences; coalitional economies 
JEL:  C02 C71 D51 
Date:  2018–05–14 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:87185&r=gth 
By:  Bergemann, Dirk; Castro, Francisco; Weintraub, Gabriel 
Abstract:  We study the classic sequential screening problem in the presence of buyers' expost participation constraints. A leading example is the online display advertising market, in which publishers frequently do not use upfront fees and instead use transactioncontingent fees. We establish conditions under which the optimal selling mechanism is static and buyers are not screened with respect to their interim type, or sequential and the buyers are screened with respect to their interim type. In particular, we provide an intuitive necessary and sufficient condition under which the static contract is optimal for general distributions of expost values. Further, we completely characterize the optimal sequential contract with binary interim types and continuum of expost values when this condition fails. Importantly, the latter contract randomizes the allocation of the low type buyer while giving a deterministic allocation to the high type. We also provide partial results for the case of multiple interim types. 
Keywords:  expost participation constraints; sequential contract.; Sequential Screening; static contract 
JEL:  C72 D82 D83 
Date:  2018–06 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:13018&r=gth 
By:  Takayuki Oishi 
Abstract:  We develop the notions of duality and antiduality for axiomatic analysis of allocation rules. First, we show basic properties of duality and antiduality for allocation rules. Next, using the notion of duality and axioms involved in axiomatizations of the Shapley rule for airport problems, we axiomatize the Shapley rule for bidding ring problems. Finally, using the notion of anti duality and axioms involved in axiomatizations of the nucleolus for airport problems, we axiomatize the nucleolus rule for bidding ring problems. From the approach proposed, we may derive appropriate interpretations of axioms involved in axiomatizations of economic rules. 
Keywords:  duality; antiduality; axiomatization; Shapley rules; nucleolus rules 
JEL:  C69 C71 
Date:  2018–03 
URL:  http://d.repec.org/n?u=RePEc:mei:wpaper:38&r=gth 
By:  Colliard, JeanEdouard; Gromb, Denis 
Abstract:  How do resolution frameworks affect the private restructuring of distressed banks? We model a distressed bank’s shareholders and creditors negotiating a restructuring given asymmetric information about asset quality and externalities onto the government. This yields negotiation delays used to signal asset quality. We find that strict bailin rules increase delays by worsening informational frictions and reducing bargaining surplus. We characterize optimal bailin rules for the government. We then consider the government’s possible involvement in negotiations. We find this can lead to shorter or longer delays. Notably, the government may gin from committing not to partake in negotiations. 
Keywords:  Bank resolution; bailout; bailin; debt restructuring 
JEL:  G21 G28 
Date:  2018–05–02 
URL:  http://d.repec.org/n?u=RePEc:ebg:heccah:1272&r=gth 
By:  Ingebretsen Carlson, Jim (Department of Economics, Lund University); Wu, Tingting (Department of Economics, Universitat Autònoma de Barcelona) 
Abstract:  Secondprice auctions with public information, such as those on eBay, provide an opportunity for sellers to use the information from finished and ongoing auctions when acting strategically in future auctions. Sellers have frequently been observed to bidding on their own item with the intent to artificially increase its price. This is known as shill bidding. Using lab experiments with two sequential auctions, we study the effect of shill bidding when the seller can choose to shill bid in the second auction. We also study the impact of different information revelation policies regarding the provision of the first auction bidding history to the seller. The experimental data confirm that shill bidding in the second auction affects outcomes in both auctions. Our findings are consistent with the predictions that the threat of shill bidding in the second auction does increase the bidders' final bid in the first auction. However, providing the seller with the bidding history from the first auction does not affect any important outcome variables. 
Keywords:  Sequential auctions; shill bidding; experiment 
JEL:  C92 D03 D44 
Date:  2018–06–18 
URL:  http://d.repec.org/n?u=RePEc:hhs:lunewp:2018_018&r=gth 
By:  O. A. Malafeyev; V. E. Onishenko; I. V. Zaytseva 
Abstract:  In this article, a gametheoretic model is constructed that is related to the problem of optimal assignments. Examples are considered. A compromise point is found, the Nash equilibriums and the decision of the Nash arbitration scheme are constructed. 
Date:  2018–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1805.09686&r=gth 
By:  Marco Tolotti (Dept. of Management, Università Ca' Foscari Venice); Jorge Yepez (Dept. of Economics, Università Ca' Foscari Venice) 
Abstract:  When dealing with consumer choices, social pressure plays a crucial role; also in the context of market competition, the impact of network/social effects has been largely recognized. However, the effects of firmspecifc social recognition on market equilibria has never been addressed so far. In this paper, we consider a duopoly where competing firms are differentiated solely by the level of social (or network) externality they induce on consumers' perceived utility. We fully characterize the subgame perfect Nash equilibria in locations, prices and market shares. Under a scenario of weak social externality, the firms opt for maximal differentiation and the one with the highest social recognition has a relative advantage in terms of profits. Surprisingly, this outcome is not persistent; excessive social recognition may lead to adverse coordination of consumers: the strongest firm can eventually be thrown out of the market with positive probability. This scenario is related to a Pareto inefficient trap of no differentiation. 
Keywords:  Consumer choice game, Duopoly price competition, Hotelling Location model, Network Externalities, Large Games, Social interaction 
JEL:  L13 C72 C63 D71 
Date:  2018–06 
URL:  http://d.repec.org/n?u=RePEc:vnm:wpdman:154&r=gth 
By:  Adriana Gama; Isabelle Maret; Virginie Masson 
Abstract:  This paper examines the standard symmetric twoperiod R&D duopoly model, but with a deterministic oneway spillover structure. Though the two firms are exante identical, one obtains a unique pair of asymmetric equilibria of R&D investments, leading to interfirm heterogeneity in the industry, in R&D roles as well as in unit costs. We analyze the impact of a change in the spillover parameter and R&D costs on firms’ levels of R&D and profits. We find that higher spillovers need not lead to lower R&D investments for both firms. In addition, equilibrium profits may improve due to the presence of spillovers, and it may be advantageous to be the R&D imitator rather than the R&D innovator. 
Keywords:  Oneway Spillovers, asymmetric R&D equilibria, R&D and interfirm heterogeneity, symmetrybreaking. 
JEL:  D45 L10 C72 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:ulp:sbbeta:201823&r=gth 
By:  Laurent, Thibault; Le Breton, Michel; Lepelley, Dominique; de Mouzon, Olivier 
Keywords:  Electoral system; Election Inversions; Impartial Anonymous Culture 
JEL:  D71 D72 
Date:  2018–02 
URL:  http://d.repec.org/n?u=RePEc:tse:iastwp:32790&r=gth 
By:  Takeru Matsuda; Akimichi Takemura 
Abstract:  We investigate upper and lower hedging prices of multivariate contingent claims from the viewpoint of gametheoretic probability and submodularity. By considering a game between "Market" and "Investor" in discrete time, the pricing problem is reduced to a backward induction of an optimization over simplexes. For European options with payoff functions satisfying a combinatorial property called submodularity or supermodularity, this optimization is solved in closed form by using the Lov\'asz extension and the upper and lower hedging prices can be calculated efficiently. This class includes the options on the maximum or the minimum of several assets. We also study the asymptotic behavior as the number of game rounds goes to infinity. The upper and lower hedging prices of European options converge to the solutions of the BlackScholesBarenblatt equations. For European options with submodular or supermodular payoff functions, the BlackScholesBarenblatt equation is reduced to the linear BlackScholes equation and it is solved in closed form. Numerical results show the validity of the theoretical results. 
Date:  2018–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1806.07626&r=gth 
By:  Anne AmarSabbah (CERGAM  Centre d'Études et de Recherche en Gestion d'AixMarseille  AMU  Aix Marseille Université  UTLN  Université de Toulon); Pierre Batteau (CERGAM  Centre d'Études et de Recherche en Gestion d'AixMarseille  AMU  Aix Marseille Université  UTLN  Université de Toulon) 
Abstract:  Often criticized in the civil society for its magnitude, though considered with mixed appreciations by academics, CEO pay has been objects of many contributions. Reviewing key papers that have raised controversies, we discuss divergent viewpoints with simple game theoretic models in the neoclassical spirit. We assert the complete inadequacy of the agency and asymmetry of information models for explaining CEO compensation, but we diverge from those who reject the optimal contracting approach and show how reasoning with the classical tools of utility maximization, rationality, freedom to participate, and price sets on markets, competitive or not, can model a broad range of situations, including those put forward as arguments against the microeconomic approaches of compensation. The CEOBoard relationship should not be studied as a delegation issue within a hierarchical organization with the shareholders sitting at the top, but rather as a market bargain in search of optimal contracting with symmetrical position and information of both parties, but with asymmetrical reservation utility because the distribution of talent to manage is itself highly asymmetrical, expressing the game power of each side. 
Keywords:  rationality,CEO compensation,agency theory,bargaining,optimal contracting,utility maximization,CEO power,game theory,Neoclassical economics 
Date:  2018–06–19 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:halshs01818600&r=gth 
By:  Stefano Galavotti (University of Padova); Luigi Moretti (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique); Paola Valbonesi (University of Padova) 
Abstract:  We study bidding behavior by firms in beautycontest auctions, i.e. auctions in which the winning bid is the one which gets closet to some function (average) of all submitted bids. Using a dataset on public procurement beautycontest auctions, we show that firms' observed bidding behavior departs from equilibrium and can be predicted by a sophistication index, which captures the firms' accumulated capacity of bidding close to optimality in the past. We show that our empirical evidence is consistent with a Cognitive Hierarchy model of bidders' behavior. We also investigate whether and how firms learn to bid strategically through experience. 
Keywords:  cognitive hierarchy,auctions,beautycontest,public procurement 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs01440891&r=gth 
By:  Simon Schopohl (EDEEM  Université Paris 1  EDEEM  European Doctorate in Economics Erasmus Mundus, Universität Bielefeld (GERMANY), CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique, UCL  Université Catholique de Louvain) 
Abstract:  We consider a SenderReceiver game in which the Sender can choose between sending a cheaptalk message, which is costless, but also not verified and a costly verified message. While the Sender knows the true state of the world, the Receiver does not have this information, but has to choose an action depending on the message he receives. The action then yields to some utility for Sender and Receiver. We only make a few assumptions about the utility functions of both players, so situations may arise where the Sender's preferences are such that she sends a message trying to convince the Receiver about a certain state of the world, which is not the true one. In a finite setting we state conditons for full revelation, i.e. when the Receiver always learns the truth. Furthermore we describe the player's behavior if only partial revelation is possible. For a continuous setting we show that additional conditions have to hold and that these do not hold for "smooth" preferences and utility, e.g. in the classic example of quadratic loss utilities. 
Keywords:  verifiable information,cheaptalk,communication,costly disclosure,full revelation,increasing differences,SenderReceiver game 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs01490688&r=gth 