
on Game Theory 
By:  Antoine Mandel (Paris School of Economics  Centre d'Economie de la Sorbonne); Xavier Venel (Paris School of Economics  Centre d'Economie de la Sorbonne) 
Abstract:  There exists a wide gap between the predictions of strategic models of network formation and empirical observations of the characteristics of socioeconomic networks. Empirical observations underline a complex structure characterized by fattailed degree distribution, short average distance, large clustering coefficient and positive assortativity. Game theoretic models offer a detailed representation of individuals' incentives but they predict the emergence of much simpler structures than these observed empirically. Random network formation processes, such as preferential attachment, provide a much better fit to empirical observations but generally lack microfoundations. in order to bridge this gap, we propose to model network formation as extensive games and investigate under which conditions equilibria of these games are observationally equivalent with random network formation process. In particular, we introduce a class of games in which players compete with their predecessors and their successors for the utility induced by the links they form with another node in the network. Such sequential competition games can represent a number of strategic economic interactions such as oligopolistic competition in supply networks or diffusion of influence in opinion networks. we show that the focal equilibrium that emerge in this setting is one where players use probability distributions with full support and target the whole network with probabilities inversely proportional to the utility of each node. Notably, when the utility of a node is inversely proportional to its degree, equilibrium play induces a preferential attachment process 
Keywords:  Socioeconomic networks; endogenous network formation; game theory 
JEL:  C71 D85 
Date:  2018–10 
URL:  http://d.repec.org/n?u=RePEc:mse:cesdoc:18035&r=all 
By:  Pierpaolo Battigalli; Fabrizio Panebianco; Paolo Pin 
Abstract:  Consider a set of agents who play a network game repeatedly. Agents may not know the network. They may even be unaware that they are interacting with other agents in a network. Possibly, they just understand that their payoffs depend on an unknown state that in reality is an aggregate of the actions of their neighbors. Each time, every agent chooses an action that maximizes her subjective expected payoff and then updates her beliefs according to what she observes. In particular, we assume that each agent only observes her realized payoff. A steady state of such dynamic is a selfconfirming equilibrium given the assumed feedback. We characterize the structure of the set of selfconfirming equilibria in network games and we relate selfconfirming and Nash equilibria. Thus, we provide conditions on the network under which the Nash equilibrium concept has a learning foundation, despite the fact that agents may have incomplete information. In particular, we show that the choice of being active or inactive in a network is crucial to determine whether agents can make correct inferences about the payoff state and hence play the best reply to the truth in a selfconfirming equilibrium. We also study learning dynamics and show how agents can get stuck in nonNash selfconfirming equilibria. In such dynamics, the set of inactive agents can only increase in time, because once an agent finds it optimal to be inactive, she gets no feedback about the payoff state, hence she does not change her beliefs and remains inactive. 
Date:  2018–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1812.11775&r=all 
By:  Pradeep Dubey 
Abstract:  We show that any transferable utility game can be represented by an assignment of costly facilities to players, in which it is intuitively obvious how to allocate the total cost of all facilities amongst the players in an equitable manner. The equitable solution in the representation turns out to be the Shapley value of the game, and thus serves as an alternative justification of the value. We show that this approach extends also to the case when not all coalitions can form, provided those that can constitute a semialgebra of sets (i.e., contain the grand coalition, and are closed under complements). 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:nys:sunysb:1811&r=all 
By:  Jørgen Vitting Andersen (Centre d'Economie de la Sorbonne); Philippe de Peretti (Centre d'Economie de la Sorbonne) 
Abstract:  We introduce a new methodology that enables the detection of onset of convergence towards Nash equilibria, in simple repeatedgames with infinite large strategy spaces. The method works by constraining on a special and finite subset of strategies. We illustrate how the method can predict (in special time periods) with a high success rate the action of participants in a series of experiments 
Keywords:  multiperiod games; infinite strategy space; decoupling; bounded rationality; agentbased modeling 
JEL:  C15 C53 C73 C92 
Date:  2018–12 
URL:  http://d.repec.org/n?u=RePEc:mse:cesdoc:18038&r=all 
By:  Andrew Mackenzie (Department of Economics, Maastricht University); Christian Trudeau (Department of Economics, University of Windsor) 
Abstract:  We investigate mechanisms in a class of production environments where each group of agents can `win' for an associated monetary cost; examples include the allocation of an indivisible object and the provision of a pure public good. A mechanism is satisfactory if and only if it is surplusmaximizing and honesty is necessarily a dominant strategy for each agent; it is autonomous if and only if it is satisfactory and production is funded through voluntary contributions of the agents; it is equitable if and only if it is satisfactory and no agent prefers another's bundle to his own. First, we introduce the notion of inclusion cost coverage for cost functions, and prove that this condition is necessary and sufficient for the existence of autonomous mechanisms (Theorem 1). Second, we prove that the cost function is symmetric and convex if and only if there are equitable mechanisms (Theorem 2); in this case, we characterize both the class of equitable mechanisms (Theorem 3) as well as the class of autonomous and equitable mechanisms (Theorem 4). We discuss a variety of applications and additional topics. 
Keywords:  game theory; second price auction, freerider problem, pivot mechanism, Walrasian price, production. 
JEL:  D82 D61 H41 D44 
Date:  2019–01 
URL:  http://d.repec.org/n?u=RePEc:wis:wpaper:1901&r=all 
By:  Streufert, Peter 
Abstract:  The literature specifies extensiveform games in several styles, and eventually I hope to formally translate games across those styles. Toward that end, this paper defines NCF, the category of nodeandchoice forms. The category's objects are game forms in any style, and the category's isomorphisms are made to accord with the literature's small handful of ad hoc style equivalences. More specifically, the paper develops two full subcategories: CsqF for forms whose nodes are choicesequences, and CsetF for forms whose nodes are choicesets. I show that NCF is ``isomorphically enclosed'' in CsqF in the sense that each NCF form is isomorphic to a CsqF form. Similarly, I show that CsqF_\tilde{a} is isomorphically enclosed in CsetF in the sense that each CsqF form with noabsentmindedness is isomorphic to a CsetF form. The converses are found to be almost immediate, and the resulting equivalences unify and simplify two ad hoc style equivalences in Kline and Luckraz (Economic Theory Bulletin, 2016) and Streufert (International Journal of Game Theory, forthcoming). Aside from the larger agenda, this paper makes three practical contributions. Style equivalences are made easier to derive by [1] a natural concept of isomorphic invariance and [2] the composability of isomorphic enclosures. In addition, [3] some new consequences of equivalence are systematically deduced. 
Keywords:  extensive form, game form, isomorphic enclosure 
JEL:  C73 
Date:  2018–11–27 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:90490&r=all 
By:  Salgado Alfredo 
Abstract:  We analyze a college admissions game with asymmetric information between students and colleges. Students' preferences for colleges depend on the observable quality of the schools. In contrast, colleges' preferences for students depend on the latter's abilities, which are private information. Students and schools are matched via a decentralized mechanism in which students signal their abilities with costly observable signals. A closedform symmetric separating equilibrium of this game that depends on the supply of and demand for schools seats and on college quality is characterized. In this equilibrium, an increase in the number of students, a reduction in the number of school seats or a drop in the quality of schools reduce the incentive of lowability students to invest in signaling and increase it for highability students. 
Keywords:  College Admissions;Decentralized Mechanisms;Incomplete Information;Coordination Problems;Costly Signaling 
JEL:  D82 C70 C71 C72 C78 
Date:  2018–12 
URL:  http://d.repec.org/n?u=RePEc:bdm:wpaper:201823&r=all 
By:  van Leeuwen, Boris (Tilburg University, Center For Economic Research); Offerman, T.J.S. (Tilburg University, Center For Economic Research); van de Ven, J. (Tilburg University, Center For Economic Research) 
Abstract:  We study a dynamic game in which players compete for a prize. In a waiting game with twosided private information about strength levels, players choose between fighting, fleeing, or waiting. Players earn a “deterrence value” on top of the prize if their opponent escapes without a battle. We show that this value is a key determinant of the type of equilibrium. For intermediate values, sorting takes place with weaker and more loss averse players fleeing before others fight. Time then helps to reduce battles. In an experiment, we find support for the key theoretical predictions, and document suboptimal predatory fighting. 
Keywords:  fightorflight; contest; sorting; loss aversion; theory; experiment 
JEL:  D74 D82 C92 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:tiu:tiucen:ed32885c31834effa0ff7307d0bb0cf8&r=all 
By:  Nobuyuki Hanaki (GREDEG  Groupe de Recherche en Droit, Economie et Gestion  UNS  Université Nice Sophia Antipolis  UCA  Université Côte d'Azur  CNRS  Centre National de la Recherche Scientifique, Université Côte d'Azur, CNRS, GREDEG (France)); Yukio Koriyama (XDEPECO  Département d'Économie de l'École Polytechnique  X  École polytechnique); Angela Sutan (BSB  Burgundy School of Business (BSB)  Ecole Supérieure de Commerce de Dijon Bourgogne (ESC)); Marc Willinger (CEEM  Centre d'Economie de l'Environnement  Montpellier  FRE2010  INRA  Institut National de la Recherche Agronomique  UM  Université de Montpellier  CNRS  Centre National de la Recherche Scientifique  Montpellier SupAgro  Institut national d’études supérieures agronomiques de Montpellier) 
Abstract:  Recent experimental studies have shown that observed outcomes deviate significantly more from the Nash equilibrium when actions are strategic complements than when they are strategic substitutes. This "strategic environment effect" offers promising insights into the aggregate consequences of interactions among heterogeneous boundedly rational agents, but its macroeconomic implications have been questioned because the underlying experiments involve a small number of agents. We studied beauty contest games with a unique interior Nash equilibrium to determine the critical group size for triggering the strategic environment effect, and we use both theory and experiments to shed light on its effectiveness. Based on cognitive hierarchy and levelK models, we show theoretically that the effect is operative for interactions among three or more agents. Our experimental results show a statistically significant strategic environment effect for groups of five or more agents, establishing its robustness against the increase in the population size. 
Keywords:  beauty contest games,iterative reasoning,strategic substitutability,strategic complementarity 
Date:  2018–11 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs01929113&r=all 
By:  Jochen Staudacher; Johannes Anwander 
Abstract:  We are studying the Gately point, an established solution concept for cooperative games. We point out that there are superadditive games for which the Gately point is not unique, i.e. in general the concept is rather setvalued than an actual point. We derive conditions under which the Gately point is guaranteed to be a unique imputation and provide a geometric interpretation. The Gately point can be understood as the intersection of a line defined by two points with the set of imputations. Our uniqueness conditions guarantee that these two points do not coincide. We provide demonstrative interpretations for negative propensities to disrupt. We briefly show that our uniqueness conditions for the Gately point include quasibalanced games and discuss the relation of the Gately point to the $\tau$value in this context. Finally, we point out relations to cost games and the ACA method and end upon a few remarks on the implementation of the Gately point and an upcoming software package for cooperative game theory. 
Date:  2019–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1901.01485&r=all 
By:  Natalia Lazzati; John K.H. Quah; Koji Shirai (School of Economics, Kwansei Gakuin University) 
Abstract:  We develop a nonparametric approach to test for monotone behavior in optimizing agents and to make outofsample predictions. Our approach could be applied to simultaneous games with ordered actions, with agents playing pure strategy Nash equilibria or Bayesian Nash equilibria. We require no parametric assumptions on payoff functions nor distributional assumptions on the unobserved heterogeneity of agents. Multiplicity of optimal solutions (or equilibria) is not excluded, and we are agnostic about how they are selected. To illustrate how our approach works, we include an empirical application to an IO entry game. 
Keywords:  revealed preference; monotone comparative statics; single crossing differences;supermodular games; entry games 
JEL:  C1 C6 C7 D4 L1 
Date:  2018–04 
URL:  http://d.repec.org/n?u=RePEc:kgu:wpaper:184&r=all 
By:  Fu, Guanxing (HU Berlin); Horst, Ulrich (HU Berlin) 
Abstract:  We analyze linear McKeanVlasov forwardbackward SDEs arising in leaderfollower games with meanfield type control and terminal state constraints on the state process. We establish an existence and uniqueness of solutions result for such systems in timeweighted spaces as well as a convergence result of the solutions with respect to certain perturbations of the drivers of both the forward and the backward component. The general results are used to solve a novel singleplayer model of portfolio liquidation under market impact with expectations feedback as well as a novel Stackelberg game of optimal portfolio liquidation with asymmetrically informed players. 
Keywords:  meanfield control; stackelberg game; meanfield game with a major player; portfolio liquidation; 
Date:  2018–12–20 
URL:  http://d.repec.org/n?u=RePEc:rco:dpaper:129&r=all 
By:  Gretschko, Vitali; Mass, Helene 
Abstract:  Bidding in firstprice auctions crucially depends on the beliefs of the bidders about their competitors' willingness to pay. We analyze bidding behavior in a firstprice auction in which the knowledge of the bidders about the distribution of their competitors' valuations is restricted to the support and the mean. To model this situation, we assume that under such uncertainty a bidder will expect to face the distribution of valuations that minimizes her expected utility, given her bid is an optimal reaction to the bids of her competitors induced by this distribution. This introduces a novel way to endogenize beliefs in games of incomplete information. We find that for a bidder with a given valuation her worstcase belief just puts sufficient probability weight on lower valuations of her competitors to induce a high bid. At the same time the worstcase belief puts as much as possible probability weight on the same valuation in order to minimize the bidder's winning probability. This implies that even though the worstcase beliefs are type dependent in a nonmonotonic way, an efficient equilibrium of the firstprice auction exists. 
Keywords:  auctions,mechanism design,beliefs,uncertainty 
JEL:  D44 D81 D82 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:zbw:zewdip:18056&r=all 
By:  Claude Meidinger (Centre d'Economie de la Sorbonne  Université Paris1 PanthéonSorbonne) 
Abstract:  Whether there is a preexisting common “language” that ties down the literal meanings of cheap talk messages or not is a distinction plainly important in practice. But it is assumed irrelevant in traditional game theory because it affects neither the payoff structure nor the theoretical possibilities for signaling. And when in experiments the “commonlanguage” assumption is simplicitly implemented, such situations ignore the metacoordination problem created by communication. Players must coordinate their beliefs on what various messages mean before they can use messages to coordinate on what to do. Using simulations with populations of artificial agents, the paper investigates the way according to which a common meaning can be constituted through a collective process of learning and compares the results thus obtained with those available in some experiments 
Keywords:  Experimental Economics; Computational Economics; Signaling games 
JEL:  C73 C91 D03 
Date:  2018–12 
URL:  http://d.repec.org/n?u=RePEc:mse:cesdoc:18036&r=all 
By:  Renaud Bourlès (AMSE  AixMarseille Sciences Economiques  EHESS  École des hautes études en sciences sociales  AMU  Aix Marseille Université  ECM  Ecole Centrale de Marseille  CNRS  Centre National de la Recherche Scientifique); Yann Bramoullé (AMSE  AixMarseille Sciences Economiques  EHESS  École des hautes études en sciences sociales  AMU  Aix Marseille Université  ECM  Ecole Centrale de Marseille  CNRS  Centre National de la Recherche Scientifique); Eduardo PerezRichet (IEP Paris  Sciences Po Paris  Institut d'études politiques de Paris, CEPR) 
Abstract:  We provide the first analysis of the risksharing implications of altruism networks. Agents are embedded in a fixed network and care about each other. We study whether altruistic transfers help smooth consumption and how this depends on the shape of the network. We identify two benchmarks where altruism networks generate efficient insurance: for any shock when the network of perfect altruism is strongly connected and for any small shock when the network of transfers is weakly connected. We show that the extent of informal insurance depends on the average path length of the altruism network and that small shocks are partially insured by endogenous risksharing communities. We uncover complex structural effects. Under iid incomes, central agents tend to be better insured, the consumption correlation between two agents is positive and tends to decrease with network distance, and a new link can decrease or increase the consumption variance of indirect neighbors. Overall, we show that altruism in networks has a firstorder impact on risk and generates specific patterns of consumption smoothing. 
Keywords:  altruism,networks,risk sharing,informal insurance 
Date:  2018–11 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:halshs01943862&r=all 
By:  Stadler, Manfred 
Abstract:  The paper studies a twostage locationprice duopoly game in a disk city with consumer concentration around the city center. When consumers are uniformly distributed over the plane, unconstrained firms locate outside of the city. Consumer concentration, however, induces firms to locate nearer to each other and, when the degree of concentration is sufficiently high, inside of the city. Prices and firm profits decrease in the degree of consumer concentration. We explicitly solve the model for classes of coneshaped, domeshaped, and bellshaped consumer densities. In all cases we identify a loss of welfare due to the strategic effect which causes the firms' spatial differentiation being too large. 
Keywords:  location strategies,disk city,concentration of consumer demand 
JEL:  C72 L13 R32 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:zbw:tuewef:113&r=all 
By:  Guillaume Cheikbossian (CEEM  Centre d'Economie de l'Environnement  Montpellier  FRE2010  INRA  Institut National de la Recherche Agronomique  UM  Université de Montpellier  CNRS  Centre National de la Recherche Scientifique  Montpellier SupAgro  Institut national d’études supérieures agronomiques de Montpellier); Philippe Mahenc (CEEM  Centre d'Economie de l'Environnement  Montpellier  FRE2010  INRA  Institut National de la Recherche Agronomique  UM  Université de Montpellier  CNRS  Centre National de la Recherche Scientifique  Montpellier SupAgro  Institut national d’études supérieures agronomiques de Montpellier) 
Abstract:  We study the ability of several identical firms to collude in the presence of a more efficient firm, which does not take part in their collusive agreement. The cartel firms adopt stickandcarrot strategies, while the efficient firm plays its oneperiod bestresponse function, regardless of the history of play. We characterize the most collusive symmetric punishment, which maximizes the scope for collusion. We then find that either a lower cost disadvantage or a smaller cartel size facilitates collusion. Finally, we compare our results with those obtained in the standard setup where all firms participate in the collusive agreement. 
Keywords:  cost asymmetry,optimal punishments,outsider,repeated game,tacit collusion,outsider JEL classification code: C73,D43,L13 
Date:  2018–05 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal01950057&r=all 
By:  Iwan Bos; Marco Marini 
Abstract:  This note considers cartel stability when the cartelized products are vertically differentiated. If market shares are maintained at precollusive levels, then the firm with the lowest competitive pricecost margin has the strongest incentive to deviate from the collusive agreement. The lowestquality supplier has the tightest incentive constraint when the difference in unit production costs is sufficiently small. 
Date:  2018–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1812.10293&r=all 
By:  Stephan Lauermann; Asher Wolinsky 
Abstract:  This paper analyzes a commonvalue, firstprice auction with statedependent participation. The number of bidders, which is unobservable to them, depends on the true value. For exogenously given participation patterns that involve many bidders in each state, the bidding equilibrium may be of a "pooling" typewith high probability, the winning bid is the same across states and is below the exante expected valueor of a "partially separating" typewith no significant atoms in the winning bid distribution and an expected winning bid increasing in the true value. Which of these forms will arise is determined by the likelihood ratio at the top of the signal distribution and the participation across states. When the statedependent participation is endogenized as the strategic solicitation by an informed seller who bears a small cost for each solicited bidder, an equilibrium of the separating type always exists and is unique of this type; for certain signal distributions there also exist equilibria of the pooling type. 
Keywords:  Search, Auctions, Adverse Selection 
JEL:  C78 D83 
Date:  2018–12 
URL:  http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_063_2018&r=all 
By:  Dütting, Paul; TalgamCohen, Inbal; Roughgarden, Tim 
Abstract:  Designing double auctions is a complex problem, especially when there are restrictions on the sets of buyers and sellers that may trade with one another. The goal of this paper is to develop a modular approach to the design of double auctions, by relating it to the exhaustivelystudied problem of designing onesided mechanisms with a single seller (or, alternatively, a single buyer). We consider several desirable properties of a double auction: feasibility, dominantstrategy incentive compatibility, the still stronger incentive constraints offered by a deferredacceptance implementation, exact and approximate welfare maximization, and budget balance. For each of these properties, we identify sufficient conditions on two onesided algorithms—one for ranking the buyers, one for ranking the sellers—and on a method for their composition into trading pairs, which guarantee the desired property of the double auction. Our framework also offers new insights into classic double auction designs, such as the VCG and McAfee auctions with unitdemand buyers and unitsupply sellers. 
Keywords:  mechanism design; double auctions; trade reduction mechanism; deferredacceptance auctions 
JEL:  J1 
Date:  2017–09–01 
URL:  http://d.repec.org/n?u=RePEc:ehl:lserod:83199&r=all 
By:  Kfir Eliaz; Ran Spiegler 
Abstract:  We formalize the argument that political disagreements can be traced to a "clash of narratives". Drawing on the "Bayesian Networks" literature, we model a narrative as a causal model that maps actions into consequences, weaving a selection of other random variables into the story. An equilibrium is defined as a probability distribution over narrativepolicy pairs that maximizes a representative agent's anticipatory utility, capturing the idea that public opinion favors hopeful narratives. Our equilibrium analysis sheds light on the structure of prevailing narratives, the variables they involve, the policies they sustain and their contribution to political polarization. 
Date:  2018–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1811.04232&r=all 
By:  Nicolas Querou (CEEM  Centre d'Economie de l'Environnement  Montpellier  FRE2010  INRA  Institut National de la Recherche Agronomique  UM  Université de Montpellier  CNRS  Centre National de la Recherche Scientifique  Montpellier SupAgro  Institut national d’études supérieures agronomiques de Montpellier) 
Abstract:  We consider a setting where agents are subject to two types of collective action problems, any group user's individual extraction inducing an externality on others in the same group (intragroup problem), while aggregate extraction in one group induces an externality on each agent in other groups (intergroup problem). One illustrative example of such a setting corresponds to a case where a commonpool resource is jointly extracted in local areas, which are managed by separate groups of individuals extracting the resource in their respective location. The interplay between both types of externality is shown to affect the results obtained in classical models of commonpool resources. We show how the fundamentals affect the individual strategies and welfare compared to the benchmark commons problems. Finally, different initiatives (local cooperation, interarea agreements) are analyzed to assess whether they may alleviate the problems, and to understand the conditions under which they do so. 
Keywords:  externalities,commonpool resource,collective action 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:halshs01936007&r=all 