nep-gth New Economics Papers
on Game Theory
Issue of 2019‒01‒14
twenty-two papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Seqential competition and the strategic origins of preferential attachment By Antoine Mandel; Xavier Venel
  2. Learning and Selfconfirming Equilibria in Network Games By Pierpaolo Battigalli; Fabrizio Panebianco; Paolo Pin
  3. Equitable Solutions in Game Representations and the Shapley Value By Pradeep Dubey
  4. New method to detect convergence in simple multi-period market games with infinite large strategy spaces By Jørgen Vitting Andersen; Philippe de Peretti
  5. On Mechanisms for Costly Inclusion By Andrew Mackenzie; Christian Trudeau
  6. The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms By Streufert, Peter
  7. Incomplete Information and Costly Signaling in College Admissions By Salgado Alfredo
  8. Fight or Flight : Endogenous Timing in Conflicts By van Leeuwen, Boris; Offerman, T.J.S.; van de Ven, J.
  9. The strategic environment effect in beauty contest games By Nobuyuki Hanaki; Yukio Koriyama; Angela Sutan; Marc Willinger
  10. Conditions for the uniqueness of the Gately point for cooperative games By Jochen Staudacher; Johannes Anwander
  11. Nonparametric analysis of monotone choice By Natalia Lazzati; John K.-H. Quah; Koji Shirai
  12. Mean-Field Leader-Follower Games with Terminal State Constraint By Fu, Guanxing; Horst, Ulrich
  13. Endogenous worst-case beliefs in first-price auctions By Gretschko, Vitali; Mass, Helene
  14. Cooperation and evolution of meaning in senders-receivers games By Claude Meidinger
  15. Altruism and Risk Sharing in Networks By Renaud Bourlès; Yann Bramoullé; Eduardo Perez-Richet
  16. Location in a disk city with consumer concentration around the center By Stadler, Manfred
  17. On the difficulty of collusion in the presence of a more efficient outsider By Guillaume Cheikbossian; Philippe Mahenc
  18. Cartel Stability under Quality Differentiation By Iwan Bos; Marco Marini
  19. A Common-Value Auction with State-Dependent Participation By Stephan Lauermann; Asher Wolinsky
  20. Modularity and greed in double auctions By Dütting, Paul; Talgam-Cohen, Inbal; Roughgarden, Tim
  21. A Model of Competing Narratives By Kfir Eliaz; Ran Spiegler
  22. Interacting collective action problems in the commons By Nicolas Querou

  1. 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 socio-economic networks. Empirical observations underline a complex structure characterized by fat-tailed 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 micro-foundations. 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: Socio-economic networks; endogenous network formation; game theory
    JEL: C71 D85
    Date: 2018–10
  2. 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 non--Nash 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
  3. 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 semi-algebra of sets (i.e., contain the grand coalition, and are closed under complements).
    Date: 2018
  4. 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 repeated-games 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: multi-period games; infinite strategy space; decoupling; bounded rationality; agent-based modeling
    JEL: C15 C53 C73 C92
    Date: 2018–12
  5. 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 surplus-maximizing 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, free-rider problem, pivot mechanism, Walrasian price, production.
    JEL: D82 D61 H41 D44
    Date: 2019–01
  6. By: Streufert, Peter
    Abstract: The literature specifies extensive-form 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 node-and-choice 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 choice-sequences, and CsetF for forms whose nodes are choice-sets. 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 no-absentmindedness 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
  7. 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 closed-form 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 low-ability students to invest in signaling and increase it for high-ability students.
    Keywords: College Admissions;Decentralized Mechanisms;Incomplete Information;Coordination Problems;Costly Signaling
    JEL: D82 C70 C71 C72 C78
    Date: 2018–12
  8. 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 two-sided 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: fight-or-flight; contest; sorting; loss aversion; theory; experiment
    JEL: D74 D82 C92
    Date: 2018
  9. 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 (X-DEP-ECO - 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 (CEE-M - 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 level-K 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
  10. 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 set-valued 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
  11. 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 out-of-sample 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
  12. By: Fu, Guanxing (HU Berlin); Horst, Ulrich (HU Berlin)
    Abstract: We analyze linear McKean-Vlasov forward-backward SDEs arising in leader-follower games with mean-field type control and terminal state constraints on the state process. We establish an existence and uniqueness of solutions result for such systems in time-weighted 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 single-player 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: mean-field control; stackelberg game; mean-field game with a major player; portfolio liquidation;
    Date: 2018–12–20
  13. By: Gretschko, Vitali; Mass, Helene
    Abstract: Bidding in first-price auctions crucially depends on the beliefs of the bidders about their competitors' willingness to pay. We analyze bidding behavior in a first-price 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 worst-case belief just puts sufficient probability weight on lower valuations of her competitors to induce a high bid. At the same time the worst-case 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 worst-case beliefs are type dependent in a non-monotonic way, an efficient equilibrium of the first-price auction exists.
    Keywords: auctions,mechanism design,beliefs,uncertainty
    JEL: D44 D81 D82
    Date: 2018
  14. By: Claude Meidinger (Centre d'Economie de la Sorbonne - Université Paris1 Panthéon-Sorbonne)
    Abstract: Whether there is a pre-existing 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 “common-language” assumption is simplicitly implemented, such situations ignore the meta-coordination 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
  15. By: Renaud Bourlès (AMSE - Aix-Marseille 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 - Aix-Marseille 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 Perez-Richet (IEP Paris - Sciences Po Paris - Institut d'études politiques de Paris, CEPR)
    Abstract: We provide the first analysis of the risk-sharing 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 risk-sharing 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 first-order impact on risk and generates specific patterns of consumption smoothing.
    Keywords: altruism,networks,risk sharing,informal insurance
    Date: 2018–11
  16. By: Stadler, Manfred
    Abstract: The paper studies a two-stage location-price 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 cone-shaped, dome-shaped, and bell-shaped 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
  17. By: Guillaume Cheikbossian (CEE-M - 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 (CEE-M - 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 stick-and-carrot strategies, while the efficient firm plays its one-period best-response 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
  18. By: Iwan Bos; Marco Marini
    Abstract: This note considers cartel stability when the cartelized products are vertically differentiated. If market shares are maintained at pre-collusive levels, then the firm with the lowest competitive price-cost margin has the strongest incentive to deviate from the collusive agreement. The lowest-quality supplier has the tightest incentive constraint when the difference in unit production costs is sufficiently small.
    Date: 2018–12
  19. By: Stephan Lauermann; Asher Wolinsky
    Abstract: This paper analyzes a common-value, first-price auction with state-dependent 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" type---with high probability, the winning bid is the same across states and is below the ex-ante expected value---or of a "partially separating" type---with 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 state-dependent 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
  20. By: Dütting, Paul; Talgam-Cohen, 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 exhaustively-studied problem of designing one-sided mechanisms with a single seller (or, alternatively, a single buyer). We consider several desirable properties of a double auction: feasibility, dominant-strategy incentive compatibility, the still stronger incentive constraints offered by a deferred-acceptance implementation, exact and approximate welfare maximization, and budget balance. For each of these properties, we identify sufficient conditions on two one-sided 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 unit-demand buyers and unit-supply sellers.
    Keywords: mechanism design; double auctions; trade reduction mechanism; deferred-acceptance auctions
    JEL: J1
    Date: 2017–09–01
  21. 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 narrative-policy 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
  22. By: Nicolas Querou (CEE-M - 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 (intra-group 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 common-pool 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 common-pool resources. We show how the fundamentals affect the individual strategies and welfare compared to the benchmark commons problems. Finally, different initiatives (local cooperation, inter-area agreements) are analyzed to assess whether they may alleviate the problems, and to understand the conditions under which they do so.
    Keywords: externalities,common-pool resource,collective action
    Date: 2018

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