nep-gth New Economics Papers
on Game Theory
Issue of 2019‒01‒21
nineteen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Learning and Selfconfirming Equilibria in Network Games By Pierpaolo Battigalli; Fabrizio Panebianco; Paolo Pin
  2. Imitation Dynamics in Oligopoly Games with Heterogeneous Players By Daan Lindeman; Marius I. Ochea
  3. Strategies under strategic uncertainty By Mass, Helene
  4. The Olson conjecture for discrete public goods By Nöldeke, Georg; Peña, Jorge
  5. Fair cake-cutting in practice By Kyropoulou, Maria; Ortega, Josué; Segal-Halevi, Erel
  6. Multi-unit assignment under dichotomous preferences By Ortega, Josué
  7. Evolutionary stability of behavioural rules in bargaining By Khan, Abhimanyu
  8. Relational Communication By Anton Kolotilin; Hongyi
  9. Optimal Management of Evolving Hierarchies By Jens Leth, Hougaard; Juan D., Moreno-Ternero; Lars Peter, Østerdal
  10. Misinterpreting Others and the Fragility of Social Learning By Mira Frick; Ryota Iijima; Yuhta Ishii
  11. Wages and the Value of Nonemployment By Jäger, Simon; Schoefer, Benjamin; Young, Samuel; Zweimüller, Josef
  12. The Voting Power in the Inter-communal Council of Martinique and Guadeloupe By Ibrahima Dia; Eric Kamwa
  13. Cooperation among strangers with and without a monetary system By Maria Bigoni; Gabriele Camera; Marco Casari
  14. Does equity induce inefficiency? An experiment on coordination By Mamadou Gueye; Nicolas Querou; Raphaël Soubeyran
  15. Double Majority and Generalized Brexit: Explaining Counterintuitive Results By Werner Kirsch; Wojciech S{\l}omczy\'nski; Dariusz Stolicki; Karol \.Zyczkowski
  16. The strategic environment effect in beauty contest games By Nobuyuki Hanaki; Yukio Koriyama; Angela Sutan; Marc Willinger
  17. Generalizing mechanism design theory to a case where agents' types are adjustable By Wu, Haoyang
  18. Information sharing is not always the right option when it comes to CPR extraction management: experimental finding By Dimitri Dubois; Stefano Farolfi; Phu Nguyen-Van; Juliette Rouchier
  19. A dynamic dual representation of the buyer's price of American options in nonlinear incomplete markets By Roxana Dumitrescu

  1. 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. JEL classification codes: C72, D83, D85.
    Date: 2018
  2. By: Daan Lindeman; Marius I. Ochea (Université de Cergy-Pontoise, THEMA)
    Abstract: We investigate the role and performance of imitative behaviour in a class of quantity- setting Cournot games. Within a framework of evolutionary competition between ra- tional, best-response and imitators players we found that the equilibrium stability de- pends on the intensity of the evolutionary pressure and on the stability of the cheapest heuristic. When the cheapest behavioural rule is the stable heuristic (i.e. imitation), the dynamics converge to a situation where most rms use this behavioural rule and all rms produce the Cournot-Nash equilibrium quantity. When the cheapest heuristic is unstable one (i.e. best-response), complicated endogenous uctuations may occur along with the co-existence of heuristics.
    Keywords: Competing heuristics, Imitation, Evolutionary dynamics.
    JEL: C72 C73 D43
    Date: 2018
  3. By: Mass, Helene
    Abstract: I investigate the decision problem of a player in a game of incomplete information who faces uncertainty about the other players' strategies. I propose a new decision criterion which works in two steps. First, I assume common knowledge of rationality and eliminate all strategies which are not rationalizable. Second, I apply the maximin expected utility criterion. Using this decision criterion, one can derive predictions about outcomes and recommendations for players facing strategic uncertainty. A bidder following this decision criterion in a first-price auction expects all other bidders to bid their highest rationalizable bid given their valuation. As a consequence, the bidder never expects to win against an equal or higher type and resorts to win against lower types with certainty.
    Keywords: Auctions,Incomplete Information,Informational Robustness,Rationalizability
    JEL: C72 D81 D82 D83
    Date: 2018
  4. By: Nöldeke, Georg; Peña, Jorge
    Abstract: We consider the private provision of a public good with non-refundable binary contributions. A fixed amount of the good is provided if and only if the number of contributors reaches an exogenous threshold. The threshold, the group size, and the identical cost of contributing to the public good are common knowledge. Our main result shows that the maximal probability of reaching the threshold (and thereby obtaining the public good) which can be supported in a symmetric equilibrium of this participation game is decreasing in group size. This generalizes a well-known result for the volunteer’s dilemma – in which the threshold is one – to arbitrary thresholds and thereby confirms a conjecture by Olson for the class of participation games under consideration. Further results characterize the limit when group size goes to infinity and provide conditions under which the expected number of contributors is decreasing or increasing in group size.
    Keywords: Participation games; Private provision of public goods; Group-size effects; Olson conjecture
    Date: 2018–11
  5. By: Kyropoulou, Maria; Ortega, Josué; Segal-Halevi, Erel
    Abstract: Using a lab experiment, we investigate the real-life performance of envy-free and proportional cake-cutting procedures with respect to fairness and preference manipulation. We nd that envy-free procedures, in particular Selfridge-Conway, are fairer and also are perceived as fairer than their proportional counterparts, despite the fact that agents very often manipulate them. Our results support the practical use of the celebrated Selfridge-Conway procedure, and more generally, of envy- free cake-cutting mechanisms. We also nd that subjects learn their opponents' preferences after repeated interaction and use this knowledge to improve their allocated share of the cake. Learning reduces truth-telling behavior, but also reduces envy.
    Keywords: cake-cutting,Selfridge-Conway,cut-and-choose,envy,perceived fairness,preference manipulation,experimentation and learning
    JEL: C71 C91 D63
    Date: 2018
  6. By: Ortega, Josué
    Abstract: I study the problem of allocating objects among agents without using money. Agents can receive several objects and have dichotomous preferences, meaning that they either consider objects to be acceptable or not. In this set-up, the egalitarian solution is more appealing than the competitive equilibrium with equal incomes because it is Lorenz dominant, unique in utilities, and group strategy- proof. Both solutions are disjoint.
    Keywords: dichotomous preferences,multi-unit assignment,Lorenz dominance,competitive equilibrium with equal incomes
    JEL: C78 D73
    Date: 2018
  7. By: Khan, Abhimanyu
    Abstract: I study the evolutionary stability of behavioural rules in a bargaining game. Individuals draw random samples of strategies used in the past and respond to it by using a behavioural rule. Even though individuals actually respond to historical demands, a necessary condition for stability is the existence of a state such that it is as-if the individuals are hardwired to make the same demand. Furthermore, the state where all individuals demand half of the pie is the unique neutrally stable state; all other states are unstable in the face of an invasion by a mutant behavioural rule.
    Keywords: bargaining; evolution; stable behavioural rules; internal stability; external stability; equal split
    JEL: C73 C78
    Date: 2018–12–24
  8. By: Anton Kolotilin (School of Economics, UNSW Business School); Hongyi (School of Economics, UNSW Business School)
    Abstract: We study a communication game between an informed sender and an uninformed receiver with repeated interactions and voluntary transfers. Transfers motivate the receiver's decision-making and signal the sender's information. Although full separation can always be supported in equilibrium, partial or complete pooling is optimal if the receiver's decision-making is highly responsive to information. In this case, the receiver's decision-making is disciplined by pooling extreme states, where she is most tempted to defect. In characterizing optimal equilibria, we establish new results on monotone persuasion.
    Keywords: strategic communication, monotone persuasion, relational contracts
    JEL: C73 D82 D83
    Date: 2019–01
  9. By: Jens Leth, Hougaard; Juan D., Moreno-Ternero; Lars Peter, Østerdal (Department of Economics, Copenhagen Business School)
    Abstract: We study the optimal management of evolving hierarchies, which abound in real-life phenomena. An initiator invests into finding a subordinate, who will bring revenues to the joint venture and who will invest herself into finding another subordinate, and so on. The higher the individual investment (which is private information), the higher the probability of finding a subordinate. A transfer scheme specifies how revenues are reallocated, via upward transfers, as the hierarchy evolves. Each transfer scheme induces a game in which agents decide their investment choices. We consider two optimality notions for schemes: initiator-optimal and socially-optimal schemes. We show that the former are schemes imposing to each member a full transfer to two recipients (the predecessor and the initiator) with a constant ratio among the transfers. We show that the latter are schemes imposing full transfers to the immediate predecessors.
    Keywords: Optimal transfer schemes; Hierarchies; Management; Nash equilibrium
    JEL: C70 L24 M52
    Date: 2018–12–30
  10. By: Mira Frick (Cowles Foundation, Yale University); Ryota Iijima (Cowles Foundation, Yale University); Yuhta Ishii (Centro de Investigación Económica, ITAM)
    Abstract: We study to what extent information aggregation in social learning environments is robust to slight misperceptions of others’ characteristics (e.g., tastes or risk attitudes). We consider a population of agents who obtain information about the state of the world both from initial private signals and by observing a random sample of other agents’ actions over time, where agents’ actions depend not only on their beliefs about the state but also on their idiosyncratic types. When agents are correct about the type distribution in the population, they learn the true state in the long run. By contrast, our first main result shows that even arbitrarily small amounts of misperception can generate extreme breakdowns of information aggregation, wherein the long run all agents incorrectly assign probability 1 to some fixed state of the world, regardless of the true underlying state. This stark discontinuous departure from the correctly specified benchmark motivates independent analysis of information aggregation under misperception. Our second main result shows that any misperception of the type distribution gives rise to a specific failure of information aggregation where agents’ long-run beliefs and behavior vary only coarsely with the state, and we provide systematic predictions for how the nature of misperception shapes these coarse long-run outcomes. Finally, we show that how sensitive information aggregation is to misperception depends on how rich agents’ payoff-relevant uncertainty is. A design implication is that information aggregation can be improved through interventions aimed at simplifying the agents’ learning environment.
    Keywords: Misspecification, Social learning, Information aggregation, Fragility
    JEL: C70 D80 D83
    Date: 2019–01
  11. By: Jäger, Simon (Massachusetts Institute of Technology); Schoefer, Benjamin (University of California, Berkeley); Young, Samuel (Massachusetts Institute of Technology); Zweimüller, Josef (University of Zurich)
    Abstract: Nonemployment is often posited as a worker's outside option in wage setting models such as bargaining and wage posting. The value of this state is therefore a fundamental determinant of wages and, in turn, labor supply and job creation. We measure the effect of changes in the value of nonemployment on wages in existing jobs and among job switchers. Our quasi-experimental variation in nonemployment values arises from four large reforms of unemployment insurance (UI) benefit levels in Austria. We document that wages are insensitive to UI benefit levels: point estimates imply a wage response of less than $0.01 per $1.00 UI benefit increase, and we can reject sensitivities larger than 0.03. In contrast, a calibrated Nash bargaining model predicts a sensitivity of 0.39 – more than ten times larger. The empirical insensitivity holds even among workers with a priori low bargaining power, with low labor force attachment, with high predicted unemployment duration, among job switchers and recently unemployed workers, in areas of high unemployment, in firms with flexible pay policies, and when considering firm-level bargaining. The insensitivity of wages to the nonemployment value we document presents a puzzle to widely used wage setting protocols, and implies that nonemployment may not constitute workers' relevant threat point. Our evidence supports wage-setting mechanisms that insulate wages from the value of nonemployment.
    Keywords: wages, bargaining, unemployment benefits, nonemployment
    JEL: J31 J60 J65
    Date: 2018–11
  12. By: Ibrahima Dia (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR1 - Université de Rennes 1 - UNIV-RENNES - Université de Rennes - CNRS - Centre National de la Recherche Scientifique); Eric Kamwa (LC2S - Laboratoire caribéen de sciences sociales - CNRS - Centre National de la Recherche Scientifique - UA - Université des Antilles)
    Abstract: This paper deals with the distribution of seats between municipalities in the inter-communal council (EPCI) of Martinique and Guadeloupe. In each of the EPCIs, we calculate the voting power of municipalities using the Shapley-Shubik and Banzhaf-Coleman indices. Our analysis allows us to show that in almost all the EPCIs of Martinique and Guadeloupe, there is no similarity between the distribution of power indices and the distribution of population percentages. There is also a distortion between the distribution of power indices and the distribution of delegate percentages.
    Abstract: Ce papier s'intéresse à la répartition des sièges entre les communes dans les établissements publics de coopération intercommunale (EPCI) de la Martinique et de la Guadeloupe. Dans chacun des EPCI, nous calculons le pouvoir de vote des communes au moyen des indices de Shapley-Shubik et de Banzhaf-Coleman. Notre analyse nous permet de montrer que dans quasiment toutes les EPCI de la Martinique et de la Guadeloupe, il n'existe pas une similarité entre la distribution des indices de pouvoir et celle des pourcentages de population. On note aussi une distorsion entre la distribution des indices de pouvoir et celle des pourcentages de délégués.
    Keywords: Banzhaf-Coleman,Indice de pouvoir,Intercommunalité,Shapley- Shubik,Vote
    Date: 2018
  13. By: Maria Bigoni (University of Bologna & IZA); Gabriele Camera (Chapman University & University of Bologna); Marco Casari (University of Bologna & IZA)
    Abstract: Human societies prosper when their members move beyond local exchange and cooperate with outsiders in the creation of wealth. Collaboration of this type presents formidable challenges because interaction is impersonal, reciprocity is unfeasible and trust cannot be easily established. Here we study this cooperation problem by modeling strategic interaction among strangers through an Intertemporal Exchange Game. The setup can be easily implemented in the laboratory to study a variety of cooperation-enhancing institutions. In particular, we study the role of a fiat monetary system by introducing intrinsically worthless tokens that can be offered in exchange for cooperation. The experiments show that a monetary system spontaneously emerges in the laboratory, and is a key institution to promote cooperation among strangers.
    Keywords: gift-giving, intertemporal trade, macroeconomic experiments, repeated games, social norms
    JEL: C70 C90 D03 E02
    Date: 2019
  14. By: Mamadou Gueye (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); 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); Raphaël Soubeyran (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: In this paper, we use a laboratory experiment to analyze the relationship between equity and coordination success in a game with Pareto ranked equilibria. Equity is decreased by increasing the coordination payoffs of some subjects while the coordination payoffs of others remain unchanged. Theoretically, in this setting, difference aversion may lead to a positive relationship between equity and coordination success, while social welfare motivations may lead to a negative relationship. Using a within-subject experimental design, we find that less equity unambiguously leads to a higher level of coordination success. Moreover, this result holds even for subjects whose payoffs remain unchanged. Our results suggest that social welfare motivations drives the negative relationship between equity and coordination success found in this experiment. Moreover, our data suggest that the order of treatment matters. Groups facing first the treatment with high inequality in coordination payoffs, then the treatment with low inequality in coordination payoffs, reach the Pareto dominant equilibrium more often in both treatments compared to groups playing first the treatment with low inequality in coordination payoffs, then the treatment with high inequality in coordination payoffs.
    Keywords: coordination game,difference aversion,equity,effciency,social welfare motivation
    Date: 2018–12–07
  15. By: Werner Kirsch; Wojciech S{\l}omczy\'nski; Dariusz Stolicki; Karol \.Zyczkowski
    Abstract: A mathematical analysis of the distribution of voting power in the Council of the European Union operating according to the Treaty of Lisbon is presented. We study the effects of Brexit on the voting power of the remaining members, measured by the Penrose--Banzhaf Index. We note that the effects in question are non-monotonic with respect to voting weights, and that some member states will lose power after Brexit. We use the normal approximation of the Penrose--Banzhaf Index in double-majority games to show that such non-monotonicity is in most cases inherent in the double-majority system, but is strongly exacerbated by the peculiarities of the EU population vector. Furthermore, we investigate consequences of a hypothetical "generalized Brexit", i.e., NN-exit of another member state (from a 28-member Union), noting that the effects on voting power are non-monotonic in most cases, but strongly depend on the size of the country leaving the Union.
    Date: 2018–12
  16. 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); 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 morefrom 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. Our results bolster other experimental ndings on the strategic environment effects that are relevant for macroeconomic issues such as price fluctuations and nominal rigidity.
    Keywords: beauty contest games,iterative reasoning,strategic complementarity,strategic substitutability
    Date: 2018–12–14
  17. By: Wu, Haoyang
    Abstract: In mechanism design theory, a designer would like to implement a desired social choice function which specifies her favorite outcome for each possible profile of all agents' types. Since the designer does not know each agent's private type, what she can do is to construct a mechanism and choose an outcome after observing a profile of agents' strategies. There is a dilemma in the sense that even if the designer is not satisfied with some outcome, she has to obey the mechanism designed by herself and announce this outcome. In this paper, we generalize the mechanism design theory to a case where the designer can take some action to actively adjust agents' private types, and yield a more favorite outcome. After defining a series of notions such as adjustable types, optimal adjustment cost and profitably Bayesian implementability, we propose that the traditional notion of Bayesian incentive compatibility does not hold in this generalized case. Finally, we construct a model to illustrate that the auctioneer can obtain an expected profit greater than what she obtains in the traditional optimal auction.
    Keywords: Mechanism design; Optimal auction; Bayesian Nash implementation.
    JEL: D71
    Date: 2018–12–24
  18. By: Dimitri Dubois (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); Stefano Farolfi (UMR G-EAU - Gestion de l'Eau, Acteurs, Usages - CIRAD - Centre de Coopération Internationale en Recherche Agronomique pour le Développement - AgroParisTech - IRSTEA - Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture - CIHEAM - Centre International des Hautes Études Agronomiques Méditerranéennes - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier); Phu Nguyen-Van (BETA - Bureau d'Économie Théorique et Appliquée - INRA - Institut National de la Recherche Agronomique - UNISTRA - Université de Strasbourg - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique); Juliette Rouchier (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique)
    Abstract: We experimentally investigate the impact of information sharing in a common pool resource game. More precisely, we test whether the voluntary disclosure of the decision by a player has a positive impact on the extraction level exhibited by the group compared to the level observed when decisions are compulsory disclosed. We design an experiment composed by three treatments: a mandatory disclosure treatment and two treatments where players are free to choose whether or not to disclose their decisions. The latter differ by the degree of freedom given to players. In the treatment « Voluntary Free Disclosure » players are also free to choose the extraction level that is displayed, while in the treatment « Voluntary Binary Disclosure » if the player discloses h(is)er decision the value displayed is the effective extraction level. We observe that the voluntary disclosure has a positive effect in the social dilemma, measured by lower average extraction levels. However the disclosure mechanism should not allow to self-declare extraction: here it reveals a large tendency to lie leading to an increase in extraction.
    Date: 2018–12–07
  19. By: Roxana Dumitrescu
    Abstract: In this paper we study the problem of nonlinear pricing of an American option with a right-continuous left-limited (RCLL) payoff process in an incomplete market with default, from the buyer's point of view. We show that the buyer's price process can be represented as the value of a stochastic control/optimal stopping game problem with nonlinear expectations, which corresponds to the maximal subsolution of a constrained reflected Backward Stochastic Differential Equation (BSDE). We then deduce a nonlinear optional decomposition of the buyer's price process. To the best of our knowledge, no dynamic dual representation of the buyer's price process can be found in the literature, even in the case of a linear incomplete market and brownian filtration. Finally, we prove the "infimum" and the "supremum" in the definition of the stochastic game problem can be interchanged. Our method relies on new tools, as simultaneous nonlinear Doob-Meyer decompositions of processes which have a $\mathscr{Y}^\nu$-submartingale property for each admissible control $\nu$.
    Date: 2019–01

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