nep-gth New Economics Papers
on Game Theory
Issue of 2020‒05‒25
fourteen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Infinite-Duration All-Pay Bidding Games By Guy Avni; Isma\"el Jecker; {\DJ}or{\dj}e \v{Z}ikeli\'c
  2. All Symmetric Equilibria in Differential Games with Public Goods By Niko Jaakkola; Florian Wagener; Florian O.O. Wagener
  3. Intelligence, Errors and Strategic Choices in the Repeated Prisoners Dilemma By Eugenio Proto; Aldo Rustichini; Andis Sofianos
  4. Costly agreement-based transfers and targeting on networks with synergies By Mohamed Belhaj; Frédéric Deroïan; Shahir Safi
  5. On importance indices in multicriteria decision making By Michel Grabisch; Christophe Labreuche; Mustapha Ridaoui
  6. The Creation of Social Norms under Weak Institutions By Diekert, Florian; Eymess, Tillmann; Luomba, Joseph; Waichman, Israel
  7. $alpha-$ robust equilibrium in anonymous games By Deepanshu Vasal; Randall Berry
  8. Covid-19, Shelter-In Place Strategies and Tipping By Zhihan Cui; Geoffrey Heal; Howard Kunreuther
  9. A Game-Theoretic Model of Sexual Harassment By Batabyal, Amitrajeet; Beladi, Hamid
  10. Dynamic effects of enforcement on cooperation By Roberto Galbiati; Emeric Henry; Nicolas Jacquemet
  11. Rationalist Explanations for Two-Front War By Nakao, Keisuke
  12. Estimating Intra-household Bargaining Power When Outside Options Are Endogenous By Chavas, Jean-Paul; Klein, Matthew J.
  13. Anti-conformism in the Threshold Model of Collective Behavior By Michel Grabisch; Fen Li
  14. Coordination with communication under oath By Nicolas Jacquemet; Stéphane Luchini; Jason Shogren; Adam Zylbersztejn

  1. By: Guy Avni; Isma\"el Jecker; {\DJ}or{\dj}e \v{Z}ikeli\'c
    Abstract: A graph game is a two-player zero-sum game in which the players move a token throughout a graph to produce an infinite path, which determines the winner or payoff of the game. In "bidding games", in each turn, we hold an 'auction' (bidding) to determine which player moves the token. The players simultaneously submit bids and the higher bidder moves the token. Several different payment schemes have been considered. In "first-price" bidding, only the higher bidder pays his bid, while in "all-pay" bidding, both players pay their bids. Bidding games were largely studied with variants of first-price bidding. In this work, we study, for the first time, infinite-duration all-pay bidding games, and show that they exhibit the elegant mathematical properties of their first-price counterparts. This is in stark contrast with reachability games, which are known to be much more complicated under all-pay bidding than first-price bidding. Another orthogonal distinction between the bidding rules is in the recipient of the payments: in "Richman" bidding, the bids are paid to the other player, and in "poorman" bidding, the bids are paid to the 'bank'. We focus on strongly-connected games with "mean-payoff" and "parity" objectives. We completely solve all-pay Richman games: a simple argument shows that deterministic strategies cannot guarantee anything in this model, and it is technically much more challenging to find optimal probabilistic strategies that achieve the same expected guarantees in a game as can be obtained with deterministic strategies under first-price bidding. Under poorman all-pay bidding, in contrast to Richman bidding, deterministic strategies are useful and guarantee a payoff that is only slightly lower than the optimal payoff under first-price poorman bidding. Our proofs are constructive and based on new and significantly simpler constructions for first-price bidding.
    Date: 2020–05
  2. By: Niko Jaakkola; Florian Wagener; Florian O.O. Wagener
    Abstract: We characterise the entire set of symmetric stationary Markov-perfect Nash equilibria (MPE) in a differential game of public good investment, using the canonical problem of climate change as an example. We provide a sufficient and necessary condition for MPE and show how the entire set of MPE is constructed. The equilibrium in continuous strategies, unique in our context, is Pareto-dominated by any other equilibrium. If a Pareto-undominated steady state exists, it is sustained by trigger-like strategies, with deviations above and below the steady state leading to different responses. We extend the theory of differential games to deal with payoffs under discontinuous strategies. Our methods work under general functional forms.
    Keywords: differential games, Markov-perfect Nash equilibrium, dynamic investment games, dynamic public goods, climate change
    JEL: C61 C73 D90 Q54
    Date: 2020
  3. By: Eugenio Proto; Aldo Rustichini; Andis Sofianos
    Abstract: A large literature in behavioral economics has emphasized in the last decades the role of individual differences in social preferences (such as trust and altruism) in influencing behavior in strategic environments. Here we emphasize the role of attention and working memory, and show that social interactions among heterogeneous groups are mediated by differences in cognitive skills. Our design uses a repeated prisoner’s dilemma; we compare rates of cooperation in groups of subjects separated according to their IQ, with those in integrated groups, where subjects of different IQ are pooled together. In integrated groups we observe higher aggregated cooperation rates and profits than in separated groups. There are gains in earnings among lower IQ subjects who learn how to cooperate faster than when they play separately, and smaller losses for higher IQ subjects. We also see that higher IQ subjects become less lenient when they are matched with lower IQ subjects than when they play separately. This pattern is an instance of a general phenomenon, which we demonstrate in an evolutionary game theory model, in which higher IQ among subjects induces –possibly thanks to better working memory– a lower frequency of errors in strategy implementation. We show that players indeed choose less-lenient strategies in environments in which subjects have higher error rates. Estimations of errors and strategies from the experimental data are consistent with the hypothesis and model’s predictions.
    Keywords: Repeated Prisoners Dilemma, Cooperation, Intelligence, IQ, Strategy, Error in Transition
    JEL: C73 C91 C92
    Date: 2020–03
  4. By: Mohamed Belhaj (Aix-Marseille Univ, CNRS, EHESS, Ecole Centrale, AMSE, Marseille, France.); Frédéric Deroïan (Aix-Marseille Univ, CNRS, EHESS, Ecole Centrale, AMSE, Marseille, France.); Shahir Safi (Aix-Marseille Univ, CNRS, EHESS, Ecole Centrale, AMSE, Marseille, France.)
    Abstract: We consider agents organized in an undirected network of local complementarities. A principal with a limited budget offers costly bilateral contracts in order to increase the sum of agents' effort. We study excess-effort linear payment schemes, i.e. contracts rewarding effort in excess to the effort made in absence of principal. The analysis provides the following main insights. First, for all contracting costs, the optimal unit returns offered to every targeted agent are positive and generically heterogeneous. This heterogeneity is due to the presence of outsiders, who create asymmetric interaction between contracting agents. Second, when contracting costs are low, it is optimal to contract with everyone and optimal unit returns are identical for all agents. Third, when contracting costs are sufficiently high, it becomes optimal to target a subset of agents, and optimal targeting can lead to NP-hard problems. In particular, when the intensity of complementarities is sufficiently low, a correspondence is established between optimal targeting and the densest k subgraph problem. Overall, the optimal targeting problem involves a trade-off between centrality and budget spending-central agents are influential, but are also more budget-consuming. These considerations can lead the principal to not target central agents.
    Keywords: networked synergies, aggregate effort, optimal group targeting, linear contract
    JEL: C72 D85
    Date: 2020–04
  5. By: Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne, PSE - Paris School of Economics); Christophe Labreuche (Thales Research and Technology [Palaiseau] - THALES); Mustapha Ridaoui (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne)
    Abstract: We address the problem of how to define an importance index in multicriteria decision problems, when a numerical representation of preferences is given. We make no restrictive assumption on the model, which could have discrete or continuous attributes, and in particular , it is not assumed that the model is monotonically increasing or decreasing with respect to the attributes. Our analysis first considers discrete models, which are seen to be equivalent to multichoice games. We propose essentially two importance indices, namely the signed importance index and the absolute importance index, both based on the average variation of the value of the model induced by a given attribute. We provide several axiomatizations for these importance indices, extend them to the continuous case, and finally illustrate them with examples: classical simple models and an example of discomfort evaluation based on real data.
    Keywords: Choquet integral,Multiple criteria analysis,Multichoice game,Shapley value
    Date: 2019–08–16
  6. By: Diekert, Florian; Eymess, Tillmann; Luomba, Joseph; Waichman, Israel
    Abstract: Preventing overfishing at Lake Victoria is a typical situation where policies have to rely on norm-based interventions to improve outcomes. Our lab-in-the-field experiment studies how information about high or low levels of previous cooperation affects the creation of social norms in a three-player prisoner’s dilemma game with/without a feedback mechanism. The provision of social information succeeds in creating norms of cooperation only if a feedback mechanism is available. Without feedback, social information cannot prevent the decline of cooperation rates. Exploring the role of the reference network, we find that the effect increases with social proximity among participants.
    Keywords: common pool resource; collective action; social norms; lab-in-the-field experiment
    Date: 2020–05–14
  7. By: Deepanshu Vasal; Randall Berry
    Abstract: In this paper, we consider the notion of $\alpha-$ robust equilibrium for finite strategic players in anonymous games, where utility of a player depends on other players' actions only through the resulting distribution of actions played. This equilibrium is defined as the set of strategies of the players such that no user wants to deviate as long as $N-\alpha-1$ number are playing the equilibrium strategies. We provide sufficient conditions for the existence of this equilibrium. In addition, we prove a part of Berge's Maximal Theorem for correspondences.
    Date: 2020–05
  8. By: Zhihan Cui; Geoffrey Heal; Howard Kunreuther
    Abstract: Social distancing via shelter-in-place strategies has emerged as the most effective way to combat Covid-19. In the United States, choices about such policies are made by individual states. Here we show that the policy choice made by one state influences the incentives that other states face to adopt similar policies: they can be viewed as strategic complements in a supermodular game. If they satisfy the condition of uniform strict increasing differences then following Heal and Kunreuther ([6]) we show that if enough states engage in social distancing, they will tip others to do the same and thus shift the Nash equilibrium with respect to the number of states engaging in social distancing.
    JEL: C72 I12 I18
    Date: 2020–05
  9. By: Batabyal, Amitrajeet; Beladi, Hamid
    Abstract: We focus on the interaction between a male employee and his supervisor and analyze a game-theoretic model of sexual harassment in the workplace. The male employee is accused of sexually harassing a female employee and the supervisor's task is to gather evidence and then determine whether to legally charge the male employee with sexual harassment. The evidence gathering process is random and concrete evidence is available to the supervisor with probability one-half. Our analysis of this strategic interaction leads to four results. First, we delineate the game in extensive form. Second, we specify the matrix that represents the normal form of the extensive form. Third, we show that there is no pure-strategy Nash equilibrium in the game between the male employee and his supervisor. Finally, we show that there exists a mixed-strategy Nash equilibrium in the same male employee-supervisor game.
    Keywords: Evidence, Mixed-Strategy Nash Equilibrium, Sexual Harassment, Supervisor
    JEL: J71 K42
    Date: 2020–02–15
  10. By: Roberto Galbiati (EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique); Emeric Henry (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique); Nicolas Jacquemet (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne, PSE - Paris School of Economics)
    Abstract: In situations where social payoffs are not aligned with private incentives, enforcement with fines can be a way to sustain cooperation. In this paper we show, by the means of a lab experiment , that past fines can have an effect on current behavior even when no longer in force. We document two mechanisms: a) past fines affect directly individuals' future propensity to cooperate; b) when fines for non cooperation are in place in the past, individuals experience higher levels of cooperation from partners and, consistent with indirect reciprocity motives, are in turn nicer towards others once these fines have been removed. This second mechanism is empirically prevalent and, in contrast with the first, induces a snowball effect of past enforcement. Our results can inform the design of costly enforcement policies.
    Keywords: experiments,Laws,social values,cooperation,learning,spillovers,persistence of institutions,repeated games
    Date: 2018–12
  11. By: Nakao, Keisuke
    Abstract: By extending the extant costly-lottery models of war to three-party bargaining scenarios, we offer rationalist explanations for two-front war, where a state at the center is fought by two enemies at opposing peripheries. We found that even though private information exists only in one front, war can break out in both fronts. Because the war outcome in one front can affect the outcome in the other through the shift of military balance, the central state may preemptively initiate war in one front to establish its preponderance in the other (e.g., World War I), or a peripheral state may preventively join the war waging in the other front to leverage its power (e.g., Napoleonic Wars). These findings echo Waltz's neorealism concern that a multi-polar system may not be so stable as the bipolar system that bargaining models of dyadic war commonly presume.
    Keywords: costly-lottery models, rationalist explanations for war, three-party bargaining, two-front war.
    JEL: C78 D74 F51
    Date: 2020–05–15
  12. By: Chavas, Jean-Paul (U of Wisconsin-Madison); Klein, Matthew J. (U of Wisconsin-Madison)
    Abstract: We generalize the collective model of the family to let partners choose their outside options, whether to act on them, and how to allocate shared resources. To do so, we apply Harsanyi's (1986) generic games framework to a limited-commitment collective model where a family's real consumption opportunities depend on each partners' specified outside option. We demonstrate uniqueness and existence of the solution by applying Rubinstein, Safra, and Thomson's (1992) appeals-immunity solution concept. We demonstrate that the expected value of bargaining power is semi-parametrically identified in an ordinal framework; the research need not assume specific utility or social welfare functional forms. In addition to empirical tractability and analytical precision, this update to the collective model provides a more nuanced view of intra-household bargaining power: partners with a greater capacity to specify more damaging threats will have more control over the decision-making process, regardless of whether they act on those threats.
    JEL: D1 D6 D7
    Date: 2020–02
  13. By: Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne, PSE - Paris School of Economics); Fen Li (Department of Entomology - Michigan State University [East Lansing] - Michigan State University System)
    Abstract: We provide a detailed study of the threshold model, where both conformist and anti-conformist agents coexist. Our study bears essentially on the convergence of the opinion dynamics in the society of agents, i.e., finding absorbing classes, cycles, etc. Also, we are interested in the existence of cascade effects, as this may constitute a undesirable phenomenon in collective behavior. We divide our study into two parts. In the first one, we basically study the threshold model supposing a fixed complete network, where every one is connected to every one, like in the seminal work of Granovetter. We study the case of a uniform distribution of the threshold, of a Gaussian distribution, and finally give a result for arbitrary distributions, supposing there is one type of anti-conformist. In a second part, we suppose that the neighborhood of an agent is random, drawn at each time step from a distribution. We distinguish the case where the degree (number of links) of an agent is fixed, and where there is an arbitrary degree distribution. We show the existence of cascades and that for most societies, the opinion converges to a chaotic situation.
    Keywords: threshold model,anti-conformism,absorbing class,opinion dynamics
    Date: 2019
  14. By: Nicolas Jacquemet (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne, PSE - Paris School of Economics); Stéphane Luchini (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université - EHESS - École des hautes études en sciences sociales, AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique); Jason Shogren (Departement of Economics and Finance, University of Wyoming - UW - University of Wyoming); Adam Zylbersztejn (GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - ENS Lyon - École normale supérieure - Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet [Saint-Étienne] - Université de Lyon - CNRS - Centre National de la Recherche Scientifique)
    Abstract: We focus on the design of an institutional device aimed to foster coordination through communication. We explore whether the social psychology theory of commitment, implemented via a truth-telling oath, can reduce coordination failure. Using a classic coordination game, we ask all players to sign voluntarily a truth-telling oath before playing the game with cheap talk communication. Three results emerge with commitment under oath: (1) coordination increased by nearly 50 percent; (2) senders' messages were significantly more truthful and actions more efficient, and (3) receivers' trust of messages increased.
    Keywords: Oath,Cheap talk communication,Coordination game
    Date: 2018–09

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