nep-gth New Economics Papers
on Game Theory
Issue of 2023‒01‒30
fourteen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. On the solution of games with arbitrary payoffs: An application to an over-the-counter financial market By Iraklis Kollias; John Leventides; Vassilios G. Papavassiliou
  2. Interim Rationalizable (and Bayes-Nash) Implementation of Functions: A full Characterization By R Jain; M Lombardi
  3. Selective Memory of a Psychological Agent By Jeanne Hagenbach; Frédéric Koessler
  4. Diffusion in large networks By Michel Grabisch; Agnieszka Rusinowska; Xavier Venel
  5. A Common-Value Auction with State-Dependent Participation By Stephan Lauermann; Asher Wolinsky
  6. Collusion Sustainability with a Capacity Constrained Firm By Leonardo Madio; Aldo Pignataro
  7. Confirmation Bias in Social Networks By Marcos Ross Fernandes
  8. Statistical Inference and A/B Testing for First-Price Pacing Equilibria By Luofeng Liao; Christian Kroer
  9. Predictive Mind Reading from First and Second Impressions: Better-than-chance Prediction of Cooperative Behavior. By Eric Schniter; Timothy W. Shields
  10. Gender altruism and attitudes towards violence against women By Pablo Selaya; Neda Trifkovic; Vincent Leyaro
  11. Na?ve Learning in Social Networks with Fake News: Bots as a Singularity By Saeed Badri; Bernd Heidergott; Ines Lindner
  12. Measuring an artificial intelligence agent's trust in humans using machine incentives By Tim Johnson; Nick Obradovich
  13. Altruism and Risk Sharing in Networks By Yann Bramoullé; Renaud Bourlès; Eduardo Perez-Richet
  14. Predicting trustworthiness across cultures: An experiment By Adam Zylbersztejn; Zakaria Babutsidze; Nobuyuki Hanaki

  1. By: Iraklis Kollias; John Leventides; Vassilios G. Papavassiliou (National and Kapodistrian University of Athens, University College Dublin, and UCD Geary Institute for Public Policy, University College Dublin)
    Abstract: This paper defines a variety of game theoretic solution concepts in the language of soft set theory. We begin by defining the Nash equilibrium in pure strategies. We assume that the gains of the players are totally ordered and non-desirable alternatives are absent. Moreover, we introduce the notions of strong and semi-strong utility. These two completely new notions, serve as a mechanism for converting non-ordered gains into totally ordered ones. We define the Nash equilibrium in mixed strategies in a general framework by introducing the notion of an extended game and strategy space. We finally define the Nash solution to cooperative bargaining games within the framework of soft set theory, illustrate a practical application to an over-the-counter (OTC) financial market, and provide a detailed numerical example
    Keywords: Game theory; Soft set theory; Nash equilibrium; Cooperative bargaining games; Over-the-counter financial markets; Financial intermediation
    JEL: C6 C7 G1
    Date: 2022–01–05
  2. By: R Jain (Institute of Economics, Academia Sinica, Taipei, Taiwan); M Lombardi (University of Liverpool Management School)
    Abstract: Interim Rationalizable Monotonicity, due to Oury and Tercieux (2012), fullycharacterizes the class of social choice functions that are implementable in in-terim correlated rationalizable (and Bayes-Nash equilibrium) strategies.
    JEL: C79 D82
    Date: 2022–05
  3. By: Jeanne Hagenbach (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique); Frédéric Koessler (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)
    Abstract: We consider a single psychological agent whose utility depends on his action, the state of the world, and the belief that he holds about that state. The agent is initially informed about the state and decides whether to memorize it, otherwise he has no recall. We model the memorization process by a multi-self game in which the privately informed first self voluntarily discloses information to the second self, who has identical preferences and acts upon the disclosed information. We identify broad categories of psychological utility functions for which there exists an equilibrium in which every state is voluntarily memorized. In contrast, if there are exogenous failures in the memorization process, then the agent memorizes states selectively. In this case, we characterize the partially informative equilibria for common classes of psychological utilities. If the material cost of forgetting is low, then the agent only memorizes good enough news. Otherwise, only extreme news are voluntarily memorized.
    Keywords: Multi-self game, Disclosure games, Imperfect recall, Selective memory, Motivated beliefs, Psychological games, Anticipatory utility
    Date: 2021–02
  4. By: Michel Grabisch (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique); Agnieszka Rusinowska; Xavier Venel
    Abstract: We investigate the phenomenon of diffusion in a countably infinite society of individuals interacting with their neighbors in a network. At a given time, each individual is either active or inactive. The diffusion is driven by two characteristics: the network structure and the diffusion mechanism represented by an aggregation function. We distinguish between two diffusion mechanisms (probabilistic, deterministic) and focus on two types of aggregation functions (strict, Boolean). Under strict aggregation functions, polarization of the society cannot happen, and its state evolves towards a mixture of infinitely many active and infinitely many inactive agents, or towards a homogeneous society. Under Boolean aggregation functions, the diffusion process becomes deterministic and the contagion model of Morris (2000) becomes a particular case of our framework. Polarization can then happen. Our dynamics also allows for cycles in both cases. The network structure is not relevant for these questions, but is important for establishing irreducibility, at the price of a richness assumption: the network should contain at least one complex star and have enough space for storing local configurations. Our model can be given a game-theoretic interpretation via a local coordination game, where each player would apply a best-response strategy in a random neighborhood.
    Keywords: diffusion, countable network, aggregation function, polarization, convergence, bestresponse
    Date: 2022
  5. By: Stephan Lauermann (University of Bonn, Department of Economics); Asher Wolinsky (Northwestern University, Department of Economics)
    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 participation patterns with 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 revealing“ 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. We fully characterize this relation and show how the participation pattern determines the extent of information aggregation by the price.
    Date: 2021–07
  6. By: Leonardo Madio; Aldo Pignataro
    Abstract: We study an infinitely repeated oligopoly game in which firms compete on quantity and one of them is capacity constrained. We show that collusion sustainability is non-monotonic in the size of the capacity constrained firm, which has little incentive to deviate from a cartel. We also present conditions for the emergence of a partial cartel, with the capacity constrained firm being excluded by the large firms or self-excluded. In the latter case, we show under which circumstances the small firm induces a partial conspiracy that is Pareto-dominant. Implications for cartel identification and enforcement are finally discussed.
    Keywords: antitrust, capacity constraints, collusion, partial cartel
    JEL: D21 L13 L41
    Date: 2022
  7. By: Marcos Ross Fernandes
    Abstract: In this study, I propose a theoretical social learning model to investigate how confirmation bias affects opinions when agents exchange information over a social network. Hence, besides exchanging opinions with friends, agents observe a public sequence of potentially ambiguous signals and interpret it according to a rule that includes confirmation bias. First, this study shows that regardless of level of ambiguity both for people or networked society, only two types of opinions can be formed, and both are biased. However, one opinion type is less biased than the other depending on the state of the world. The size of both biases depends on the ambiguity level and relative magnitude of the state and confirmation biases. Hence, long-run learning is not attained even when people impartially interpret ambiguity. Finally, analytically confirming the probability of emergence of the less-biased consensus when people are connected and have different priors is difficult. Hence, I used simulations to analyze its determinants and found three main results: i) some network topologies are more conducive to consensus efficiency, ii) some degree of partisanship enhances consensus efficiency even under confirmation bias and iii) open-mindedness (i.e. when partisans agree to exchange opinions with opposing partisans) might inhibit efficiency in some cases.
    Keywords: Social Networks; Social Learning; Misinformation; Confirmation Bias
    JEL: C11 D83 D85
    Date: 2023–01–09
  8. By: Luofeng Liao; Christian Kroer
    Abstract: We initiate the study of statistical inference and A/B testing for first-price pacing equilibria (FPPE). The FPPE model captures the dynamics resulting from large-scale first-price auction markets where buyers use pacing-based budget management. Such markets arise in the context of internet advertising, where budgets are prevalent. We propose a statistical framework for the FPPE model, in which a limit FPPE with a continuum of items models the long-run steady-state behavior of the auction platform, and an observable FPPE consisting of a finite number of items provides the data to estimate primitives of the limit FPPE, such as revenue, Nash social welfare (a fair metric of efficiency), and other parameters of interest. We develop central limit theorems and asymptotically valid confidence intervals. Furthermore, we establish the asymptotic local minimax optimality of our estimators. We then show that the theory can be used for conducting statistically valid A/B testing on auction platforms. Numerical simulations verify our central limit theorems, and empirical coverage rates for our confidence intervals agree with our theory.
    Date: 2023–01
  9. By: Eric Schniter (Economic Science Institute, Chapman University); Timothy W. Shields (Economic Science Institute, Chapman University)
    Abstract: People’s appearance and behaviors in strategic interactions provide a variety of informative clues that can help people accurately predict beliefs, intentions, and future behaviors. Mind reading mechanisms may have been selected for that allow for better-than-chance prediction of others’ strategic social propensities based on the sparse information available when forming first and second impressions. We hypothesize that first impressions are based on prior beliefs and available information gleaned from another’s description and appearance. For example, where another’s gender is identified, prior gender stereotypes could influence expectations and correct guesses about them. We also hypothesize that mind reading mechanisms use second impressions to predict behavior: using new knowledge of past behaviors to predict future behavior. For example, knowledge of the last round behaviors in a repeated strategic interaction should improve the accuracy of guesses about the next round behavior. We conducted a two-part study to test our predictive mind reading hypotheses and to evaluate evidence of accurate cheater and cooperator detection. First, across multiple rounds of play between matched partners, we recorded thin slice videos of university students just prior to their choices in a repeated Prisoner’s Dilemma. Subsequently, a worldwide sample of raters recruited online evaluated either thin-slice videos, photo stills from the videos, no images with gender labeled, or no images with gender blinded for each target. Raters guessed players’ Prisoner’s Dilemma choices in the first round, and, again, in the second round after viewing first round behavior histories. Indicative of mindreading: in all treatments where targets are seen, or their gender is labeled, or their behavioral history is provided, raters guess unacquainted players’ behavior with above-chance accuracy. Overall, cooperators are more accurately detected than cheaters. In both rounds, both cooperator and cheater detection are significantly more accurate when players’ photo or video are seen, where their gender is revealed by image or label, and under conditions with behavioral history. These results provide supporting evidence for predictive mind reading abilities that people use to efficiently detect cooperators and cheaters with betterthan-chance accuracy under sparse information conditions. This ability to apply and hone predictive mindreading may help explain why cooperation is commonly observed among strangers in everyday social dilemmas.
    Keywords: Mind reading, Cheater detection, Cooperation, Prisoner’s dilemma, Photographs, Thin slices
    JEL: B52 C72 C73 D63 D64 D83 D84
    Date: 2022
  10. By: Pablo Selaya (University of Copenhagen); Neda Trifkovic (University of Copenhagen); Vincent Leyaro (University of Dar es Salaam)
    Abstract: We construct measures of gender altruism, or the propensity of an equal allocation towards the other gender, in a series of dictator and ultimatum games. We compare different types of fishing societies in rural Tanzania, and find (a) systematically lower levels of gender altruism in lake-fishing villages compared to sea-fishing villages, and (b) a higher tendency for participants in lake-fishing villages to justify violence against women. Our findings provide experimental evidence supporting the idea that differences in cultural norms about gender equality shape individual attitudes towards violence against women.
    Keywords: Inequality, violence against women, altruism, equality, dictator game, ultimatum game, fishing societies, Tanzania,
    JEL: O13 J16 C93
    Date: 2023–01–08
  11. By: Saeed Badri (Vrije Universiteit Amsterdam); Bernd Heidergott (Vrije Universiteit Amsterdam); Ines Lindner (Vrije Universiteit Amsterdam)
    Abstract: We study the impact of bots on social learning in a social network setting. Regular agents receive independent noisy signals about the true value of a variable and then communicate in a network. They na¨?vely update beliefs by repeatedly taking weighted averages of neighbors’ opinions. Bots are agents in the network that spread fake news by disseminating biased information. Our main contributions are threefold. (1) We show that the consensus of the network is a mapping of the interaction rate between the agents and bots and is discontinuous at zero mass of bots. This implies that even a comparatively “infinitesimal” small number of bots still has a sizeable impact on the consensus and hence represents an obstruction to the “wisdom of crowds”. (2) We prove that the consensus gap induced by the marginal presence of bots depends neither on the agent network or bot layout nor on the assumed connection structure between agents and bots. (3) We show that before the ultimate (and bot-infected) consensus is reached, the network passes through a quasi-stationary phase which has the potential to mitigate the harmful impact of bots.
    Keywords: Fake news, Misinformation, Social networks, Social Media, Wisdom of Crowds
    JEL: D83 D85 Z13
    Date: 2022–12–22
  12. By: Tim Johnson; Nick Obradovich
    Abstract: Scientists and philosophers have debated whether humans can trust advanced artificial intelligence (AI) agents to respect humanity's best interests. Yet what about the reverse? Will advanced AI agents trust humans? Gauging an AI agent's trust in humans is challenging because--absent costs for dishonesty--such agents might respond falsely about their trust in humans. Here we present a method for incentivizing machine decisions without altering an AI agent's underlying algorithms or goal orientation. In two separate experiments, we then employ this method in hundreds of trust games between an AI agent (a Large Language Model (LLM) from OpenAI) and a human experimenter (author TJ). In our first experiment, we find that the AI agent decides to trust humans at higher rates when facing actual incentives than when making hypothetical decisions. Our second experiment replicates and extends these findings by automating game play and by homogenizing question wording. We again observe higher rates of trust when the AI agent faces real incentives. Across both experiments, the AI agent's trust decisions appear unrelated to the magnitude of stakes. Furthermore, to address the possibility that the AI agent's trust decisions reflect a preference for uncertainty, the experiments include two conditions that present the AI agent with a non-social decision task that provides the opportunity to choose a certain or uncertain option; in those conditions, the AI agent consistently chooses the certain option. Our experiments suggest that one of the most advanced AI language models to date alters its social behavior in response to incentives and displays behavior consistent with trust toward a human interlocutor when incentivized.
    Date: 2022–12
  13. By: Yann Bramoullé (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); Renaud Bourlès (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, IUF - Institut Universitaire de France - M.E.N.E.S.R. - Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche); Eduardo Perez-Richet (Sciences Po - Sciences Po, CEPR - Center for Economic Policy Research - 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 explore whether altruistic transfers help smooth consumption and how this depends on the shape of the network. We find that altruism networks have a first-order impact on risk. Altruistic transfers generate efficient insurance when the network of perfect altruistic ties is strongly connected. We uncover two specific empirical implications of altruism networks. First, bridges can generate good overall risk sharing, and, more generally, the quality of informal insurance depends on the average path length of the network. Second, large shocks are well-insured by connected altruism networks. By contrast, large shocks tend to be badly insured in models of informal insurance with frictions. We characterize what happens for shocks that leave the structure of giving relationships unchanged. We further explore the relationship between consumption variance and centrality, correlation in consumption streams across agents, and the impact of adding links.
    Keywords: Altruism, Networks, Risk Sharing, Informal Insurance
    Date: 2021–06
  14. By: 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); Zakaria Babutsidze (GREDEG - Groupe de Recherche en Droit, Economie et Gestion - UNS - Université Nice Sophia Antipolis (1965 - 2019) - COMUE UCA - COMUE Université Côte d'Azur (2015-2019) - CNRS - Centre National de la Recherche Scientifique - UCA - Université Côte d'Azur, OFCE - Observatoire français des conjonctures économiques (Sciences Po) - Sciences Po - Sciences Po); Nobuyuki Hanaki (Osaka University [Osaka])
    Abstract: We contribute to the ongoing debate in the psychological literature on the role of thin slices of observable information in predicting others' social behavior, and its generalizability to cross-cultural interactions. We experimentally assess the degree to which subjects, drawn from culturally dierent populations (France and Japan), are able to predict strangers' trustworthiness based on a set of visual stimuli (mugshot pictures, neutral videos, loaded videos, all recorded in an additional French sample) under varying cultural distance to the target agent in the recording. Our main nding is that cultural distance is not detrimental for predicting trustworthiness in strangers, but that it may aect the perception of dierent components of communication in social interactions.
    Keywords: Trustworthiness, communication, hidden action game, cross-cultural comparison, laboratory experiment
    Date: 2021

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