nep-gth New Economics Papers
on Game Theory
Issue of 2022‒10‒31
eighteen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Viable Nash Equilibria: An Experiment By Duk Gyoo Kim; Daehong Min; John Wooders
  2. Optimin achieves super-Nash performance By Mehmet S. Ismail
  3. A Game-Theoretic Model of Superpowers Competing for a Sphere of Influence By Tomoo Kikuchi; Shuige Liu
  4. Inverse Game Theory for Stackelberg Games: the Blessing of Bounded Rationality By Jibang Wu; Weiran Shen; Fei Fang; Haifeng Xu
  5. The Uncertainty of Fairness: a Game Theory Analysis for a Debt Mutualization Scheme in the Euro Area By D'Andrea, Sara; Vassalli, Federica
  6. Equilibrium (non-)Existence in Games with Competing Principals By Attar, Andrea; Campioni, Eloisa; Piaser, Gwenaël
  7. Exit game with private information By H. Dharma Kwon; Jan Palczewski
  8. Stake-governed tug-of-war and the biased infinity Laplacian By Alan Hammond; G\'abor Pete
  9. Measuring strategic-uncertainty attitudes By Lisa Bruttel; Muhammed Bulutay; Camille Cornand; Frank Heinemann; Adam Zylbersztejn
  10. Key players in bullying networks By Atay, Ata; Mauleon, Ana; Schopohl, Simon; Vannetelbosch, Vincent
  11. Implementation with Uncertain Evidence By Soumen Banerjee; Yi-Chun Chen
  12. Friendship networks with farsighted agents By Luo, Chenghong; Mauleon, Ana; Vannetelbosch, Vincent
  13. Information Design in Cheap Talk By Qianjun Lyu; Wing Suen
  14. Efficient networks in connections models with heterogeneous nodes and links By Olaizola, Norma; Valenciano, Federico
  15. Setting reserve prices in repeated procurement auctions By Sümeyra Atmaca; Riccardo Camboni; Elena Podkolzina; Koen Schoors; Paola Valbonesi
  16. "Equilibrium Pricing of Securities in the Co-presence of Cooperative and Non-cooperative Populations" By Masaaki Fujii
  17. News Media Bargaining Codes By Luca Sandrini; Robert Somogyi
  18. Learning from Viral Content By Krishna Dasaratha; Kevin He

  1. By: Duk Gyoo Kim; Daehong Min; John Wooders
    Abstract: This paper examines the usefulness of Kalai (2020)’s measure of the viability of Nash equilibrium. We experimentally study a class of participation games, which differ in the number of players, the success threshold, and the payoff to not participating. We find that Kalai’s measure captures well how the viability of the everyone-participates (eP) equilibrium depends on the success threshold; the measure does not capture other elements of the game which affect the likelihood that the eP equilibrium is played.
    Keywords: Nash equilibrium, viability, laboratory experiments, coordination game
    JEL: C00 C70 C92 D90
    Date: 2022
  2. By: Mehmet S. Ismail
    Abstract: Since the 1990s, AI systems have achieved superhuman performance in major zero-sum games where "winning" has an unambiguous definition. However, most social interactions are mixed-motive games, where measuring the performance of AI systems is a non-trivial task. In this paper, I propose a novel benchmark called super-Nash performance to assess the performance of AI systems in mixed-motive settings. I show that a solution concept called optimin achieves super-Nash performance in every n-person game, i.e., for every Nash equilibrium there exists an optimin where every player not only receives but also guarantees super-Nash payoffs even if the others deviate unilaterally and profitably from the optimin.
    Date: 2022–10
  3. By: Tomoo Kikuchi; Shuige Liu
    Abstract: We build a model where two superpowers play a Stackelberg game of choosing a location for their club good that has a production externality. The production cost depends on how many small countries are willing to join the club. By integrating non-cooperative and cooperative games into a unified model where two groups of heterogenous players have interrelated objectives we study how two superpowers compete to form their clubs. We simulate the game for the US and China based on data from 2006 to 2019 and projections from 2030 to 2100.
    Date: 2022–09
  4. By: Jibang Wu; Weiran Shen; Fei Fang; Haifeng Xu
    Abstract: Optimizing strategic decisions (a.k.a. computing equilibrium) is key to the success of many non-cooperative multi-agent applications. However, in many real-world situations, we may face the exact opposite of this game-theoretic problem -- instead of prescribing equilibrium of a given game, we may directly observe the agents' equilibrium behaviors but want to infer the underlying parameters of an unknown game. This research question, also known as inverse game theory, has been studied in multiple recent works in the context of Stackelberg games. Unfortunately, existing works exhibit quite negative results, showing statistical hardness and computational hardness, assuming follower's perfectly rational behaviors. Our work relaxes the perfect rationality agent assumption to the classic quantal response model, a more realistic behavior model of bounded rationality. Interestingly, we show that the smooth property brought by such bounded rationality model actually leads to provably more efficient learning of the follower utility parameters in general Stackelberg games. Systematic empirical experiments on synthesized games confirm our theoretical results and further suggest its robustness beyond the strict quantal response model.
    Date: 2022–10
  5. By: D'Andrea, Sara; Vassalli, Federica
    Abstract: This paper aims to briefly present the fairness approach in game theory and its potential application. Fairness means that players consider not only personal payoffs but also others’ payoffs and beliefs regarding their actions. In this context, we distinguish two approaches, one based on the material payoff and the other on beliefs. We adopt the fairness approach in proposing three games for studying the strategic interaction between a hypothetical country and the European Union in proposing a debt mutualization scheme. We find that the optimal debt quota to share with the European Union is 50%; concerning the moral hazard problem, commitment to structural reforms for countries with high public debt leads to the best equilibrium, that can be preserved following an incentive strategy.
    Keywords: Game Theory, Fairness Approach, Debt Mutualization, Euro Area
    JEL: C7 H63
    Date: 2022–09–23
  6. By: Attar, Andrea; Campioni, Eloisa; Piaser, Gwenaël
    Abstract: We study competing-mechanism games, in which multiple principals contract with multiple agents. We reconsider the issue of non-existence of an equilibrium as first raised by Myerson (1982). In the context of his example, we establish the existence of a perfect Bayesian equilibrium. We clarify that Myerson (1982)’s non-existence result is an implication of the additional requirement he imposes, that each principal selects his preferred continuation equilibrium in the agents’ game.
    Keywords: Competing Mechanisms; Equilibrium Existence
    JEL: D82
    Date: 2022–09–27
  7. By: H. Dharma Kwon; Jan Palczewski
    Abstract: The timing of strategic exit is one of the most important but difficult business decisions, especially under competition and uncertainty. Motivated by this problem, we examine a stochastic game of exit in which players are uncertain about their competitor's exit value. We construct an equilibrium for a large class of payoff flows driven by a general one-dimensional diffusion. In the equilibrium, the players employ sophisticated exit strategies involving both the state variable and the posterior belief process. These strategies are specified explicitly in terms of the problem data and a solution to an auxiliary optimal stopping problem. The equilibrium we obtain is further shown to be unique within a wide subclass of symmetric perfect Bayesian equilibria.
    Date: 2022–10
  8. By: Alan Hammond; G\'abor Pete
    Abstract: We introduce a two-person zero-sum game that we call stake-governed tug-of-war. The game develops the classic tug-of-war random-turn game from~\cite{PSSW09}. In tug-of-war, two players compete by moving a counter along adjacent edges of a graph, each winning the right to move at a given turn according to the outcome of the flip of a fair coin; a payment is made from one player to the other when the counter reaches a boundary set on which the terminal payment value is specified. The player Mina who makes the payment seeks to minimize its mean; her opponent Maxine seeks to maximize it. The game's value is the infinity harmonic extension of the payment boundary data. In the stake-governed version, both players first receive a limited budget. At the start of each turn, each stakes an amount drawn from her present budget, and the right to move at the turn is won randomly by a player with probability equal to the ratio of her stake and the combined stake just offered. For certain graphs, we present the solution of a leisurely version of the game, in which, after stakes are bid at a turn, the upcoming move is cancelled with probability $1 - \epsilon \in (0,1)$. With the parameter $\epsilon$ small enough, and for finite trees whose leaves are the boundary set and whose payment function is the indicator on a given leaf, we determine the value of the game and the set of Nash equilibria. When the ratio of the initial fortunes of Maxine and Mina is $\lambda$, Maxine wins each turn with a probability $\tfrac{\lambda}{1+\lambda}$ under optimal play, and game value is a biased infinity harmonic function $h(\lambda,v)$; each player stakes a shared non-random proportion of her present fortune, a formula for which we give in terms of the spatial gradient and $\lambda$-derivative of $h(\lambda,v)$. We also show with some examples how the solution can differ when $\epsilon$ is one.
    Date: 2022–06
  9. By: Lisa Bruttel (University of Potsdam); Muhammed Bulutay (Technische Universität Berlin); Camille Cornand (Univ Lyon, CNRS, GATE UMR 5824); Frank Heinemann (Technische Universität Berlin); Adam Zylbersztejn (Univ Lyon, Université Lumière Lyon 2, GATE UMR 5824, Vistula University Warsaw)
    Abstract: Strategic uncertainty is the uncertainty that players face with respect to the purposeful behavior of other players in an interactive decision situation. Our paper develops a new method for measuring strategic-uncertainty attitudes and distinguishing them from risk and ambiguity attitudes. We vary the source of uncertainty (whether strategic or not) across conditions in a ceteris paribus manner. We elicit certainty equivalents of participating in two strategic 2x2 games (a stag-hunt and a market-entry game) as well as certainty equivalents of related lotteries that yield the same possible payoffs with exogenously given probabilities (risk) and lotteries with unknown probabilities (ambiguity). We provide a structural model of uncertainty attitudes that allows us to measure a preference for or an aversion against the source of uncertainty, as well as optimism or pessimism regarding the desired outcome. We document systematic attitudes towards strategic uncertainty that vary across contexts. Under strategic complementarity [substitutability], the majority of participants tend to be pessimistic [optimistic] regarding the desired outcome. However, preferences for the source of uncertainty are distributed around zero.
    Keywords: risk attitudes, ambiguity attitudes, strategic-uncertainty attitudes, stag-hunt game, market-entry game
    JEL: C72 C91 C92 D81
    Date: 2022–10
  10. By: Atay, Ata; Mauleon, Ana (Université catholique de Louvain, LIDAM/CORE, Belgium); Schopohl, Simon; Vannetelbosch, Vincent (Université catholique de Louvain, LIDAM/CORE, Belgium)
    Abstract: Individuals are embedded in a network of relationships and they can be victims, bystanders, or perpetrators of bullying and harassment. Each individual decides non-cooperatively how much effort to exert in preventing misbehavior. Each indi- vidual’s optimal effort depends on the contextual effect, the social multiplier effect and the social conformity effect. We characterize the Nash equilibrium and we derive an inter-centrality measure for finding the key player who once isolated increases the most the aggregate effort. An individual is more likely to be the key player if she is influencing many other individuals, she is exerting a low effort because of her characteristics, and her neighbors are strongly influenced by her. The key player policy increases substantially the aggregate effort and the targeted player should never be selected randomly. The key player is likely to remain the key player in presence of social workers except if she is becoming much less influential due to her closeness to social workers. Finally, we consider alternative policies (e.g. training bystanders for helping victims) and compare them to the policy of isolating the key player.
    Keywords: Social networks ; bullying ; harassment ; peer effects ; key player ; conformity ; #MeToo
    JEL: A14 C72 D85 Z13
    Date: 2022–05–23
  11. By: Soumen Banerjee; Yi-Chun Chen
    Abstract: We study a full implementation problem with hard evidence where the state is common knowledge but agents face uncertainty about the evidence endowments of other agents. We identify a necessary and sufficient condition for implementation in mixed-strategy Bayesian Nash equilibria called No Perfect Deceptions. The implementing mechanism requires only two agents and a finite message space, imposes transfers only off the equilibrium, and invoke no device with "...questionable features..." such as integer or modulo games. Requiring only implementation in pure-strategy equilibria weakens the necessary and sufficient condition to No Pure-Perfect Deceptions. In general type spaces where the state is not common knowledge, a condition called higher-order measurability is necessary and sufficient for rationalizable implementation with arbitrarily small transfers alongside.
    Date: 2022–09
  12. By: Luo, Chenghong; Mauleon, Ana (Université catholique de Louvain, LIDAM/CORE, Belgium); Vannetelbosch, Vincent (Université catholique de Louvain, LIDAM/CORE, Belgium)
    Abstract: We reconsider de Marti and Zenou (2017) model of friendship network formation where individuals belong to two different communities and costs of forming links depend on community memberships. Many inefficient friendship networks such as segregation can arise when all individuals are myopic. Once there are myopic and farsighted individuals in both communities, we show that if there are enough farsighted individuals in the dominant community relatively to the number of individuals in the small community, then the friendship network where the smaller community ends up being assimilated into the dominant community is likely to emerge and is strongly and Pareto efficient. Moreover, this friendship network Pareto dominates the complete segregation network.
    Keywords: Friendship networks ; stable sets ; myopia ; farsightedness ; assimilation ; segregation
    JEL: A14 C70 D20
    Date: 2022–05–25
  13. By: Qianjun Lyu (University of Bonn); Wing Suen (University of HongKong)
    Abstract: An uninformed sender publicly commits to an informative experiment about an uncertain state, privately observes its outcome, and sends a cheap-talk message to a receiver. We provide an algorithm valid for arbitrary state-dependent preferences that will determine the sender’s optimal experiment, and give sufficient conditions for information design to be valuable or not under different payoff structures. These conditions depend more on marginal incentives—how payoffs vary with the state—than on the alignment of sender’s and receiver’s rankings over actions within a state.
    Keywords: Information design, cheap talk
    JEL: D82 D83
    Date: 2022–09
  14. By: Olaizola, Norma; Valenciano, Federico
    Abstract: We culminate the extension of the results on efficiency in the seminal connections model of Jackson and Wolinsky (1996), partially addressed in previous papers. In a model where both nodes and links are heterogeneous, we prove that efficiency is reached by networks with a particular type of architecture that we call "hierarchical flower networks". These networks have a unique non-trivial component, within which one of the nodes with a highest value is directly connected with the others in the component, among which some pairs are directly connected. Moreover, the greatest the sum of the values of two nodes, the greatest the strength of their connection, be it direct by a link or indirect by means of two links through the central node.
    Keywords: Networks; Connections model; Heterogeneity; Efficiency
    JEL: A14 C72 D85
    Date: 2022–10–05
  15. By: Sümeyra Atmaca (University of Ghent); Riccardo Camboni (University of Padova); Elena Podkolzina (HSE-NRU); Koen Schoors (University of Ghent); Paola Valbonesi (University of Padova)
    Abstract: We use a large dataset of Russian public procurement auctions for standard gasoline over the period 2011-2013, to investigate how buyers set the reserve price - i.e. the buyer’s announced maximum willingness to pay for the good awarded. We provide empirical evidence that repeated past contracts between a buyer and a supplier affect the reserve price set by this buyer in future auctions where the same supplier takes part and wins. Specifically, we find that in these auctions the reserve price, the level of competition, and the winning unit price are lower than in the average auction in the dataset. We conjecture that, in setting the reserve price for a new auction, public buyers exploit information gained about the winners of previous auctions. This intuition is supported by empirically studying the reserve price in a dynamic framework, which allows buyers to take into account information from previous procurement transactions with given suppliers. Finally, we show that our empirical results are in line with a simple theoretical setting in which the buyer collects information about one supplier’s costs and exploits this in setting the reserve price in future auctions.
    Keywords: Publicprocurement, First-priceauction, Buyer-supplier repeated interactions, Reserve price
    JEL: D44 H57
    Date: 2022–10
  16. By: Masaaki Fujii (Faculty of Economics, The University of Tokyo)
    Abstract: In this work, we develop an equilibrium model for price formation of securities in a market composed of two populations of different types: the first one consists of cooperative agents, while the other one consists of non-cooperative agents. The trading of every cooperative member is assumed to be coordinated by a central planner. In the large population limit, the problem for the central planner is shown to be a conditional extended mean-field control. In addition to the convexity assumptions, if the relative size of the cooperative population is small enough, then we are able to show the existence of a unique equilibrium for both the finite-agent and the mean-field models. The strong convergence to the mean-field model is also proved under the same conditions.
    Date: 2022–09
  17. By: Luca Sandrini (Research Center of Quantitative Social and Management Sciences, Faculty of Economics and Social Sciences, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary.); Robert Somogyi (Budapest University of Technology and Economics, and Centre for Economic and Regional Studies, Műegyetem rkp. 3., H-1111 Budapest, Hungary.)
    Abstract: In this paper, we build a model of the news market where advertisers choose to allocate their ads between a social media platform and a news website that is the content creator. Our main objective is to evaluate a policy intervention that aims to foster news creation by transferring revenues from social media to news websites. Such interventions, commonly referred to as news media bargaining codes were first introduced in Australia in 2021 and are being implemented worldwide. We build on a novel trade-off between the higher advertising efficiency of social media and the value of content creation by news websites. When news quality is unaffected by the policy, we find that the equilibrium level of news creation may be socially sub-optimal. Moreover, we show that the policy intervention mandated by the bargaining code is always welfare-increasing. When news quality is endogenous, we nuance our results by showing that a poorly designed transfer can be inefficient. However, it still holds that the policy never harms consumers. Finally, we also provide some guidance on how to design the policy.
    Keywords: social media; news website; bargaining code; platform regulation
    JEL: D43 L13 L51 L82
    Date: 2022–09
  18. By: Krishna Dasaratha; Kevin He
    Abstract: We study learning on social media with an equilibrium model of users interacting with shared news stories. Rational users arrive sequentially and each observes an original story (i.e., a private signal) and a sample of predecessors' stories in a news feed, then decides which stories to share. The observed sample of stories depends on what predecessors share as well as the sampling algorithm, which represents a design choice of the platform. We focus on how much the algorithm relies on virality (how many times a story has been previously shared) when generating news feeds. Showing users more viral stories can increase information aggregation, but it can also generate steady states where most shared stories are wrong. Such misleading steady states self-perpetuate, as users who observe these wrong stories develop wrong beliefs, and thus rationally continue to share them. We find that these bad steady states appear discontinuously, and even a benevolent platform designer either accepts these misleading steady states or induces fragile learning outcomes in the optimal design.
    Date: 2022–10

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