nep-gth New Economics Papers
on Game Theory
Issue of 2023‒06‒12
24 papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Best-Response dynamics in two-person random games with correlated payoffs By Hlafo Alfie Mimun; Matteo Quattropani; Marco Scarsini
  2. The Regularity of the Value Function of Repeated Games with Switching Costs By Yevgeny Tsodikovich; Xavier Venel; Anna Zseleva
  3. The optimal reinsurance strategy with price-competition between two reinsurers By Liyuan Lin; Fangda Liu; Jingzhen Liu abd Luyang Yu
  4. Why firms should care for consumers: Complementary goods By Ohnishi, Kazuhiro
  5. To request or not to request: charitable giving, social information, and spillover By Valeria Fanghella; Lisette Ibanez; John Thøgersen
  6. (Un)Trustworthy Pledges and Cooperation in Social Dilemmas By Goeschl, Timo; Soldà, Alice
  7. Suspecting Collusion By Ceesay, Muhammed
  8. Communicating Preferences to Improve Recommendations By Amir Habibi
  9. Debt management game and debt ceiling By Dammann, Felix; Rodosthenous, Néofytos; Villeneuve, Stéphane
  10. Robust Equilibrium Strategy for Mean-Variance Portfolio Selection By Mengge Li; Shuaijie Qian; Chao Zhou
  11. A More Informed Sender Benefits the Receiver When the Sender Has Transparent Motives By Mark Whitmeyer
  12. Beyond "Horizontal" and "Vertical": The Welfare Effects of Complex Integration By Margaret Loudermilk; Gloria Sheu; Charles Taragin
  13. Pollution in strategic multilateral exchange: taxing emissions or trading on permit markets? By Ludovic A. Julien; Anicet Kabre; Louis de Mesnard
  14. Learning, Diversity and Adaptation in Changing Environments: The Role of Weak Links By Daron Acemoglu; Asuman Ozdaglar; Sarath Pattathil
  15. Broadcasting revenue sharing after cancelling sports competitions By Gustavo Bergantiños; Juan D. Moreno-Ternero
  16. Selfish in payments, selfish in opportunities to obtain the payment By Giselli Castillo
  17. Strategic Foundations of Rational Expectations By Barelli, Paulo; Govindan, Srihari; Wilson, Robert
  18. Target versus budget reverse auctions: an online experiment using the strategy method By Adrien Coiffard; Raphaële Préget; Mabel Tidball
  19. Persuading a Wishful Thinker By Victor Augias; Daniel M A Barreto
  20. Influencing Opinion Networks - Optimization and Games By de Vos, Wout; Borm, Peter; Hamers, Herbert
  21. A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy By Ren\'e Aid; Matteo Basei; Giorgio Ferrari
  22. Nudging in complex environments By Alexander K. Koch; Dan Mønster; Julia Nafziger
  23. Motivated Beliefs, Independence and Cooperation By Wei Huang; Yu Wang; Xiaojian Zhao
  24. Network Goods, Price Discrimination, and Two-sided Platforms By Paul Belleflamme; Martin Peitz

  1. By: Hlafo Alfie Mimun; Matteo Quattropani; Marco Scarsini
    Abstract: We consider finite two-player normal form games with random payoffs. Player A's payoffs are i.i.d. from a uniform distribution. Given p in [0, 1], for any action profile, player B's payoff coincides with player A's payoff with probability p and is i.i.d. from the same uniform distribution with probability 1-p. This model interpolates the model of i.i.d. random payoff used in most of the literature and the model of random potential games. First we study the number of pure Nash equilibria in the above class of games. Then we show that, for any positive p, asymptotically in the number of available actions, best response dynamics reaches a pure Nash equilibrium with high probability.
    Date: 2022–09
  2. By: Yevgeny Tsodikovich (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, Bar-Ilan University [Israël]); Xavier Venel (LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma]); Anna Zseleva (Department of Quantitative Economics, School of Business and Economics, Maastricht University)
    Abstract: We study repeated zero-sum games where one of the players pays a certain cost each time he changes his action. We derive the properties of the value and optimal strategies as a function of the ratio between the switching costs and the stage payoffs. In particular, the strategies exhibit a robustness property and typically do not change with a small perturbation of this ratio. Our analysis extends partially to the case where the players are limited to simpler strategies that are history independent―namely, static strategies. In this case, we also characterize the (minimax) value and the strategies for obtaining it.
    Keywords: Zero-sum games, Switching Costs, Repeated Games, Stochastic Games
    Date: 2022
  3. By: Liyuan Lin; Fangda Liu; Jingzhen Liu abd Luyang Yu
    Abstract: We study optimal reinsurance in the framework of stochastic game theory, in which there is an insurer and two reinsurers. A Stackelberg model is established to analyze the non-cooperative relationship between the insurer and reinsurers, where the insurer is considered as the follower and the reinsurers are considered as the leaders. The insurer is a price taker who determines reinsurance demand in the reinsurance market, while the reinsurers can price the reinsurance treaties. Our contribution is to use a Nash game to describe the price-competition between two reinsurers. We assume that one of the reinsurers adopts the variance premium principle and the other adopts the expected value premium principle. The insurer and the reinsurers aim to maximize their respective mean-variance cost functions which lead to a time-inconsistency control problem. To overcome the time-inconsistency issue in the game, we formulate the optimization problem of each player as an embedded game and solve it via a corresponding extended Hamilton-Jacobi-Bellman equation. We find that the insurer will sign propositional and excess loss reinsurance strategies with reinsurer 1 and reinsurer 2, respectively. When the claim size follows exponential distribution, there exists a unique equilibrium reinsurance premium strategy. Our numerical analysis verifies the impact of claim size, risk aversion and interest rates of the insurer and reinsurers on equilibrium reinsurance strategy and premium strategy, which can help to understand competition in the reinsurance market
    Date: 2023–04
  4. By: Ohnishi, Kazuhiro
    Abstract: Corporate social responsibility (CSR) is a business approach that cares about social and environmental issues, and customer orientation (CO) is a business strategy that centres on the needs and wishes of customers in all decision-making. This paper examines two games of Cournot duopoly where two profit-maximizing firms produce complementary goods. The first game is that both firms consider the surplus of all consumers (CSR) as corporate culture, and the second game is that both firms care only for their own customers (CO). This paper presents the respective optimal levels of CSR and CO. Furthermore, the paper shows that all the profits in these optimal levels are equal.
    Keywords: Complementary goods; Consumer surplus; Cournot model; Customer surplus
    JEL: C72 D21
    Date: 2023–05–12
  5. By: Valeria Fanghella (EESC-GEM Grenoble Ecole de Management); Lisette Ibanez (CEE-M - Centre d'Economie de l'Environnement - Montpellier - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - UM - Université de Montpellier); John Thøgersen (Aarhus University [Aarhus])
    Abstract: Prosocial behavior is important for a well-functioning society, but many people try to avoid situations where they could act prosocially. This paper studies the avoidance of a prosocial request, how it is affected by social pressure, and whether request avoidance and social pressure generate spillover effects on following prosocial behaviors. To this aim, we conduct an incentivized online experiment (N=1400), where participants play two consecutive dictator games with a charity. In the first game, we vary the type of game and information provided in a 2 x 2 between-subject design: (i) standard dictator game or dictator game with costly opt-out; (ii) with or without social information (mean donation in a previous session). The second game is a standard dictator game for all and aims to capture spillover effects from the first decision. We find that the opt-out option leads to significantly lower donations, especially when social information is present (but this effect is not statistically significant). The negative effect of the opt-out option spills over to the second donation decision. We also observe a negative spillover effect after a standard dictator game. Social information reduces donations in a standard dictator game, but also allows to mitigate the negative spillover effect from the first to the second behavior.
    Keywords: prosocial behavior, opt-out option, social information, spillover, charitable giving, selfimage
    Date: 2023
  6. By: Goeschl, Timo; Soldà, Alice
    Abstract: Pledges feature in international climate cooperation since the 2015 Paris Agreement. We explore how differences in pledgers' trustworthiness affect outcomes in a social dilemma that parallels climate change. In an online experiment, two participants interact with a randomly matched third player in a repeat maintenance game with a pledge stage. Treatments vary whether participants are matched with a player that is more or less trustworthy as revealed by behavior in a promise-keeping game; and whether they observe that trustworthiness. We find that participants knowingly matched with more trustworthy players cooperate more than participants matched with less trustworthy players (knowingly or unknowingly), but also more than participants unknowingly matched with more trustworthy players. In contrast, participants knowingly matched with less trustworthy players do not cooperate less than participants who are unknowingly so. Our findings suggest that the use of pledges, as per the Paris Agreement, can leverage the power of trustworthiness to enhance cooperation.
    Keywords: social dilemmas; pre-play communication; pledges; cooperation; credibility; group formation
    Date: 2023–05–15
  7. By: Ceesay, Muhammed
    Abstract: When collusion is analyzed for Independent private value auctions, it is implicitly assumed that ring presence is commonly known to colluding and non-colluding bidders. We drop this assumption and analyze a simple model of a first price Independent Private Value auction with uniformly distributed values where a single bidder knows privately of the existence of collusion by others. We show that this knowledge leads him to bid shading (weakly) in the first price auction compared to what he would have bid otherwise. This in turn yields the result that the second price auction dominates the first price auction in terms of seller revenue. This contrasts results from the literature showing that under our framework, when bidding is done while the presence of colluding bidders is common knowledge, the first price auction dominates the second price auction.
    Keywords: Almost-All-Inclusive-Ring, Informational Structures
    JEL: D44
    Date: 2023
  8. By: Amir Habibi (HU Berlin)
    Abstract: I study a cheap talk model between a buyer and a seller with two goods for sale. There is two-sided (independent) private information with sequential, two-way communication. In the first stage, the buyer communicates her private preferences to the seller. In the second stage, the seller communicates the quality of the goods to the buyer. When the buyer’s preference is about which attribute common to both goods she prefers, the seller strictly benefits from the buyer communicating her preferences. Whereas when the buyer’s preference is about which good she prefers, this is never the case.
    Keywords: cheap talk; strategic communication; product recommendations;
    JEL: D82 L15
    Date: 2023–05–10
  9. By: Dammann, Felix; Rodosthenous, Néofytos; Villeneuve, Stéphane
    Abstract: We introduce a non zero-sum game between a government and a legislative body to study the optimal level of debt. We succeed in characterising Nash equilibria in the class of Skorokhodreflection policies which implies that the legislator imposes a debt ceiling. In addition, we highlight the importance of the time preferences in the magnitude of the optimal level of the statutory debt ceiling. In particular, we show that laissez-faire policy can be optimal for high values of the legislator’s discount rate.
    Keywords: non-zero-sum game; singular stochastic control; free-boundary problem; debt-to-GDP ratio
    Date: 2023–05–03
  10. By: Mengge Li; Shuaijie Qian; Chao Zhou
    Abstract: The classical mean-variance portfolio selection problem induces time-inconsistent (precommited) strategies (see Zhou and Li (2000)). To overcome this time-inconsistency, Basak and Chabakauri (2010) introduce the game theoretical approach and look for (sub-game perfect Nash) equilibrium strategies, which is solved from the corresponding partial differential equations (PDE) system. In their model, the investor perfectly knows the drift and volatility of the assets. However, in reality investors only have an estimate on them, e.g, a 95% confidence interval. In this case, some literature (e.g., Pham, Wei and Zhou (2022)) derives the optimal precommited strategy under the worst parameters, which is the robust control. The relation between the equilibrium strategy and the PDE system has not been justified when incorporating robust control. In this paper, we consider a general dynamic mean-variance framework and propose a novel definition of the robust equilibrium strategy. Under our definition, a classical solution to the corresponding PDE system implies a robust equilibrium strategy. We then explicitly solve for some special examples.
    Date: 2023–05
  11. By: Mark Whitmeyer
    Abstract: A sender with state-independent preferences (i.e., transparent motives) privately observes a signal about the state of the world before sending a message to a receiver, who subsequently takes an action. Regardless of whether the receiver can mediate--and commit to a garbling of the sender's message--or delegate--commit to a stochastic decision rule as a function of the message--and understanding the statement ``the receiver is better off as a result of an improvement of the sender's information'' to mean that her maximal and minimal equilibrium payoffs (weakly) increase as the sender's signal improves (in a Blackwell sense), we find that if the sender is more informed, the receiver is better off.
    Date: 2023–03
  12. By: Margaret Loudermilk; Gloria Sheu; Charles Taragin
    Abstract: We study the welfare impacts of mergers in markets where some firms are already vertically integrated. Our model features logit Bertrand competition downstream and Nash Bargaining upstream. We numerically simulate four merger types: vertical mergers between an unintegrated retailer and an unintegrated wholesaler, downstream "horizontal" mergers between an unintegrated retailer and an integrated retailer/wholesaler, upstream "horizontal" mergers between an unintegrated wholesaler and an integrated retailer/wholesaler, and integrated mergers between two integrated retailer/wholesaler pairs. We find that mergers that have both horizontal and vertical characteristics typically harm consumers. We apply the model to the Republic/Santek merger as a real-world example.
    Keywords: Bargaining models; Merger simulation; Vertical markets; Vertical mergers
    JEL: L13 L40 L41 L42
    Date: 2023–01–18
  13. By: Ludovic A. Julien; Anicet Kabre; Louis de Mesnard
    Abstract: We introduce polluting emissions in a sequential noncooperative oligopoly model of bilateral exchange. In one sector a leader and a follower use polluting technologies which create negative externalities on the payoffs of strategic traders who belong to the other sector. By modeling emissions as a negative externality, we show that the leader pollutes more (less) than the follower when strategies are substitutes (complements). Then, we consider the implementation of public policies to control the levels of emissions, namely two taxation mechanisms and a permit market. We study the effects of these public policies. Moreover, we determine the conditions under which these public policies can implement a Pareto-improving allocation.
    Keywords: Stackelberg competition; pollution; fiscal policy; permit market
    JEL: C72 D43 Q50
    Date: 2023
  14. By: Daron Acemoglu; Asuman Ozdaglar; Sarath Pattathil
    Abstract: Adaptation to dynamic conditions requires a certain degree of diversity. If all agents take the best current action, learning that the underlying state has changed and behavior should adapt will be slower. Diversity is harder to maintain when there is fast communication between agents, because they tend to find out and pursue the best action rapidly. We explore these issues using a model of (Bayesian) learning over a social network. Agents learn rapidly from and may also have incentives to coordinate with others to whom they are connected via strong links. We show, however, that when the underlying environment changes sufficiently rapidly, any network consisting of just strong links will do only a little better than random choice in the long run. In contrast, networks combining strong and weak links, whereby the latter type of links transmit information only slowly, can achieve much higher long-run average payoffs. The best social networks are those that combine a large fraction of agents into a strongly-connected component, while still maintaining a sufficient number of smaller communities that make diverse choices and communicate with this component via weak links.
    JEL: D83 D85
    Date: 2023–05
  15. By: Gustavo Bergantiños (ECOSOT, Universidade de Vigo); Juan D. Moreno-Ternero (Department of Economics, Universidad Pablo de Olavide)
    Abstract: The COVID-19 pandemic forced the partial or total cancellation of most sports competitions worldwide. Sports organizations crucially rely on revenues raised from broadcasting. How should the allocation of these revenues be modified when sports leagues are cancelled? We aim to answer that question in this paper by means of the axiomatic approach. Two extension operators (dubbed zero and leg operators, respectively) will play a major role in our analysis. We show that several combinations of axioms (formalizing ethical or strategic principles) characterize the image via those operators of two focal rules: the equal-split rule and concede-and-divide.
    Keywords: Game theory, resource allocation, broadcasting, cancelled seasons.
    JEL: D63 C71 Z20
    Date: 2023
  16. By: Giselli Castillo
    Abstract: Following the contemporary analysis on justice and preferences in distribution decisions, the present study analyzes the responses given by the participants in a laboratory experiment where they had to compete developing a real effort task and decide, in a distribution game, how the opportunities of winning and payments of both participants will be distributed. It is shown that preferences in distributions of opportunities of winning the game are extreme, that is, perfect equality or perfect inequality is preferred, while intermediate distributions are rare. Furthermore, those who prefer unequal opportunity distributions are also more likely to choose inequitable payments distributions.
    Date: 2023–01
  17. By: Barelli, Paulo (U of Rochester); Govindan, Srihari (U of Rochester); Wilson, Robert (Stanford U)
    Abstract: We study an economy with traders whose payoffs are quasilinear and their private signals are informative about an unobserved state parameter. The limit economy has infinitely many traders partitioned into a finite set of symmetry classes called types. It has a unique rational expectations Walrasian equilibrium (REE) whose price reveals the state. Total monotonicity, a property that limits heterogeneity across types, determines whether an efficient social choice function (SCF) is attainable using mechanisms in a class that includes auctions. An average crossing property on the primitives is a sufficient condition for total monotonicity. The REE is an efficient SCF so it is attainable by an auction if and only if it satisfies total monotonicity. REE with total monotonicity is not only attainable, but also implementable: it is approximated by the equilibrium outcomes of auctions with finitely many traders of each type and fine grids of the state, signals and bids.
    JEL: C7 D44 D82
    Date: 2022–08
  18. By: Adrien Coiffard (CEE-M - Centre d'Economie de l'Environnement - Montpellier - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - UM - Université de Montpellier); Raphaële Préget (CEE-M - Centre d'Economie de l'Environnement - Montpellier - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - UM - Université de Montpellier); Mabel Tidball (CEE-M - Centre d'Economie de l'Environnement - Montpellier - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - UM - Université de Montpellier)
    Abstract: Reverse auctions are used in various fields by public or corporate buyers to purchase goods and services from multiple sellers at the best price. Unlike in selling auctions, in reverse auctions a budget constraint rather than a target quantity is often announced by the auctioneer. However, in auction theory no optimal bidding strategy has yet been found in the case when a budget constraint is announced. Here we compare the two auction formats in an online experiment with 329 participants. We use the strategy method to obtain participants' bidding strategies from which we run exhaustive simulations of auction outcomes. This innovative methodology allows to overcome the issue of randomness of the auction outcome related to bidders' values. When each bidder has a single unit to sell, from the buyer's perspective, we find that, on average, the budget-constrained auction format outperforms the target-constrained auction format.
    Keywords: Reverse auctions, Online experiments, Strategy Method, Budget constraint, Target constraint.
    Date: 2023–04–03
  19. By: Victor Augias (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique); Daniel M A Barreto (Département d'économie - UPP - Université Pascal Paoli)
    Abstract: We analyze a model of persuasion in which Receiver forms wishful non-Bayesian beliefs. The effectiveness of persuasion depends on Receiver's material stakes: it is more effective when intended to encourage risky behavior that potentially lead to a high payoff and less effective when intended to encourage more cautious behavior. We illustrate this insight with applications showing why informational interventions are often ineffective in inducing greater investment in preventive health treatments, how financial advisors might take advantage of their clients overoptimistic beliefs and why strategic information disclosure to voters with different partisan preferences can lead to belief polarization in an electorate.
    Keywords: Non-Bayesian persuasion, Motivated thinking, Overoptimism, Optimal beliefs
    Date: 2022–02–15
  20. By: de Vos, Wout (Tilburg University, School of Economics and Management); Borm, Peter (Tilburg University, School of Economics and Management); Hamers, Herbert (Tilburg University, School of Economics and Management)
    Date: 2023
  21. By: Ren\'e Aid; Matteo Basei; Giorgio Ferrari
    Abstract: We consider a mean-field model of firms competing \`a la Cournot on a commodity market, where the commodity price is given in terms of a power inverse demand function of the industry-aggregate production. Investment is irreversible and production capacity depreciates at a constant rate. Production is subject to Gaussian productivity shocks, while large non-anticipated macroeconomic events driven by a two-state continuous-time Markov chain can change the volatility of the shocks, as well as the price function. Firms wish to maximize expected discounted revenues of production, net of investment and operational costs. Investment decisions are based on the long-run stationary price of the commodity. We prove existence, uniqueness and characterization of the stationary mean-field equilibrium of the model. The equilibrium investment strategy is of barrier-type and it is triggered by a couple of endogenously determined investment thresholds, one per state of the economy. We provide a quasi-closed form expression of the stationary density of the state and we show that our model can produce Pareto distribution of firms' size. This is a feature that is consistent both with observations at the aggregate level of industries and at the level of a particular industry. We establish a relation between economic instability and market concentration and we show how macroeconomic instability can harm firms' profitability more than productivity fluctuations.
    Date: 2023–04
  22. By: Alexander K. Koch (Department of Economics and Business Economics, Aarhus University); Dan Mønster (Department of Economics and Business Economics, Aarhus University); Julia Nafziger (Department of Economics and Business Economics, Aarhus University)
    Abstract: To study the effects of reminder nudges in complex environments, we apply a novel experimental approach based on a computer game in which decision makers have to pay attention to and perform multiple actions within a short period of time. The set-up allows us, first, to test the effect of reminders both on reminded and non-reminded actions and thus to observe whether reminders have (positive or negative) spillovers. Second, we investigate spillovers between multiple nudges by testing the effect of scaling up the number of reminded actions. Third, we study intertemporal spillovers by investigating whether the effects of having been exposed to reminders persist after reminders are withdrawn. We observe that reminders have positive effects in the short run - multiple reminders more so than single reminders: while reminders lead to crowding-out of non-reminded actions, the positive effect on the reminded actions dominates. After withdrawal of the reminders, the negative spillover effect persists, while the positive effect partially fades out so that, overall, reminders have no effect.
    Keywords: Nudging, spillover effects, attention, reminders, persistence, game-based experiments
    JEL: C9 D91
    Date: 2023–05–12
  23. By: Wei Huang (CUHK Business School, Chinese University of Hong Kong); Yu Wang (China Center For Behavioral Economics and Finance, Southwestern University of Finance and Economics); Xiaojian Zhao (Department of Economics, Monash Business School, Monash University)
    Abstract: Humans are social animals but sometimes stay alone. The paper theoretically investigates the connection between an intraperson game and an interperson interaction. Motivated beliefs supplied from memory management due to present bias in the individual investment problem give rise to a positive spillover on others through social interactions, suggesting that a high frequency of social interactions reduces an individual’s tendency to cooperate with others, exacerbating the free-riding problem. We also establish a positive relationship between overconfidence and prosocial behaviors. Evidence from cross-country observational data and cross-sectional data collected from an online experiment is largely consistent with our theoretical implications.
    Keywords: motivated beliefs, self-confidence, present bias, cooperation, cultural difference
    JEL: C91 D01 D91 O57 Z10
    Date: 2023–05
  24. By: Paul Belleflamme; Martin Peitz
    Abstract: A monopolist selling a network good to heterogeneous users is shown to become a twosided platform if it can condition prices on some user characteristics or if it cannot but induces user self-selection by offering screening contracts. This shows that the availability of sophisticated pricing instruments is essential to make a platform two-sided, not the ability to distinguish separate user groups. The use of freemium strategies (which consists of offering a base version at zero price and a premium version at a positive price) emerges as a special case of versioning.
    Keywords: Network goods, two-sided platforms, platform pricing, group pricing, versioning, freemium
    JEL: D21 D42 L12 L14
    Date: 2023–03

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