nep-gth New Economics Papers
on Game Theory
Issue of 2023‒12‒18
twenty-six papers chosen by
Sylvain Béal, Université de Franche-Comté

  1. Uniformly Strict Equilibrium for Repeated Games with Private Monitoring and Communication By Richard McLean; Ichiro Obara; Andrew Postlewaite
  2. Evolutionarily stable networks By Bayer, Péter
  3. Ambiguity aversion as a route to randomness in a duopoly game By Davide Radi; Laura Gardini
  4. Cournot Meets Bayes-Nash: A Discontinuity in Behavior in Finitely Repeated Duopoly Games By Cédric Argenton; Radosveta Ivanova-Stenzel; Wieland Müller
  5. The minimax property in infinite two-person win-lose games By Ron Holzman
  6. An Experimental Nash Program: A Comparison of Non-Cooperative v.s. Cooperative Bargaining Experiments By Michela Chessa; Nobuyuki Hanaki; Aymeric Lardon; Takashi Yamada
  7. Coordination with Differential Time Preferences: Experimental Evidence By Marina Agranov; Jeongbin Kim; Leeat Yariv
  8. Underreaction and dynamic inconsistency in communication games under noise By Gerrit Bauch
  9. Collective Sampling: An Ex Ante Perspective By Yangfan Zhou
  10. Successive Incentives By Jens Gudmundsson; Jens Leth Hougaard; Juan D. Moreno-Ternero; Lars Peter {\O}sterdal
  11. Modeling trading games in a stochastic non-life insurance market By Leonard Mushunje; David Edmund Allen
  12. Strategic Complementarities in a Model of Commercial Media Bias By Anna Kerkhof; Johannes Münster
  13. Asymmetric Models of Sales By David P. Myatt; David Ronayne
  14. Inference in Auctions with Many Bidders Using Transaction Prices By Federico A. Bugni; Yulong Wang
  15. Do Individualists and Collectivists Cooperate Differently? By Aidin Hajikhameneh; Erik O. Kimbrough; Brock Stoddard
  16. Why do committees work? By Breitmoser, Yves; Valasek, Justin
  17. Restricted bargaining sets in a club economy By Bhowmik, Anuj; Saha, Sandipan
  18. Optimal Investment and Fair Sharing Rules of the Incentives for Renewable Energy Communities By Almendra Awerkin; Paolo Falbo; Tiziano Vargiolu
  19. The Use of Symmetry for Models with Variable-size Variables By Takeshi Fukasawa
  20. Strategic Choice of Price-Setting Algorithms By Buchali, Katrin; Grüb, Jens; Muijs, Matthias; Schwalbe, Ulrich
  21. Strategic anonymity and behavior-based pricing By Stefano Colombo; Paolo G. Garella; Noriaki Matsushima
  22. Relative entropy-regularized robust optimal order execution By Meng Wang; Tai-Ho Wang
  23. Taking the competitor’s pill: when combination therapies enter pharmaceutical markets By Brekke, Kurt R.; Dalen, Dag Morten; Straume, Odd Rune
  24. A Vertically Differentiated Duopoly Model with Environmental Awards By Heidelmeier, Lisa; Sahm, Marco
  25. Efficiently Breaking the Folk Theorem by Reliably Communicating Long Term Commitments By David K Levine
  26. A Framework for Geoeconomics By Christopher Clayton; Matteo Maggiori; Jesse Schreger

  1. By: Richard McLean; Ichiro Obara; Andrew Postlewaite
    Abstract: Cooperation through repetition is an important theme in game theory. In this regard, various celebrated ``folk theorems'' have been proposed for repeated games in increasingly more complex environments. There has, however, been insufficient attention paid to the robustness of a large set of equilibria that is needed for such folk theorems. Starting with perfect public equilibrium as our starting point, we study uniformly strict equilibria in repeated games with private monitoring and direct communication (cheap talk). We characterize the limit equilibrium payoff set and identify the conditions for the folk theorem to hold with uniformly strict equilibrium.
    Date: 2023–11
  2. By: Bayer, Péter
    Abstract: This paper studies the evolution of behavior governing strategic network formation. I first propose a general framework of evolutionary selection in non-cooperative games played in heterogeneous groups under assortative matching. I show that evolution selects strate-gies that (i) execute altruistic actions towards others in the interaction group with rate of altruism equal to the rate of assortative matching and (ii) are stable against pairwise coali-tional deviations under two qualifications: pairs successfully coordinate their deviations with probability equaling the rate of assortative matching and externalities are taken into account with the same weight. I then restrict the domain of interaction games to strategic network formation and define a new stability concept for networks called ‘evolutionarily stable networks’. The concept fuses ideas of solution concepts used by evolutionary game theory and network formation games. In a game of communication, evolutionarily stable networks prescribe equal information access. In the classic co-authorship game only the least efficient network, the complete network, is evolutionarily stable. Finally, I present an evolutionary model of homophilistic network formation between identity groups and show that extreme high degrees of homophily may persist even in groups with virtually no preference for it; thus societies may struggle to eliminate segregation between identity groups despite becoming increasingly tolerant.
    Keywords: Networks; evolution; relatedness; stability, homophily
    JEL: C73 D85
    Date: 2023–11–20
  3. By: Davide Radi; Laura Gardini
    Abstract: The global dynamics is investigated for a duopoly game where the perfect foresight hypothesis is relaxed and firms are worst-case maximizers. Overlooking the degree of product substitutability as well as the sensitivity of price to quantity, the unique and globally stable Cournot-Nash equilibrium of the complete-information duopoly game, loses stability when firms are not aware if they are playing a duopoly game, as it is, or an oligopoly game with more than two competitors. This finding resembles Theocharis' condition for the stability of the Cournot-Nash equilibrium in oligopolies without uncertainty. As opposed to complete-information oligopoly games, coexisting attractors, disconnected basins of attractions and chaotic dynamics emerge when the Cournot-Nash equilibrium loses stability. This difference in the global dynamics is due to the nonlinearities introduced by the worst-case approach to uncertainty, which mirror in bimodal best-reply functions. Conducted with techniques that require a symmetric setting of the game, the investigation of the dynamics reveals that a chaotic regime prevents firms from being ambiguity averse, that is, firms are worst-case maximizers only in the quantity-expectation space. Therefore, chaotic dynamics are the result and at the same time the source of profit uncertainty.
    Date: 2023–11
  4. By: Cédric Argenton (CentER & TILEC, Tilburg University); Radosveta Ivanova-Stenzel (TU Berlin); Wieland Müller (VCEE, University of Vienna, CentER & TILEC, Tilburg University)
    Abstract: We conduct a series of Cournot duopoly market experiments with a high number of repetitions and fixed matching. Our treatments include markets with (a) complete cost symmetry and complete information, (b) slight cost asymmetry and complete information, and (c) varying cost asymmetries and incomplete information. For the case of complete cost symmetry and complete information, our data confirm the well-known result that duopoly players achieve, on average, partial collusion. However, as soon as any level of cost asymmetry or incomplete information is introduced, observed average individual quantities are remarkably close to the static Bayes-Nash equilibrium predictions.
    Keywords: Cournot; Bayesian game; Bayes-Nash equilibrium; repeated games; collusion; cooperation; experimental economics;
    JEL: D43 L13 C72 C92
    Date: 2023–11–21
  5. By: Ron Holzman
    Abstract: We explore a version of the minimax theorem for two-person win-lose games with infinitely many pure strategies. In the countable case, we give a combinatorial condition on the game which implies the minimax property. In the general case, we prove that a game satisfies the minimax property along with all its subgames if and only if none of its subgames is isomorphic to the "larger number game." This generalizes a recent theorem of Hanneke, Livni and Moran. We also propose several applications of our results outside of game theory.
    Date: 2023–10
  6. By: Michela Chessa; Nobuyuki Hanaki; Aymeric Lardon; Takashi Yamada
    Abstract: This paper aims to contribute to the literature on Nash program by experimentally comparing the results of “structured” (non-cooperative) demand-based and offer-based mechanisms that implement the Shapley value as an ex-ante equilibrium outcome with the results of corresponding “semi-structured” (cooperative) bargaining procedures. A significantly higher frequency of the grand coalition formation, the higher efficiency, and the allocation belonging to the bargaining set is observed in the latter than in the former regardless of whether it is demand-based or an offer-based. While significant differences in the resulting allocations are observed between the two non-cooperative mechanisms, little difference is observed between the two cooperative procedures.
    Date: 2023–11
  7. By: Marina Agranov (California Institute of Technology and NBER); Jeongbin Kim (Florida State University); Leeat Yariv (Princeton University, CEPR, and NBER)
    Abstract: The experimental literature on repeated games has largely focused on settings where players discount the future identically. In applications, however, interactions often occur between players whose time preferences differ. We study experimentally the effects of discounting differentials in infinitely repeated coordination games. In our data, differential discount factors play two roles. First, they provide a coordination anchor: more impatient players get higher payoffs first. Introducing even small discounting differentials reduces coordination failures significantly. Second, with pronounced discounting differentials, intertemporal trades are prevalent: impatient players get higher payoffs for an initial phase and patient players get higher payoffs in perpetuity afterward.
    Keywords: Repeated Games, Discounting, Intertemporal Trade, Experiments
    JEL: C73 C92 D15 D25
    Date: 2023–09
  8. By: Gerrit Bauch
    Abstract: Communication is rarely perfect, but rather prone to error of transmission and reception. Often the origin of these errors cannot be properly quantified and is thus imprecisely known. We analyze the impact of an ambiguous noise which may alter the received message on a communication game of common interest. The noise is ambiguous in the sense that the parameters of the error-generating process and thus the likelihood to receive a message by mistake are Knightianly unknown. Ex-ante and interim responses are characterized under maxmin preferences. While the sender can disregard ambiguity, the receiver reveals a dynamically inconsistent, but astonishing behavior under a quadratic loss. Their interim actions will be closer to the pooling action than their ex-ante ones, as if facing a higher likelihood of an occurring error.
    Date: 2023–11
  9. By: Yangfan Zhou
    Abstract: I study collective dynamic information acquisition. Players determine when to end sequential sampling via a collective choice rule. My analysis focuses on the case of two players, but extends to many players. With two players, collective stopping is determined either unilaterally or unanimously. I develop a methodology to characterize equilibrium outcomes using an ex ante perspective on posterior distributions. Under unilateral stopping, each player chooses a mean-preserving contraction of the other's posterior distribution; under unanimous stopping, they choose meanpreserving spreads. Equilibrium outcomes can be determined via concavification. Players learn Pareto inefficiently: too little under unilateral stopping, while too much under unanimous stopping; these learning inefficiencies are amplified when players' preferences become less aligned. I demonstrate the value of my methodological approach in three applications: committee search, dynamic persuasion, and competition in persuasion.
    Date: 2023–11
  10. By: Jens Gudmundsson; Jens Leth Hougaard; Juan D. Moreno-Ternero; Lars Peter {\O}sterdal
    Abstract: We study the design of optimal incentives in sequential processes. To do so, we consider a basic and fundamental model in which an agent initiates a value-creating sequential process through costly investment with random success. If unsuccessful, the process stops. If successful, a new agent thereafter faces a similar investment decision, and so forth. For any outcome of the process, the total value is distributed among the agents using a reward rule. Reward rules thus induce a game among the agents. By design, the reward rule may lead to an asymmetric game, yet we are able to show equilibrium existence with optimal symmetric equilibria. We characterize optimal reward rules that yield the highest possible welfare created by the process, and the highest possible expected payoff for the initiator of the process. Our findings show that simple reward rules invoking short-run incentives are sufficient to meet long-run objectives.
    Date: 2023–11
  11. By: Leonard Mushunje; David Edmund Allen
    Abstract: We studied the behavior and variation of utility between the two conflicting players in a closed Nash-equilibrium loop. Our modeling approach also captured the nexus between optimal premium strategizing and firm performance using the Lotka-Volterra completion model. Our model robustly modeled the two main cases, insurer-insurer and insurer-policyholder, which we accompanied by numerical examples of premium movements and their relationship to the market equilibrium point. We found that insurers with high claim exposures tend to set high premiums. The other competitors either set a competitive premium or adopt the fixed premium charge to remain in the game; otherwise, they will operate below the optimal point. We also noted an inverse link between trading premiums and claims in general insurance games due to self-interest and utility indifferences. We concluded that while an insurer aims to charge high premiums to enjoy more, policyholders are willing to avoid these charges by paying less.
    Date: 2023–11
  12. By: Anna Kerkhof; Johannes Münster
    Abstract: Media content is an important privately supplied public good. While it has been shown that contributions to a public good crowd out other contributions in many cases, the issue has not been thoroughly studied for media markets yet. We show that in a standard model of commercial media bias, qualities of media content are strategic complements, whereby investments into quality crowd in further investments and engage competitors in a race to the top. Therefore, financially strong public service media can mitigate commercial media bias: the content of commercial media can be more in line with the preferences of the audience and less advertiser-friendly in a dual (mixed public and commercial) media system than in a purely commercial media market.
    Keywords: commercial media bias, public service media, advertising two-sided markets, supermodular games, strategic complements, public goods
    JEL: C70 H41 L13 L51 L82
    Date: 2023
  13. By: David P. Myatt (London Business School); David Ronayne (ESMT Berlin)
    Abstract: We broaden and develop the classic captive-and-shopper model of sales. Firstly, we allow for asymmetric marginal costs as well as asymmetric captive audiences. These asymmetries jointly determine the identities of the two or more firms we find compete (via randomized sales) to serve shoppers. In a leading case, the prices paid by shoppers fall following a cost rise for the firm that serves most of them. Secondly, we study asymmetric price adjustment opportunities via a two-stage game in which firms may cut but not raise their initial prices. In this setting (and in scenarios with risk aversion or endogenous move order) we predict the play of pure strategies and that a unique firm serves the shoppers. Despite the different pricing predictions across games, firms’ profits are equivalent. Welfare properties depend on whether firm asymmetry is predominantly on the supply side (costs) or on the demand side (captive audiences). Thirdly, we allow firms to choose production technologies via process innovations. One firm innovates distinctly more than others, attains a lower marginal cost, and ultimately serves the shoppers. We connect the distinctive asymmetric pattern of innovations to demand-side asymmetries and the shape of technology opportunity.
    Keywords: model of sales; captives; shoppers; price dispersion; clearinghouse models;
    JEL: D43 L11 M3
    Date: 2023–11–13
  14. By: Federico A. Bugni; Yulong Wang
    Abstract: This paper considers inference in first-price and second-price sealed-bid auctions with a large number of symmetric bidders having independent private values. Given the abundance of bidders in each auction, we propose an asymptotic framework in which the number of bidders diverges while the number of auctions remains fixed. This framework allows us to perform asymptotically exact inference on key model features using only transaction price data. Specifically, we examine inference on the expected utility of the auction winner, the expected revenue of the seller, and the tail properties of the valuation distribution. Simulations confirm the accuracy of our inference methods in finite samples. Finally, we also apply them to Hong Kong car license auction data.
    Date: 2023–11
  15. By: Aidin Hajikhameneh; Erik O. Kimbrough; Brock Stoddard
    Abstract: Research in social science has shown the importance of individualism and collectivism (I/C) in human behavior. Individualists tend to see people in isolation, while collectivists are more prone to see people as interconnected members of groups, and this has consequences for behavior, governance, and economic outcomes. We examine the role of I/C on cooperation experimentally in infinitely repeated prisoner’s dilemmas (IRPD) played with in- and outgroup members. We predict that collectivists will be more cooperative, forgiving and defect less with in-group members than out-group members. Individualists are predicted to make similar strategic decisions for in- and out-group members. In an effort to causally affect the I/C scores of our subjects, as well as to strengthen in- and out-group connections, subjects completed a group-identity task prior to the I/C instrument and IRPD in the Strong Identity treatment. In our Weak Identity treatment, subjects completed a task on their own and were simply told they were assigned to groups. During the experiment, across supergames, subjects were randomly matched with in- and out-group partners. Findings reveal that our treatment effects are largely null. The only significant effect on strategic behavior was that larger defection payoffs led to more defection and less cooperation by subjects in all treatments. Key Words: Individualism, collectivism, cooperation, repeated games, strategy, experiments
    JEL: C91 C92 C73
    Date: 2023
  16. By: Breitmoser, Yves (Universität Bielefeld); Valasek, Justin (Dept. of Economics, Norwegian School of Economics and Business Administration)
    Abstract: We report on the results of an experiment designed to disentangle behavioral biases in information aggregation of committees. Subjects get private signals about the state of world, send binary messages, and finally vote under either majority or unanimity rules. Committee decisions are significantly more efficient than predicted by Bayesian equilibrium even with lying aversion. Messages are truthful, subjects correctly anticipate the truthfulness (contradicting limited depth of reasoning), but strikingly overestimate their pivotality when voting (contradicting plain lying aversion). That is, committees are efficient because members message truthfully and vote non-strategically. We show that all facets of behavior are predicted by overreaction, subjects overshooting in Bayesian updating, which implies that subjects exaggerate the importance of truthful messages and sincere voting. A simple one-parameteric generalization of quantal response equilibrium capturing overreaction covers 87 percent of observed noise.
    Keywords: committees; incomplete information; cheap talk; information aggregation; laboratory experiment; Bayesian updating; lying aversion; limited depth of reasoning
    JEL: C90 D71 D72
    Date: 2023–11–21
  17. By: Bhowmik, Anuj; Saha, Sandipan
    Abstract: The core as a solution concept captures the set of allocations against which there exists no objection by any coalition of agents. Aumann and Maschler (1961) however emphasized the shortcomings of the objection mechanism and hence the core to further repercussions from agents. In that spirit, they introduced the bargaining set which later was adapted to the case of exchange economies by Mas-Colell (1989) and Vind (1992). In this paper, we consider a club economy where club goods are consumed parallel to private goods to capture the social aspects of consumption. We consider the framework proposed by Ellickson et al. (1999) in this regard and refer to the bargaining sets introduced in line with Mas-Colell and Vind as the local and global bargaining sets in our framework. We provide characterizations of the global bargaining set in terms of the size of the (counter-) objecting coalitions thereby extending the works of Schødt and Sloth (1994) and Herves- Estvez and Moreno-Garcıa (2015). We provide further interpretations of the global bargaining set in terms of several notions of robustly efficient states of a club economy.
    Keywords: Club goods, Consistency, Local (Global) bargaining set, εδ-Bargaining set, Sequential robust efficiency.
    JEL: C7 D5 D6 H4
    Date: 2023–11–14
  18. By: Almendra Awerkin; Paolo Falbo; Tiziano Vargiolu
    Abstract: The focus on Renewable Energy Communities (REC) is fastly growing after the European Union (EU) has introduced a dedicated regulation in 2018. The idea of creating local groups of citizens, small- and medium-sized companies, and public institutions, which self-produce and self-consume energy from renewable sources is at the same time a way to save money for the participants, increase efficiency of the energy system, and reduce CO$_2$ emissions. Member states inside the EU are fixing more detailed regulations, which describe, how public incentives are measured. A natural objective for the incentive policies is of course to promote the self-consumption of a REC. A sophisticated incentive policy is that based on the so called 'virtual framework'. Under this framework all the energy produced by a REC is sold to the market, and all the energy consumed must be paid to retailers: self-consumption occurs only 'virtually', thanks a money compensation (paid by a central authority) for every MWh produced and consumed by the REC in the same hour. In this context, two problems have to be solved: the optimal investment in new technologies and a fair division of the incentive among the community members. We address these problems by considering a particular type of REC, composed by a representative household and a biogas producer, where the potential demand of the community is given by the household's demand, while both members produce renewable energy. We set the problem as a leader-follower problem: the leader decide how to share the incentive for the self-consumed energy, while the followers decide their own optimal installation strategy. We solve the leader's problem by searching for a Nash bargaining solution for the incentive's fair division, while the follower problem is solved by finding the Nash equilibria of a static competitive game between the members.
    Date: 2023–11
  19. By: Takeshi Fukasawa
    Abstract: This paper shows the universal representation of symmetric functions with multidimensional variable-size variables, which justifies the use of approximation methods aggregating the information of each variable. I then discuss how the results give insights into economic applications, including two-step policy function estimation, moment-based Markov equilibrium, and aggregative games.
    Date: 2023–11
  20. By: Buchali, Katrin; Grüb, Jens; Muijs, Matthias; Schwalbe, Ulrich
    JEL: D43 D83 L13 L49
    Date: 2023
  21. By: Stefano Colombo; Paolo G. Garella; Noriaki Matsushima
    Abstract: In a model of behavior-based price discrimination (BBPD), we argue that sellers may have discretionary power to let buyers decide whether to be identified (e.g., creating an account) or remain anonymous (no account creation). The price equilibria generate a more fragmented market segmentation than under the standard BBPD. Firms might prefer a policy where they leave buyers the decision to remain or not be anonymous, breaking the standard BBPD result. Furthermore, firms can realize higher profits than under uniform pricing, contrary to the standard BBPD. Also, firms may adopt asymmetric policies concerning the account creation requirement.
    Date: 2023–11
  22. By: Meng Wang; Tai-Ho Wang
    Abstract: The problem of order execution is cast as a relative entropy-regularized robust optimal control problem in this article. The order execution agent's goal is to maximize an objective functional associated with his profit-and-loss of trading and simultaneously minimize the execution risk and the market's liquidity and uncertainty. We model the market's liquidity and uncertainty by the principle of least relative entropy associated with the market volume. The problem of order execution is made into a relative entropy-regularized stochastic differential game. Standard argument of dynamic programming yields that the value function of the differential game satisfies a relative entropy-regularized Hamilton-Jacobi-Isaacs (rHJI) equation. Under the assumptions of linear-quadratic model with Gaussian prior, the rHJI equation reduces to a system of Riccati and linear differential equations. Further imposing constancy of the corresponding coefficients, the system of differential equations can be solved in closed form, resulting in analytical expressions for optimal strategy and trajectory as well as the posterior distribution of market volume. Numerical examples illustrating the optimal strategies and the comparisons with conventional trading strategies are conducted.
    Date: 2023–11
  23. By: Brekke, Kurt R. (Dept. of Economics, Norwegian School of Economics and Business Administration); Dalen, Dag Morten (Dept. of Economics, BI Norwegian Business School); Straume, Odd Rune (Dept. of Economics, University of Bergen)
    Abstract: We study the competitive effects of combination therapies in pharmaceutical markets, which crucially hinge on the additional therapeutic value of combinatory use of drugs and the therapeutic substitutability with the most relevant monotherapy. With large additional therapeutic value, the introduction of combination therapies leads to higher prices and, somewhat paradoxically, may reduce the health plan's surplus. Although combination therapies imply that drugs become both substitutes and complements, we show that drug prices increase if the firms are allowed to coordinate their prices. Allowing for price discrimination might increase allocational efficiency, but only at the expense of higher purchasing costs.
    Keywords: Pharmaceutical markets; Combination therapies; Therapeutic competition
    JEL: I11 I18 L13 L65
    Date: 2023–11–22
  24. By: Heidelmeier, Lisa; Sahm, Marco
    JEL: C7 D1 D2 D6 H4 L1 Q5
    Date: 2023
  25. By: David K Levine
    Date: 2023–12–04
  26. By: Christopher Clayton; Matteo Maggiori; Jesse Schreger
    Abstract: Governments use their countries’ economic strength from existing financial and trade relationships to achieve geopolitical and economic goals. We refer to this practice as geoeconomics. We build a framework based on three core ingredients: input output linkages, limited contract enforceability, and externalities. Geoeconomic power arises from the ability to jointly exercise threats arising from separate economic activities. Being able to retaliate against a deviating country across multiple arenas, often involving indirect threats from third parties also being pressured, increases the off equilibrium threats and, thus, helps in equilibrium to increase enforceability. A world hegemon, like the United States, exerts its power on firms and governments in its economic network by asking these entities to take costly actions that benefit the hegemon. We characterize the optimal actions and show that they take the form of mark-ups on goods or higher rates on lending, but also import restrictions and tariffs. The input-output amplification makes controlling some sectors more valuable for the hegemon since changes in the allocation of these strategic sectors have a larger influence on the world economy. This formalizes the idea of economic coercion as a combination of strategic pressure and costly actions. We apply the framework to two leading examples: national security externalities and the Belt and Road Initiative.
    JEL: F02 F10 F5
    Date: 2023–11

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