nep-gth New Economics Papers
on Game Theory
Issue of 2021‒07‒19
seventeen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Uncertainty-driven symmetry-breaking and stochastic stability in a generic differential game of lobbying By Raoul Bouccekine; Fabien Prieur; Weihua Ruan; Benteng Zou
  2. Disjointly and jointly productive players and the Shapley value By Besner, Manfred
  3. Emission tax and strategic environmental corporate social responsibility in a Cournot–Bertrand comparison By Xu, Lili; Chen, Yuyan; Lee, Sang-Ho
  4. A Concavification Approach to Ambiguous Persuasion By Xiaoyu Cheng
  5. Testable implications of multiple equilibria in discrete games with correlated types By Áureo de Paula; Xun Tang
  6. Mechanism Design for Efficient Nash Equilibrium in Oligopolistic Markets By Kaiying Lin; Beibei Wang; Pengcheng You
  7. Price Competition Online: Platforms vs. Branded Websites By Oksana Loginova
  8. Colonel Blotto's Tug of War By Klumpp, Tilman
  9. On the Impact of Information Acquisition and Aftermarkets on Auction Efficiency By Moshe Babaioff; Nicole Immorlica; Yingkai Li; Brendan Lucier
  10. Proof-of-Stake Mining Games with Perfect Randomness By Matheus V. X. Ferreira; S. Matthew Weinberg
  11. The environmental effect of ambient charges in mixed triopoly with diverse firm objectives By Ohnishi, Kazuhiro
  12. Coalition Formation Under Dominance Invariance By Kimya, Mert
  13. Profit Shifting and Equilibrium Principles of International Taxation By Manon François
  14. Ore Money Ore Problems: A Resource Extraction Game By Sarah Jacobson
  15. Group Selection of Handicap Signaling By Ethan Holdalh; Jiabin Wu
  16. Trade credit contracts: Design and regulation By Florina Silaghi; Franck Moraux
  17. The Roots of Cooperation By Zvonimir Basic; Parampreet Christopher Bindra; Daniela Glätzle-Rützler; Angelo Romano; Matthias Sutter; Claudia Zoller

  1. By: Raoul Bouccekine (Aix-Marseille Université); Fabien Prieur (Université de Montpellier); Weihua Ruan (Purdue University Northwest); Benteng Zou (Department of Economics and Management, Université du Luxembourg)
    Abstract: We study a 2-players stochastic differential game of lobbying. Players have opposite interests; at any date, each player invests in lobbying activities to alter the legislation, the continuous state variable of the game, in her own benefit. The payoffs are quadratic and uncertainty is driven by a Wiener process. We prove that while a symmetric Markov Perfect Equilibrium (MPE) always exists, (two) asymmetric MPE only emerge when uncertainty is large enough. In the latter case, the legislative state converges to a stationary invariant distribution. We fully characterize existence and stochastic stability of the legislative state for both types of MPE. We finally study the implications for rent dissipation asymptotically. We show in particular that while the average rent dissipation is lower with asymmetric equilibria relative to the symmetric, the former yield larger losses at the most likely asymptotic states for large enough but moderate uncertainty.
    Keywords: Political lobbying, symmetric versus asymmetric equilibrium, stochastic differential games, stochastic stability, social cost of lobbying.
    JEL: D72 C73
    Date: 2021
  2. By: Besner, Manfred
    Abstract: Central to this study is the concept of disjointly productive players. Two players are disjointly productive if there is no synergy effect if one of these players joins a coalition containing the other. Our first new axiom states that the payoff to a player does not change when another player, disjointly productive with that player, leaves the game. The second new axiom means that if we merge two disjointly productive players into a new player, the payoff to a third player does not change. These two axioms, along with efficiency, characterize the Shapley value and may be useful in improving the run time for computing the Shapley value in games with some disjointly productive players. Further axiomatizations of the Shapley value are provided in which jointly productive players, known as mutually dependent players, also play a role. Using a change of behavior property, the payoff for two players in two games in which their behavior changed once to total dislike and once to total like is equal to the payoff in the original game. Another axiomatization uses an additivity property for games in which two players have also changed their behavior to total non-cooperation.
    Keywords: Cooperative game; Shapley value; Disjointly productive players; Mutually dependent players; Merged (disjointly productive) players game
    JEL: C7 C71
    Date: 2021–06–09
  3. By: Xu, Lili; Chen, Yuyan; Lee, Sang-Ho
    Abstract: This study considers strategic relations between emission tax and environmental corporate social responsibility (ECSR) in a Cournot–Bertrand comparison, and analyzes two different timings of the games between a tax-then-ECSR (T game) and an ECSR-then-tax (E game). We show that the T game always yields higher emission tax than the E game irrespective of competition modes, but lower ECSR under Cournot while higher ECSR when the marginal damage is high under Bertrand. Additionally, compared with Bertrand, Cournot yields lower (higher) ECSR in the T (E) game, but lower emission tax in the E game while higher emission tax when the product substitutability is low in the T game. We finally show that firms always prefer Cournot competition with the commitment of E game irrespective of the product substitutability and marginal damage.
    Keywords: Emission tax; environmental corporate social responsibility; Cournot–Bertrand comparison; tax-then-ECSR; ECSR-then-tax
    JEL: H23 L13 M14
    Date: 2021–06
  4. By: Xiaoyu Cheng
    Abstract: This note shows that the value of ambiguous persuasion characterized in Beauchene, Li and Li(2019) can be given by a concavification program as in Bayesian persuasion (Kamenica and Gentzkow, 2011). More specifically, it implies that an ambiguous persuasion game can be equivalently formalized as a Bayesian persuasion game with distorted utility functions. This result is obtained under a novel construction of ambiguous persuasion.
    Date: 2021–06
  5. By: Áureo de Paula (Institute for Fiscal Studies and University College London); Xun Tang (Institute for Fiscal Studies and Rice University)
    Abstract: We study testable implications of multiple equilibria in discrete games with incomplete information. Unlike de Paula and Tang (2012), we allow the players’ private signals to be correlated. In static games, we leverage independence of private types across games whose equilibrium selection is correlated. In dynamic games with serially correlated discrete unobserved heterogeneity, our testable implication builds on the fact that the distribution of a sequence of choices and states are mixtures over equilibria and unobserved heterogeneity. The number of mixture components is a known function of the length of the sequence as well as the cardinality of equilibria and unobserved heterogeneity support. In both static and dynamic cases, these testable implications are implementable using existing statistical tools.
    Date: 2020–12–02
  6. By: Kaiying Lin; Beibei Wang; Pengcheng You
    Abstract: This paper investigates the efficiency loss in social cost caused by strategic bidding behavior of individual participants in a supply-demand balancing market, and proposes a mechanism to fully recover equilibrium social optimum via subsidization and taxation. We characterize the competition among supply-side firms to meet given inelastic demand, with linear supply function bidding and the proposed efficiency recovery mechanism. We show that the Nash equilibrium of such a game exists under mild conditions, and more importantly, it achieves the underlying efficient supply dispatch and the market clearing price that reflects the truthful system marginal production cost. Further, the mechanism can be tuned to guarantee self-sufficiency, i.e., taxes collected counterbalance subsidies needed. Extensive numerical case studies are run to validate the equilibrium analysis, and we employ individual net profit and a modified version of Lerner index as two metrics to evaluate the impact of the mechanism on market outcomes by varying its tuning parameter and firm heterogeneity.
    Date: 2021–06
  7. By: Oksana Loginova (Department of Economics, University of Missouri)
    Abstract: The focus of this theoretical study is price competition when some firms operate their own branded website while others sell their products through an online platform, such as Amazon Marketplace. On one hand, selling through Amazon expands a firm's reach to more customers, but on the other hand, starting a website can help the firm to increase the perceived value of its product, that is, to build brand equity. In the short run the composition of firms is fixed, whereas in the long run each firm chooses between Amazon and its own website. I derive the equilibrium prices and profits, analyze the firms' behavior in the long run, and compare the equilibrium outcome with the social optimum. Comparative statics analysis reveals some interesting results. For example, I find that the number of firms that choose Amazon may go down in response to an increase in the total number of firms. A pure-strategy Nash equilibrium may not exist; I show that price dispersion among firms of the same type is more likely in less concentrated markets and/or when the increase in the perceived value of the product is relatively small.
    Keywords: pricing, competition, platforms, online marketplace, Amazon, brand equity
    JEL: C72 D43 L11 L13 M31
    Date: 2021–03–21
  8. By: Klumpp, Tilman (University of Alberta, Department of Economics)
    Abstract: We examine Tug of War contests with the Blotto specification. Players have fixed effort budgets and must allocate these budgets to a sequence of battles. The outcome of each battle is a function of the efforts allocated to that battle. The player who first wins L more battles than the opponent wins the contest. We prove the one-step deviation principle for the undiscounted version of this game. We then derive a pure strategy, subgame perfect equilibrium for the case where the contest success function that governs each battle is a generalized Tullock function with exponent 1/2 or less. In the equilibrium, the players invest the same percentage of their remaining resources into each battle. The value of this percentage depends on how close each player is to winning the contest. Escalation of efforts, measured in relation to the players' remaining budgets, occurs when the player with the smaller budget is close to winning. At the same time, the probability that a player wins any individual battle remains constant along the entire equilibrium path.
    Keywords: Tug of War games; Colonel Blotto games; sequential contests; multibattle contests
    JEL: D72 D74
    Date: 2021–07–07
  9. By: Moshe Babaioff; Nicole Immorlica; Yingkai Li; Brendan Lucier
    Abstract: A common assumption in auction theory is that the information available to the agents is given exogenously and that the auctioneer has full control over the market. In practice, agents might be able to acquire information about their competitors before the auction (by exerting some costly effort), and might be able to resell acquired items in an aftermarket. The auctioneer has no control over those aspects, yet their existence influences agents' strategic behavior and the overall equilibrium welfare can strictly decrease as a result. We show that if an auction is smooth (e.g., first-price auction, all-pay auction), then the corresponding price of anarchy bound due to smoothness continues to hold in any environment with (a) information acquisition on opponents' valuations, and/or (b) an aftermarket satisfying two mild conditions (voluntary participation and weak budget balance). We also consider the special case with two ex ante symmetric bidders, where the first-price auction is known to be efficient in isolation. We show that information acquisition can lead to efficiency loss in this environment, but aftermarkets do not: any equilibrium of a first-price or all-pay auction combined with an aftermarket is still efficient.
    Date: 2021–07
  10. By: Matheus V. X. Ferreira; S. Matthew Weinberg
    Abstract: Proof-of-Stake blockchains based on a longest-chain consensus protocol are an attractive energy-friendly alternative to the Proof-of-Work paradigm. However, formal barriers to "getting the incentives right" were recently discovered, driven by the desire to use the blockchain itself as a source of pseudorandomness \cite{brown2019formal}. We consider instead a longest-chain Proof-of-Stake protocol with perfect, trusted, external randomness (e.g. a randomness beacon). We produce two main results. First, we show that a strategic miner can strictly outperform an honest miner with just $32.8\%$ of the total stake. Note that a miner of this size {\em cannot} outperform an honest miner in the Proof-of-Work model. This establishes that even with access to a perfect randomness beacon, incentives in Proof-of-Work and Proof-of-Stake longest-chain protocols are fundamentally different. Second, we prove that a strategic miner cannot outperform an honest miner with $30.8\%$ of the total stake. This means that, while not quite as secure as the Proof-of-Work regime, desirable incentive properties of Proof-of-Work longest-chain protocols can be approximately recovered via Proof-of-Stake with a perfect randomness beacon. The space of possible strategies in a Proof-of-Stake mining game is {\em significantly} richer than in a Proof-of-Work game. Our main technical contribution is a characterization of potentially optimal strategies for a strategic miner, and in particular, a proof that the corresponding infinite-state MDP admits an optimal strategy that is positive recurrent.
    Date: 2021–07
  11. By: Ohnishi, Kazuhiro
    Abstract: This paper examines a quantity-setting mixed triopoly model comprising a profit-maximizing firm, a partially cooperating firm and a socially concerned firm to reassess the environmental effect of an increase in ambient charges. The paper demonstrates that an increase in the ambient charge can reduce pollutant emissions.
    Keywords: ambient charge; Cournot triopoly; partially cooperating firm; pollution; socially concerned firm
    JEL: C72 D21 Q58
    Date: 2021–06–29
  12. By: Kimya, Mert
    Abstract: An abstract game satisfies Dominance Invariance if the indirect and the direct dominance relations, or myopic and farsighted dominance, are equivalent. Mauleon, Molis, Vannetelbosch, and Vergote (2014) study Dominance Invariance in match- ing problems as an attractive condition that eliminates the differences between a farsighted solution concept and its myopic counterpart. We show that Dominance Invariance can also be used to eliminate the differences between various farsighted solution concepts in any abstract game. Together with an additional condition called No Infinite Chains, Dominance Invariance implies the existence and unique- ness of the farsighted stable set, its equivalence to the largest consistent set and its equivalence to the (strong) rational expectations farsighted stable set when the latter exists. This also implies that both the farsighted stable set and the largest consistent set do not su er from the problem of maximality under these conditions.
    Keywords: Farsighted stability; Coalitional games; Farsighted stable set; Largest Consistent Set
    Date: 2021–06
  13. By: Manon François (PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - 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 Paris - 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 study the choice between source-based and destination-based corporate taxes in a twocountry model, allowing multinational firms to use transfer pricing to allocate profits across tax jurisdictions. We show that source-based taxation is a Nash equilibrium for tax revenue maximizing jurisdictions if domestic and/or foreign firms generate large revenues. We also show that destination-based taxes are a Nash equilibrium when firms generate low revenues, which implies the presence of multiple equilibria. Both the source and the destination principle coexist in equilibrium when domestic and foreign corporate revenues are average. However, the source principle always Pareto-dominates the destination principle.
    Keywords: Corporate taxes,Multinational firms,Tax competition,Transfer pricing
    Date: 2021–06
  14. By: Sarah Jacobson (Williams College)
    Abstract: Economic theories of the exploitation of depletable natural resources are built around a core model of intertemporal profit maximization that predicts that (barring unforeseen shocks) scarcity crises will not arise because forward looking resource owners will smooth extraction over time. The model that provides this result can seem opaque to students, but its intuition can be more easily grasped from experience. This paper shares a game that provides that experience. Participants play the role of mine owners who must decide how much to extract in each of two periods. In addition to showing how market pressures moderate intertemporal scarcity, the game also provides lessons about discounting, market power, information, and property rights. I provide all materials needed to play the game immediately or customize it.
    Keywords: classroom game, natural resource extraction, Hotelling rule, active learning
    JEL: A20 Q30 D25 D40 Q02
    Date: 2021–07–04
  15. By: Ethan Holdalh; Jiabin Wu
    Abstract: This paper proposes a group selection model to explain the rise and fall of handicap signaling. In one population, assortative matching according to types is sustained by handicap signaling. In the other population, individuals do not signal and they are randomly matched. Types evolve within each population. At the same time, the two populations may engage in competition. Due to assortative matching, high types grow faster in the population with signaling, yet they bear the cost of signaling, which lowers their population's fitness in the long run. We show that the survival of the signaling population depends crucially on the timing and the intensity of inter-population competition.
    Date: 2021–06
  16. By: Florina Silaghi (UAB - Universitat Autònoma de Barcelona); Franck Moraux (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR1 - Université de Rennes 1 - UNIV-RENNES - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)
    Abstract: This paper provides a theoretical analysis of trade credit within a real options framework. We show that under trade credit the buyer delays the decision to stop production, getting closer to the supply chain optimal stopping decision. Therefore, trade credit may serve as a coordination device. The supplier can optimally choose to offer trade credit for free, since this will guarantee her business for a longer period of time. Optimal trade credit design is analyzed for an integrated supply chain (cooperative solution) and for external procurement (Nash bargaining and Stackelberg solutions). When regulation imposes a limit on trade credit maturity, the wholesale price is reduced, trade credit decreases and internal procurement increases. The model's predictions are in line with recent empirical evidence on the effects of regulation in the retail industry.
    Keywords: Finance,Real options,Supply chain coordination,Trade credit,Vertical integration
    Date: 2021–04–24
  17. By: Zvonimir Basic; Parampreet Christopher Bindra; Daniela Glätzle-Rützler; Angelo Romano; Matthias Sutter; Claudia Zoller
    Abstract: Understanding the roots of human cooperation among strangers is of great importance for solving pressing social dilemmas and maintening public goods in human societies. We study the development of cooperation in 929 young children, aged 3 to 6. In a unified experimental framework, we examine which of three fundamental pillars of human cooperation – direct and indirect reciprocity as well as third-party punishment – emerges earliest as an effective means to increase cooperation in a repeated prisoner’s dilemma game. We find that third-party punishment exhibits a strikingly positive effect on cooperation rates by doubling them in comparison to a control condition. It promotes cooperative behavior even before punishment of defectors is applied. Children also engage in reciprocating others, showing that reciprocity strategies are already prevalent at a very young age. However, direct and indirect reciprocity treatments do not increase overall cooperation rates, as young children fail to anticipate the benefits of reputation building. We also show that the cognitive skills of children and the socioeconomic background of parents play a vital role in the early development of human cooperation.
    Keywords: cooperation, reciprocity, third-party punishment, reputation, children, parents, cognitive abilities, socioeconomic status, prisoner’s dilemma game, experiment
    JEL: C91 C93 D01 D91 H41
    Date: 2021

This nep-gth issue is ©2021 by Sylvain Béal. It is provided as is without any express or implied warranty. It may be freely redistributed in whole or in part for any purpose. If distributed in part, please include this notice.
General information on the NEP project can be found at For comments please write to the director of NEP, Marco Novarese at <>. Put “NEP” in the subject, otherwise your mail may be rejected.
NEP’s infrastructure is sponsored by the School of Economics and Finance of Massey University in New Zealand.