nep-gth New Economics Papers
on Game Theory
Issue of 2019‒04‒22
fourteen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Targeting the key player: An incentive-based approach By Mohamed Belhaj; Frédéric Deroïan
  2. The alpha-constant-sum games By Wenna Wang; Rene van den Brink; Hao Sun; Genjiu Xu; Zhengxing Zou
  3. Cultural Transmission with Incomplete Information: Parental Perceived Efficacy and Group Misrepresentation By Sebastiano Della Lena; Fabrizio Panebianco
  4. Bayesian Comparative Statics By Leal Vizcaíno René; Mekonnen Teddy
  5. Marketing Agencies and Collusive Bidding in Online Ad Auctions By Francesco Decarolis; Maris Goldmanis; Antonio Penta
  6. Transboundary Pollution Control and Competitiveness Concerns in a Two-Country Differential Game By Simone Marsiglio; Nahid Masoudi
  7. Theory of Mind and Strategic Decision-Making By Bose, Neha; Sgroi, Daniel
  8. Price Setting on a Network By Toomas Hinnosaar
  9. Cohesive efficiency in TU-games: Two extensions of the Shapley value By Sylvain Béal; André Casajus; Eric Rémila; Philippe Solal
  10. Relationship between labeled network games and museum pass games By Encarnación Algaba; Sylvain Béal; Vito Fragnelli; Natividad Llorca; Joaquin Sánchez-Soriano
  11. Robust Partially Observable Markov Decision Processes By Rasouli, Mohammad; Saghafian, Soroush
  12. Nash Bargaining Over Margin Loans to Kelly Gamblers By Alex Garivaltis
  13. Anticompetitive Vertical Merger Waves By Johan Hombert; Jérôme Pouyet; Nicolas Schutz
  14. On the optimal setting of protected areas By Sonia Schwartz; Johanna Choumert-Nkolo; Jean-Louis Combes; Pascale Combes Motel; Éric Nazindigouba Kere

  1. By: Mohamed Belhaj (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - Ecole Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique); Frédéric Deroïan (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - ECM - Ecole Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université - EHESS - École des hautes études en sciences sociales, AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - Ecole Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)
    Abstract: We consider a network game with local complementarities. A policymaker, aiming at minimizing or maximizing aggregate effort, contracts with a single agent on the network to trade effort change against transfer. The policymaker has to find the best agent and the optimal contract to offer. Our study shows that for all utilities with linear best-responses, it only takes two statistics about the position of each agent on the network to identify the key player: the Bonacich centrality and the self-loop centrality. We also characterize key players under linear quadratic utilities for various contractual arrangements.
    Date: 2018–12
  2. By: Wenna Wang (Northwestern Polytechnical University, VU University); Rene van den Brink (VU University); Hao Sun (Northwestern Polytechnical University); Genjiu Xu (Northwestern Polytechnical University); Zhengxing Zou (Beijing Institute of Technology, VU University, Amsterdam)
    Abstract: Given any alpha in [0,1], an alpha-constant-sum game on a finite set of players, N, is a function that assigns a real number to any coalition S (being a subset of the player set N), such that the sum of the worth of the coalition S and the worth of its complementary coalition N\S is alpha times of the worth of the grand coalition N. This class contains the constant-sum games of Khmelnitskaya (2003) (for alpha = 1) and games of threats of Kohlberg and Neyman (2018) (for alpha = 0) as special cases. An alpha-constant-sum game may not be a classical TU cooperative game as it may fail to satisfy the condition that the worth of the empty set is 0, except when alpha = 1. In this paper, we will build a value theory for the class of alpha-constant-sum games, and mainly introduce the alpha-quasi-Shapley value. We characterize this value by classical axiomatizations for TU games. We show that axiomatizations of the equal division value do not work on these classes of alpha-constant-sum games.
    Keywords: alpha-constant-sum game, alpha-quasi-Shapley value, threat game, constant-sum-game
    JEL: C71
  3. By: Sebastiano Della Lena (Department of Economics, University Of Venice Cà Foscari); Fabrizio Panebianco (Department of Economics and Finance, Università Cattolica del Sacro Cuore, Milano)
    Abstract: This paper introduces incomplete information in the standard model of cultural transmission (Bisin and Verdier, 2001). We allow parents to ignore own group size and the efficiency of their cultural transmission technology, while receiving a feedback from their children. Using the selfconfirming equilibrium concept, parents may end up to sustain, and be confirmed about, wrong conjectures. We show that in equilibrium optimal socialization efforts display cultural complementarity with respect to own population share, while the standard substitution result holds with respect their own conjectured population shares. Considering the population dynamics, if conjectures about population shares are shaped by cultural leaders who want to maximize the presence of own traits in the next period, then conjectures are characterized by negative biases. Our main finding is that, depending on the magnitude of the bias, the dynamics can display stable or unstable polymorphic equilibria, or just a stable homomorphic equilibrium, potentially reverting standard predictions.
    Keywords: Cultural Transmission, Incomplete Information, Selfconfirming Equilibrium, Group Under-Representation, Parental Perceived Efficacy, Cultural leaders
    JEL: C72 D10 D80 J10 Z10
    Date: 2019
  4. By: Leal Vizcaíno René; Mekonnen Teddy
    Abstract: We study how information affects equilibria and welfare in games. For an agent, more precise information about an unknown state of the world leads to a mean-preserving spread of beliefs. We provide necessary and sufficient conditions to obtain either a non-increasing mean or a non-decreasing-mean spread of actions whenever information precision increases for at least one agent. We apply our Bayesian comparative statics framework to study informational externalities in strategic environments. In persuasion games, we derive sufficient conditions that lead to extremal disclosure of information. In oligopolistic markets, we characterize the incentives of firms to share information. In macroeconomic models, we show that information not only drives the amplitude of business cycles but also affects aggregate output.
    Keywords: Comparative Statics;Information Acquisition;Information Orders;Persuasion;Value of Information;Supermodular Games
    JEL: C44 C61 D42 D81
    Date: 2019–03
  5. By: Francesco Decarolis; Maris Goldmanis; Antonio Penta
    Abstract: The transition of the advertising market from traditional media to the internet has induced a proliferation of marketing agencies specialized in bidding in the auctions that are used to sell ad space on the web. We analyze how collusive bidding can emerge from bid delegation to a common marketing agency and how this can undermine the revenues and allocative effciency of both the Generalized Second Price auction (GSP, used by Google and Microsoft-Bing and Yahoo!) and the of VCG mechanism (used by Facebook). We nd that, despite its well-known susceptibility to collusion, the VCG mechanism outperforms the GSP auction both in terms of revenues and effciency.
    Keywords: Collusion, digital marketing agencies, facebook, Google, GSP, internet auctions, online advertising, VCG
    JEL: C72 D44 L81
    Date: 2019–04
  6. By: Simone Marsiglio (Department of Economcis, University of Pisa, and Center for Financial Development and Stability at Henan University, and School of Economics at Henan University, Kaifeng, Henan); Nahid Masoudi (Memorial University of Newfoundland, and Center for Financial Development and Stability at Henan University, and School of Economics at Henan University, Kaifeng, Henan)
    Abstract: We analyze a transboundary pollution control problem in a heterogeneous two-country differential game in which each country’s regulator cares for the implications of environmental policy on its compet- itiveness. We characterize and compare the noncooperative and the cooperative solutions, showing that under both scenarios, the heterogeneous countries impose different tax rates despite such competitiveness concerns. This may suggest that, while implementing some kind of mitigation policy is necessary to com- bat climate change, a universally homogeneous environmental tax may not be either desirable or optimal.
    Keywords: Climate Change; Competitiveness; Mitigation Policies; Transboundary Pollution
    JEL: C70 Q54 Q58
  7. By: Bose, Neha (University of Warwick); Sgroi, Daniel (University of Warwick)
    Abstract: In a laboratory experiment, 338 participants were asked to communicate in pairs and then play two games with their partners: the 11-20 money request game (a tool for assessing level-k reasoning) and a public goods game. The communication occurred prior to any knowledge of what was to follow but played an important rolein allowing them to develop theories or mental models of their partners (“theory of mind”) which proved to be crucial explanatory factors for decision-making. We examine the players’ beliefs about the personality and intelligence of their partner, how they play in the games and analysed the language used during communication. The results indicate that beliefs about partner’s type is biased by own-type. In particular, extraverts, characterised by positive affect, projected their positivity onto their partners. The level-k strategy chosen in the 11-20 game increased with the perceived similarity between players and in the public goods game, players cooperated more when they believed their partners to be extraverted. An analysis of the text used during communication explains how it was possible for participants to draw inferences about other’s type: for instance, use of more words and more dominant words were associated with being an extravert.
    Keywords: theory of mind, cheap talk, communication, level-k reasoning, public goods game, cooperation, extraversion, perceived similarity, self-projection bias, laboratory experiment, text analysis. JEL Classification: D91, D83, C92.
    Date: 2019
  8. By: Toomas Hinnosaar
    Abstract: Most products are produced and sold by supply chain networks, where an interconnected network of producers and intermediaries set prices to maximize their profits. I show that there exists a unique equilibrium in a price-setting game on a network. The key distortion reducing both total profits and social welfare is multiple-marginalization, which is magnified by strategic interactions. Individual profits are proportional to influentiality, which is a new measure of network centrality defined by the equilibrium characterization. The results emphasize the importance of the network structure when considering policy questions such as mergers or trade tariffs.
    Date: 2019–04
  9. By: Sylvain Béal (Université de Bourgogne Franche-Comté, CRESE); André Casajus (HHL Leipzig Graduate School of Management, Dr. Hops Craft Beer Bar, Leipzig, Germany); Eric Rémila (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne, France); Philippe Solal (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne, France)
    Abstract: We relax the assumption that the grand coalition must form by imposing the axiom of Cohesive efficiency: the total payoffs that the players can share is equal to the maximal total worth generated by a coalition structure. We determine how the three main axiomatic characterizations of the Shapley value are affected when the classical axiom of Efficiency is replaced by Cohesive efficiency. We introduce and characterize two variants of the Shapley value that are compatible with Cohesive efficiency. We show that our approach is not limited to variants of the Shapley value.
    Date: 2019–04
  10. By: Encarnación Algaba (Department of Applied Mathematics II and IMUS. University of Sevilla); Sylvain Béal (Université de Bourgogne Franche-Comté, CRESE); Vito Fragnelli (Department of Science and Innovative Technologies. University of Eastern Piedmont); Natividad Llorca (Research Institute CIO and Department of Statistics, Mathematics and Computer Science. University Miguel Hernández of Elche); Joaquin Sánchez-Soriano (Research Institute CIO and Department of Statistics, Mathematics and Computer Science. University Miguel Hernández of Elche)
    Abstract: We study the relationship between two cooperative games which arise from very different situations. On the one hand, the labeled network game which is defined to study how to allocate a certain flow in a network among agents that control different parts of the network. On the other hand, the museum pass game which is defined to analyze how to distribute the profit obtained from the use of passes which provide visitors unlimited access to the collaborating museums. We establish that both problems are related in the sense that a museum pass game can be written as a labeled network game and some labeled network games can be written as museum pass games.
    Date: 2019–04
  11. By: Rasouli, Mohammad (Stanford University); Saghafian, Soroush (Harvard Kennedy School)
    Abstract: In a variety of applications, decisions need to be made dynamically after receiving imperfect observations about the state of an underlying system. Partially Observable Markov Decision Processes (POMDPs) are widely used in such applications. To use a POMDP, however, a decision-maker must have access to reliable estimations of core state and observation transition probabilities under each possible state and action pair. This is often challenging mainly due to lack of ample data, especially when some actions are not taken frequently enough in practice. This significantly limits the application of POMDPs in real world settings. In healthcare, for example, medical tests are typically subject to false-positive and false-negative errors, and hence, the decision-maker has imperfect information about the health state of a patient. Furthermore, since some treatment options have not been recommended or explored in the past, data cannot be used to reliably estimate all the required transition probabilities regarding the health state of the patient. We introduce an extension of POMDPs, termed Robust POMDPs (RPOMDPs), which allows dynamic decision-making when there is ambiguity regarding transition probabilities. This extension enables making robust decisions by reducing the reliance on a single probabilistic model of transitions, while still allowing for imperfect state observations. We develop dynamic programming equations for solving RPOMDPs, provide a sucient statistic and an information state, discuss ways in which their computational complexity can be reduced, and connect them to stochastic zero-sum games with imperfect private monitoring.
    Date: 2018–09
  12. By: Alex Garivaltis
    Abstract: I derive practical formulas for optimal arrangements between sophisticated stock market investors (namely, continuous-time Kelly gamblers) and the brokers who lend them cash for leveraged bets on a high Sharpe asset (i.e. the market portfolio). Rather than, say, the broker posting a monopoly price for margin loans, the gambler agrees to use a greater quantity of margin debt than he otherwise would in exchange for an interest rate that is lower than the broker would otherwise post. The gambler thereby attains a higher asymptotic capital growth rate and the broker enjoys a greater rate of intermediation profit than would obtain under non-cooperation. If the threat point represents a vicious breakdown of negotiations (resulting in zero margin loans), then we get an elegant rule of thumb: $r_L^*=(3/4)r+(1/4)(\nu-\sigma^2/2)$, where $r$ is the broker's cost of funds, $\nu$ is the compound-annual growth rate of the market index, and $\sigma$ is the annual volatility. We show that, regardless of the particular threat point, the gambler will negotiate to size his bets as if he himself could borrow at the broker's call rate.
    Date: 2019–04
  13. By: Johan Hombert; Jérôme Pouyet; Nicolas Schutz
    Abstract: We develop a model of vertical merger waves and use it to study the optimal merger policy. As a merger wave can result in partial foreclosure, it can be optimal to ban a vertical merger that eliminates the last unintegrated upstream firm. Such a merger is more likely to worsen market performance when the number of downstream firms is large relative to the number of upstream firms, and when upstream contracts are nondiscriminatory, linear, and public. On the other hand, the optimal merger policy can be non-monotonic in the strength of synergies or in the degree of downstream product differentiation.
    Keywords: vertical mergers, vertical foreclosure, merger waves, merger policy
    JEL: L13
    Date: 2019–04
  14. By: Sonia Schwartz (CERDI - Centre d'Études et de Recherches sur le Développement International - Clermont Auvergne - UCA - Université Clermont Auvergne - CNRS - Centre National de la Recherche Scientifique); Johanna Choumert-Nkolo (EDI - Economic Development Initiatives Limited); Jean-Louis Combes (CERDI - Centre d'Études et de Recherches sur le Développement International - Clermont Auvergne - UCA - Université Clermont Auvergne - CNRS - Centre National de la Recherche Scientifique); Pascale Combes Motel (CERDI - Centre d'Études et de Recherches sur le Développement International - Clermont Auvergne - UCA - Université Clermont Auvergne - CNRS - Centre National de la Recherche Scientifique); Éric Nazindigouba Kere (BAD - Banque africaine de développement / African Development Bank)
    Abstract: This paper analyses the determinants of the optimal size of protected areas and what conducts neighboring effects. We investigate in which measure the infrastructure effect and the scarcity effect matter. We obtain several results. The size of protected area mainly depends on preferences toward forest, on the firms' production costs and on the relation between municipalities. As far as total deforestation is concerned asymmetric regulation is better than no regulation. The infrastructure effect always leads to smaller protected areas than the scarcity effect. Under the infrastructure effect, centralized decisions do not always work in favor of larger protected areas than decentralized decisions contrary to the scarcity effect. We also show that decentralized decisions can reach the first best under the infrastructure effect without public intervention. A study of protected areas in the Brazilian Legal Amazônia corroborates our theoretical results.
    Keywords: Protected areas,Deforestation,Nash equilibrium,Environmental federalism,Brazilian Legal Amazônia
    Date: 2019–03–12

This nep-gth issue is ©2019 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.
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