nep-gth New Economics Papers
on Game Theory
Issue of 2021‒07‒12
twenty papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. The Bonacich Shapley centrality By Nizar Allouch; A. Meca; K. Polotskaya
  2. Psychological Nash Equilibria under Ambiguity By Giuseppe De Marco; Maria Romaniello; Alba Roviello
  3. A theory of simplicity in games and mechanism design By Marek Pycia; Peter Troyan
  4. A Game-Theoretic Model of Water Theft During a Drought By Batabyal, Amitrajeet; Beladi, Hamid
  5. The effect of algorithm capabilities on cooperative games By van Zon, M.; Spliet, R.; van den Heuvel, W.
  6. Set-weighted games and their application to the cover problem By Vasily V. Gusev
  7. Keeping the Agents in the Dark: Private Disclosures in Competing Mechanisms By Attar, Andrea; Campioni, Eloisa; Mariotti, Thomas; Pavan, Alessandro
  8. The Value of the Coordination Game By Willemien Kets; Wouter Kager; Alvaro Sandroni
  9. Did the Cold War Produce Development Clusters in Africa? By Le Breton, Michel; Weber, Shlomo; Castañeda Dower, Paul; Gokmen, Gunes
  10. Patterns of Competitive Interaction By Armstrong, Mark; Vickers, John
  11. Social Metacognition: A Correlational Device for Strategic Interactions By Chiara Scarampi; Richard Fairchild; Luca Fumarco; Alberto Palermo; Neal Hinvest
  12. Limited Farsightedness in R&D Network Formation By Mauleon, Ana; Sempere-Monerris, Jose J.; Vannetelbosch, Vincent
  13. Myopic-Farsighted Absorbing Networks By de Callatay, Pierre; Mauleon, Ana; Vannetelbosch, Vincent
  14. The Equivalence Between Sequential and Simultaneous Firm Decisions By Francisco Silva; Samir Mamadehussene
  15. Game theory and scholarly publishing: premises for an agreement around open access By Abdelghani Maddi
  16. Horizon-K Farsightedness in Criminal Networks By Herings, Jean-Jacques; Mauleon, Ana; Vannetelbosch, Vincent
  17. Hidden Testing and Selective Disclosure of Evidence By Claudia Herresthal
  18. Consumer Information and the Limits to Competition By Armstrong, Mark; Zhou, Jidong
  19. The collusive efficacy of competition clauses in Bertrand Markets with capacity-constrained retailers By Trost, Michael
  20. Horizontal Mergers under Bertrand Competition By X. Henry Wang; Jingang Zhao

  1. By: Nizar Allouch; A. Meca; K. Polotskaya
    Abstract: In this paper, we develop a new game theoretic network centrality measure based on the Shapley value. To do so, we consider a coalitional game, where the worth of each coalition is the total play in the game introduced in Ballester et al. (2006). We first establish that the game is convex. As a consequence, the Shapley value belongs to the core, which enhances the attractive features of our new centrality measure. Then, we compute the Shapley value for various examples and illustrate some of its properties.
    Keywords: Social networks; network games; peer effects; centrality measures; Bonacich centrality; Shapley value
    JEL: C71 C72 C78 D85
    Date: 2021–06
  2. By: Giuseppe De Marco (Università di Napoli Parthenope, Università di Napoli Federico II and CSEF); Maria Romaniello (Università della Campania Luigi Vanvitelli); Alba Roviello (Università della Campania Luigi Vanvitelli)
    Abstract: Psychological games aim to represent situations in which players have belief-dependent motivations or believe that their opponents have belief-dependent motivations. In this setting, utility functions are directly dependent on the entire hierarchy of beliefs of each player. On the other hand, the literature on strategic ambiguity in classical games highlights that players may have ambiguous (or imprecise) beliefs about opponents' strategy choices. In this paper, we look at the issue of strategic ambiguity in the framework of psychological games by taking into account ambiguous hierarchies of beliefs and we study the natural generalization of the psychological Nash equilibrium concept to this framework. We give an existence result for this new concept of equilibrium and provide examples that show that even an infinitesimal amount of ambiguity may alter significantly the equilibria of the game or can work as an equilibrium selection device. Finally, we look at the problem of stability of psychological equilibria with respect to ambiguous trembles on the entire hierarchy of correct beliefs and we provide a limit result that gives conditions so that sequences of psychological equilibria under ambiguous perturbation converge to psychological equilibria of the unperturbed game.
    Keywords: Psychological Games, Ambiguous Beliefs, Equilibrium Existence, Equilibrium Selection.
    Date: 2021–06–28
  3. By: Marek Pycia; Peter Troyan
    Abstract: We introduce a general class of simplicity standards that vary the foresight abilities required of agents in extensive-form games. Rather than planning for the entire future of a game, agents are presumed to be able to plan only for those histories they view as simple from their current perspective. Agents may update their so-called strategic plan as the game progresses, and, at any point, for the called-for action to be simply dominant, it must lead to unambiguously better outcomes, no matter what occurs at non-simple histories. We use our gradated approach to simplicity to provide characterizations of simple mechanisms. While more demanding simplicity standards may reduce the flexibility of the designer in some cases, this is not always true, and many well-known mechanisms are simple, including ascending auctions, posted prices, and serial dictatorship-style mechanisms. In particular, we explain the widespread popularity of the well-known Random Priority mechanism by characterizing it as the unique mechanism that is efficient, fair, and simple to play.
    Keywords: Simplicity, simple dominance, limited foresight, obvious dominance, strongly obvious dominance, market design, mechanism design, extensive-form games, auctions, allocation
    JEL: C72 C78 D01 D02 D44 D47 D82
    Date: 2021–06
  4. By: Batabyal, Amitrajeet; Beladi, Hamid
    Abstract: We study water use by two geographically proximate farmers in a particular region during a drought. The two farmers each have an endowment of time that can be used either to produce water or to steal water. The price of water is exogenously given. The goal of the two farmers is to maximize their wealth from water production and water theft. In this setting, we perform three tasks. First, we determine the Nash equilibrium of the game-theoretic interaction between the two farmers. Second, we study how this equilibrium depends on the ease with which water can be stolen. Finally, we show how the preceding equilibrium is impacted when there is no water theft and then we determine the maximum amount that a farmer would be willing to pay to prevent theft.
    Keywords: Drought, Nash Equilibrium, Static Game, Water Theft, Willingness to Pay
    JEL: D74 Q25
    Date: 2020–09–06
  5. By: van Zon, M.; Spliet, R.; van den Heuvel, W.
    Abstract: Collaborations lead to cost reductions, both monetary and environmentally. However, it is not immediately clear how multiple companies with a shared optimisation problem should arrive at solutions to this shared problem or a fair allocation of the resulting cost or profit. In contrast to the literature, we assume each company, also referred to as a player, to have access to a potentially heuristic algorithm that is used to determine solutions to this shared optimisation problem. Together, the players can use these algorithms to determine solutions to shared problem instances. We call a cooperative game in which player algorithms are explicitly taken into account an algorithm quality induced game (AQI game). In an AQI game, the cost that is allocated to a player also depends on their algorithmic capabilities, that is, the quality of their algorithms. Moreover, it also allows us to model consultants, i.e., players that do have a good algorithm for the shared optimisation problem, but do not contribute in any other manner to the shared operations. In an AQI game, such players can be allocated a profit. In this paper we describe the core of AQI games and analyse the effects of improving the algorithm of a single player and of adding a consultant to a collaboration. Moreover, we present numerical results for 580,800 instances of the AQI game. We quantify the effect of improving an algorithm on the allocated cost to this player. We show that a player in general is allocated less after improving their algorithm, while in some cases the allocated cost increases. Moreover, we find that in general players with a bad algorithm benefit most from the addition of a consultant while players with a good algorithm may not benefit at all.
    Keywords: Collaborative transportation, Cooperative game theory, Vehicle Routing
    Date: 2021–06–01
  6. By: Vasily V. Gusev (National Research University Higher School of Economics)
    Abstract: The cover of a transport, social, or communication network is a computationally complex problem. To deal with it, this paper introduces a special class of simple games in which the set of minimal winning coalitions coincides with the set of least covers. A distinctive feature of such a game is that it has a weighted form, in which weights and quota are sets rather than real numbers. This game class is termed set-weighted games. A real-life network has a large number of least covers, therefore this paper develops methods for analyzing set-weighted games in which the weighted form is taken into account. The necessary and sufficient conditions for a simple game to be a set-weighted game were found. The vertex cover game (Gusev, 2020) was shown to belong to the set-weighted game class, and its weighted form was found. The set-weighted game class has proven to be closed under operations of union and intersection, which is not the case for weighted games. The sample object is the transport network of a district in Petrozavodsk, Russia. A method is suggested for efficiently deploying surveillance cameras at crossroads so that all transport network covers are taken into account.
    Keywords: simple games,set-weighted games,vertex covergame,cover problem,cooperative generating functions,power indexes
    JEL: C70 C71
    Date: 2021
  7. By: Attar, Andrea; Campioni, Eloisa; Mariotti, Thomas; Pavan, Alessandro
    Abstract: We study games in which several principals contract with several privately-informed agents. We show that enabling the principals to engage in contractible private disclosures – by sending private signals to the agents about how the mechanisms will respond to the agents’ messages – can significantly affect the predictions of such games. Our first result shows that private disclosures may generate equilibrium outcomes that cannot be supported in any game without private disclosures, no matter the richness of the message spaces and the availability of public randomizing devices. The result thus challenges the canonicity of the universal mechanisms of Epstein and Peters (1999). Our second result shows that equilibrium outcomes of games without private disclosures need not be sustainable when private disclosures are allowed. The result thus challenges the robustness of the “folk theorems” of Yamashita (2010) and Peters and Troncoso-Valverde (2013). These findings call for a novel approach to the analysis of competing-mechanism games.
    Keywords: Incomplete Information; Competing Mechanisms; Private Disclosures;; Signals; Universal Mechanisms; Folk Theorems
    JEL: D82
    Date: 2021–06
  8. By: Willemien Kets; Wouter Kager; Alvaro Sandroni
    Abstract: The value of a game is the payoff a player can expect (ex ante) from playing the game. Understanding how the value changes with economic primitives is critical for policy design and welfare.
    Date: 2021–06–03
  9. By: Le Breton, Michel; Weber, Shlomo; Castañeda Dower, Paul; Gokmen, Gunes
    Abstract: This paper examines the lasting impact of the alignment of African countries during the Cold War on their modern economic development. We find that the division of the continent into two blocs (East/West) led to two clusters of development outcomes that reflect the Cold War’s ideological divide. To determine alignment, we introduce a non-cooperative game of social interactions where each country chooses one of the two existing blocs based on its predetermined bilateral similarities with other members of the bloc. We show the existence of a strong Nash equilibrium in our game and apply the celebrated MaxCut method to identify such a partition. The alignment predicts UN General Assembly voting patterns during the Cold War but not after. Our approach, linking global political interdependence to distinct development paths in Africa, relies on history to extract a micro-founded treatment assignment, while allowing for an endogenous, process-oriented view of historical events.
    Keywords: Cold War; Political Alliances; Africa; Blocs; Development Clusters; Strong Nash Equilibrium; Landscape Theory
    JEL: C62 C72 F54 F55 N47 O19 Y10 O57
    Date: 2021–06–22
  10. By: Armstrong, Mark; Vickers, John
    Abstract: We explore patterns of price competition in an oligopoly where consumers vary in the set of firms they consider for their purchase and buy from the lowest-priced firm they consider. We study a pattern of consideration, termed "symmetric interactions", that generalises models used in existing work (duopoly, symmetric firms, and firms with independent reach). Within this class, equilibrium profits are proportional to a firm's reach, firms with a larger reach set higher average prices, and a reduction in the number of firms (either by exit or by merger) harms consumers. However, increased competition (either by entry of by increased consumer awareness) does not always benefit consumers. We go on to study patterns of consideration with asymmetric interactions. In situations with disjoint reach and with nested reach we find equilibria in which price competition is "duopolistic": only two firms compete within each price range. We characterize the contrasting equilibrium patterns of price competition for all patterns of consideration in the three-firm case.
    Keywords: Price competition, consideration sets, price dispersion, entry and merger.
    JEL: C72 D43 D83 L13 L4
    Date: 2021–05
  11. By: Chiara Scarampi (University of Geneva); Richard Fairchild (University of Bath); Luca Fumarco (Tulane University); Alberto Palermo (Trier University); Neal Hinvest (University of Bath)
    Abstract: This study reports a laboratory experiment wherein we investigate the role of social metacognition– i.e., the ability to monitor and control one’s own and others’ mental states – in a chicken game. In the first part of the experiment, we try to implement a correlated equilibrium, a generalisation of the Nash equilibrium where players’ strategies are correlated by a third party/mechanism/choreographer. We find that social metacognition is a signif- icant predictor of subjects’ strategy choices. The experiment proceeds without third party recommendations. We find evidence that subjects with high social metacognition are more likely to play a correlated equilibrium; that is, social metacognition acts “as if” it is the correlating mechanism. We relate our findings to the individual social metacognitive ability as well as to the group composition.
    Keywords: Correlated Equilibrium, Social Metacognition, Experimental Economics
    JEL: C72 C92 D91
    Date: 2021–06
  12. By: Mauleon, Ana (Université catholique de Louvain, LIDAM/CORE, Belgium); Sempere-Monerris, Jose J. (University of Valencia); Vannetelbosch, Vincent (Université catholique de Louvain, LIDAM/CORE, Belgium)
    Abstract: We adopt the horizon-K farsighted set of Herings, Mauleon and Vannetelbosch (2019) to study the R&D networks that will emerge in the long run when firms are neither myopic nor fully farsighted but have some limited degree of farsightedness. We find that a singleton set consisting of a pairwise stable network is a horizon-K farsighted set for any degree of farsightedness K ≥ 2. That is, each R&D network consisting of two components of nearly equal size satisfies both horizon-K deterrence of external deviations and horizon-K external stability for K ≥ 2. On the contrary, each R&D network consisting of two components with the largest one comprising three-quarters of firms, predicted when all firms are fully farsighted, violates horizon-K deterrence of external deviations. Thus, when firms are homogeneous in their degree of farsightedness, pairwise stable R&D networks consisting of two components of nearly equal size are robust to limited farsightedness.
    Keywords: Limited farsightedness, Stability, R&D Networks
    JEL: C70 L13 L20
    Date: 2021–06–04
  13. By: de Callatay, Pierre (Université catholique de Louvain, LIDAM/CORE, Belgium); Mauleon, Ana (Université catholique de Louvain, LIDAM/CORE, Belgium); Vannetelbosch, Vincent (Université catholique de Louvain, LIDAM/CORE, Belgium)
    Abstract: We propose the notion of myopic-farsighted absorbing set to determine the networks that emerge in the long run when some players are myopic while others are farsighted. A set of networks is a myopic-farsighted absorbing set if (no external deviation) there is no myopic-farsighted improving path from networks within the set to some networks outside the set, (external stability) there is a myopic-farsighted improving path from any network outside the set to some network within the set, and (minimality) there is no proper subset satisfying no external deviation and external stability. Contrary to the notion of myopic-farsighted stable set [Herings, Mauleon and Vannetelbosch (J. Econ. Theory, 2020), Luo, Mauleon and Vannetelbosch (Econ. Theory, 2021)], we show that a myopic-farsighted absorbing set always exists. We partially characterize the myopic-farsighted absorbing sets and we provide sufficient conditions for the equivalence between a myopic-farsighted absorbing set and a myopic-farsighted stable set. We also introduce and fully characterize the notion of proper myopic-farsighted absorbing set that refines the concept of myopic-farsighted absorbing set by selecting the more absorbing networks. Finally, we consider a threshold game that illustrates the role of the relative number of farsighted and myopic players for reaching efficiency.
    Keywords: networks; absorbing sets; myopic and farsighted players
    JEL: A14 C70 D20
    Date: 2021–04–23
  14. By: Francisco Silva; Samir Mamadehussene
    Abstract: When ?rms compete by choosing two strategic variables (e.g. quality and price), the timing under which ?rms make their decisions (simultaneous vs sequential choice of the strategic variables) plays a critical role, as the equilibrium may be drastically di?erent depending on the timing that is assumed. We rely on the marketing and psychology literatures that provide well-established evidence that consumers do not consider all products in a market, i.e. consumers form “consideration sets”. Under this assumption, we ?nd that in markets where (i) ?rms’ strategies do not in?uence the consideration set formation, and (ii) ?rms are su?ciently uncertain regarding the rivals that each consumer considers, the equilibrium of the game in which ?rms choose the strategic variables sequentially is close to the equilibrium of the simultaneous game. Moreover, the equilibrium of the simultaneous game does not depend on whether or not consumers consider all available alternatives. Therefore, we argue that the analysis of these markets can be performed with standard models provided that the simultaneous timing is used (even if ?rms make their decisions sequentially).
    Date: 2020
  15. By: Abdelghani Maddi (HCERES, CEPN)
    Abstract: Actors in research and scientific publishing are gradually joining the Open-Access (OA) movement, which is gaining momentum to become nowadays at the heart of scientific policies in high-income countries. The rise of OA generates profound changes in the chain of production and dissemination of knowledge. Free access to peer-reviewed research methods and results has contributed to the dynamics of science observed in recent years. The modes of publication and access have also evolved; the classic model, based on journal subscriptions is gradually giving way to new economic models that have appeared with the arrival of OA. The objective of this article is twofold. First, propose a model for the publishing market based on the literature as well as on changes in open science policies. Second, analyze publishing strategies of publishers and institutions. To do so, we relied on game theory in economics. Results show that in the short term, the publisher's equilibrium strategy is to adopt a hybridpublishing model, while the institutions' equilibrium strategy is to publish in OA. This equilibrium is not stable and that in the medium/long term, the two players will converge on an OA publishing strategy. The analysis of the equilibrium in mixed-strategies confirms this result.
    Date: 2021–06
  16. By: Herings, Jean-Jacques; Mauleon, Ana (Université catholique de Louvain, LIDAM/CORE, Belgium); Vannetelbosch, Vincent (Université catholique de Louvain, LIDAM/CORE, Belgium)
    Abstract: We study the criminal networks that will emerge in the long run when criminals are neither myopic nor completely farsighted but have some limited degree of farsightedness. We adopt the horizon-K farsighted set of Herings, Mauleon and Vannetelbosch (2019) to answer this question. We Önd that in criminal networks with n criminals, the set consisting of the complete network is a horizon-K farsighted set whenever the degree of farsightedness of the criminals is larger than or equal to (n 1). Moreover, the complete network is the unique horizon-(n 1) farsighted set. Hence, the predictions obtained in case of completely farsighted criminals still hold when criminals are much less farsighted.
    Keywords: Limited farsightedness, Stability, Criminal Networks
    JEL: A14 C70 D20
    Date: 2021–04–26
  17. By: Claudia Herresthal
    Abstract: An agent can sequentially run informative tests about an unknown state and disclose (some or all) outcomes to a decision maker who then faces an approval choice. Players agree on the optimal choice under certainty, but the decision maker has a higher approval threshold than the agent. I compare the case where testing is hidden and the agent chooses which test outcomes to verifiably disclose to the case where testing is observable. When testing is observable, I show that the agent may strategically stop testing even if further tests could yield a mutual benefit. I find conditions under which the decision maker is strictly better off under hidden testing and in some equilibria both players are strictly better off under hidden testing than in the unique equilibrium under observable testing.
    Keywords: endogenous information acquisition, verifiable disclosure, transparency, questionable research practices
    JEL: D83 D82
    Date: 2020–01
  18. By: Armstrong, Mark; Zhou, Jidong
    Abstract: This paper studies competition between firms when consumers observe a private signal of their preferences over products. Within the class of signal structures which induce pure-strategy pricing equilibria, we derive signal structures which are optimal for firms and those which are optimal for consumers. The firm-optimal policy amplifies underlying product differentiation, thereby relaxing competition, while ensuring consumers purchase their preferred product, thereby maximizing total welfare. The consumer-optimal policy dampens differentiation, which intensifies competition, but induces some consumers to buy their less-preferred product. Our analysis sheds light on the limits to competition when the information possessed by consumers can be designed flexibly.
    Keywords: Information design, Bertrand competition, product differentiation, online platforms
    JEL: D43 D47 D8 L13 L15
    Date: 2021–06
  19. By: Trost, Michael
    Abstract: We study the collusive efficacy of competition clauses (CC) such as the meeting competition clause (MCC) and the beating competition clauses (BCC) in a general framework. In contrast to previous theoretical studies, we allow for repeated interaction among the retailers and heterogeneity in their sales capacities. Besides that, the selection of the form of the CC is endogeneized. The retailers choose among a wide range of CC types - including the conventional ones such as the MCC and the BCCs with lump sum refunds. Several common statements about the collusive (in)efficacy of CCs cannot be upheld in our framework. We show that in the absence of hassle costs, MCCs might induce collusion in homogeneous markets even if they are adopted only by few retailers. If hassle and implementation costs are mild, collusion can be enforced by BCCs with lump sum refunds. Remarkably, these fundings hold for any reasonable rationing rule. However, a complete specification of all collusive CCs is in general impossible without any further reference to the underlying rationing rule.
    Keywords: Competition clauses,price-matching guarantee,price-beating guarantee,anti-competitivepractice,capacity-constrained oligopoly
    JEL: L11 L13 L41
    Date: 2021
  20. By: X. Henry Wang (Department of Economics, University of Missouri); Jingang Zhao (Economics Department, University of Saskatchewan)
    Abstract: This paper draws on recent results from the study of hybrid games and multi-product oligopolies to analyze horizontal mergers under Bertrand competition. We identify a set of linear Bertrand models in which a horizontal merger will reduce both the outsiders' profits and consumer surplus when the insiders' cost savings are sufficiently large. We also show that mergers in Bertrand models will normally increase the insiders' profits even without generating any cost-savings. Such results suggest that the increase in the insiders' profits may arise at the expense of rival firms and consumers, and thus raise new concerns about the anti-competitive effects of mergers under price competition.
    Keywords: Horizontal merger, Bertrand competition, consumer surplus
    JEL: D43 L13 L41
    Date: 2021

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