nep-gth New Economics Papers
on Game Theory
Issue of 2021‒09‒13
sixteen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Learning and Acyclicity in the Market Game By Artur Dolgopolov; Cesar Martinelli
  2. Marginalism, Egalitarianism and Efficiency in Multi-Choice Games By David Lowing; Kevin Techer
  3. Multi-agent Bayesian Learning with Best Response Dynamics: Convergence and Stability By Manxi Wu; Saurabh Amin; Asuman Ozdaglar
  4. Ultimatum Game Behavior in a Social-Preferences Vacuum Chamber By Volker Benndorf; Thomas Große Brinkhaus; Ferdinand von Siemens
  5. Overcoming coordination failure in games with focal points By David Rojo Arjona; Stefania Sitzia; Jiwei Zheng
  6. Winning coalitions in plurality voting democracies By René van den Brink; Dinko Dimitrov; Agnieszka Rusinowska
  7. Pollution, partial privatization and the effect of ambient charges By Ohnishi, Kazuhiro
  8. Fuzzy Conventions By Marcin P\k{e}ski
  9. On the axiomatic approach to sharing the revenues from broadcasting sports leagues By Gustavo Bergantiños; Juan D. Moreno-Ternero
  10. Cournot-Bertrand equilibria under two-part tariff contract By Basak, Debasmita
  11. Optimal Management of Evolving Hierarchies By Jens L. Hougaard; Juan D. Moreno-Ternero; Lars P. Osterdal
  12. Designing a Competitive Monotone Signaling Equilibrium By Seungjin Han; Alex Sam; Youngki Shin
  13. Cycling and Categorical Learning in Decentralized Adverse Selection Economies By Jehiel, Philippe; Mohlin, Erik
  14. Efficient Bilateral Trade via Two-Stage Mechanisms under One- Sided Asymmetric Information By Kunimoto, Takashi; Zhang, Cuiling
  15. How should durable goods firms combine online and mass media advertisements to promote sales? By Fujisawa, Chieko; Kasuga, Norihiro
  16. Direct network externalities and dynamics of two-sided platforms By Aslan, Fatma; Haouel, Chourouk; Nemeslaki, Andras; Somogyi, Robert

  1. By: Artur Dolgopolov (Department of Economics, European University Institute); Cesar Martinelli (Interdisciplinary Center for Economic Science and Department of Economics, George Mason University)
    Abstract: We show that strategic market games, the non-cooperative implementation of a matching with transfers or an assignment game, are weakly acyclic. This property ensures that many common learning algorithms will converge to Nash equilibria in these games, and that the allocation mechanism can therefore be de- centralized. Convergence hinges on the appropriate price clearing rule and has di erent properties for better- and best-response dynamics. We tightly characterize the robustness of this convergence in terms of so-called schedulers for both types of dynamics.
    Date: 2021–09
  2. By: David Lowing (Univ Lyon, UJM Saint-Etienne, GATE UMR 5824, F-42023 Saint- Etienne, France; Gaz Réseau Distribution France, Direction Economie et Régulation.); Kevin Techer (Univ Lyon, UJM Saint-Etienne, GATE UMR 5824, F-42023 Saint- Etienne, France)
    Abstract: The search for a compromise between marginalism and egalitarianism has given rise to many discussions. In the context of cooperative games, this compromise can be understood as a trade-off between the Shapley value and the Equal division value. We investigate this compromise in the context of multi-choice games in which players have several activity levels. To do so, we propose new extensions of the Shapley value and of the Weighted Division values to multi-choice games. Contrary to the existing solution concepts for multi-choice games, each one of these values satisfies a core condition introduced by Grabisch and Xie (2007), namely Multi-Efficiency. We compromise between marginalism and egalitarianism by introducing the multi-choice Egalitarian Shapley values, computed as the convex combination of our extensions. To conduct this study, we introduce new axioms for multi-choice games. This allows us to provide an axiomatic foundation for each of these values.
    Keywords: Multi-choice games, Multi-choice Shapley value, Multi-choice Equal division value, Multi-choice Egalitarian Shapley values
    JEL: C71
    Date: 2021
  3. By: Manxi Wu; Saurabh Amin; Asuman Ozdaglar
    Abstract: We study learning dynamics induced by strategic agents who repeatedly play a game with an unknown payoff-relevant parameter. In this dynamics, a belief estimate of the parameter is repeatedly updated given players' strategies and realized payoffs using Bayes's rule. Players adjust their strategies by accounting for best response strategies given the belief. We show that, with probability 1, beliefs and strategies converge to a fixed point, where the belief consistently estimates the payoff distribution for the strategy, and the strategy is an equilibrium corresponding to the belief. However, learning may not always identify the unknown parameter because the belief estimate relies on the game outcomes that are endogenously generated by players' strategies. We obtain sufficient and necessary conditions, under which learning leads to a globally stable fixed point that is a complete information Nash equilibrium. We also provide sufficient conditions that guarantee local stability of fixed point beliefs and strategies.
    Date: 2021–09
  4. By: Volker Benndorf; Thomas Große Brinkhaus; Ferdinand von Siemens
    Abstract: We study strategic interaction in an experimental social-preferences vacuum chamber. We mute social preferences by letting participants knowingly interact with computers. Our new design allows for indirect strategic interaction: there are several waves in which computer players inherit the behavior of human players from the previous wave. We apply our method to investigate trembling-hand perfection in a normal-form version of the ultimatum game. We find that behavior remains far off from a trembling-hand perfect equilibrium under selfish preferences even towards the end of our experiment. The likely reasons for our findings are strategic uncertainty and incomplete learning.
    Keywords: social preferences, induced-value theory, learning, ultimatum game, strategic interaction
    JEL: C92 C72 D91
    Date: 2021
  5. By: David Rojo Arjona; Stefania Sitzia; Jiwei Zheng
    Abstract: Focal points (Schelling, 1960) have shown limitations as coordination devices in games with conflict, such as the battle of the sexes games. We experimentally test whether an increase in their salience can counteract the negative impact of conflict on coordination. The intuition is that, in the presence of conflict, the solution to the coordination dilemma offered by the focal point loses importance. Increasing its salience increases its relevance and therefore coordination success. Our results provide strong support for this conjecture. Furthermore, when games feature outcomes with different degrees of payoffs’ inequality (i.e. the difference of players’ payoffs) and efficiency (i.e. the sum of players’ payoffs), increasing salience does not lead to an obvious increase in coordination, unless the salience of the focal point is maximal.
    Keywords: coordination games, focal points, salience, conflict of interests, battle-of-the-sexes, intermixed-blocked effect
    JEL: C72 C78 C91 D91
    Date: 2021
  6. By: René van den Brink (VU University Amsterdam); Dinko Dimitrov (Saarland University [Saarbrücken]); Agnieszka Rusinowska (CNRS - Centre National de la Recherche Scientifique, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, 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)
    Abstract: We consider plurality voting games being simple games in partition function form such that in every partition there is at least one winning coalition. Such a game is said to be weighted if it is possible to assign weights to the players in such a way that a winning coalition in a partition is always one for which the sum of the weights of its members is maximal over all coalitions in the partition. A plurality game is called decisive if in every partition there is exactly one winning coalition. We show that in general, plurality games need not be weighted, even not when they are decisive. After that, we prove that (i) decisive plurality games with at most four players, (ii) majority games with an arbitrary number of players, and (iii) decisive plurality games that exhibit some kind of symmetry, are weighted. Complete characterizations of the winning coalitions in the corresponding partitions are provided as well.
    Date: 2021–04
  7. By: Ohnishi, Kazuhiro
    Abstract: This paper examines a mixed Cournot duopoly model comprising a private firm and a partially privatized public firm to reassess the effect of an increase in ambient charges, and demonstrates that the result of this study is about the same as that obtained from private Cournot duopoly competition.
    Keywords: ambient charge; Cournot duopoly; environmental regulation; partial privatization; pollution
    JEL: C72 D21 L33 Q58
    Date: 2021–02–27
  8. By: Marcin P\k{e}ski
    Abstract: We study binary coordination games with random utility played in networks. A typical equilibrium is fuzzy -- it has positive fractions of agents playing each action. The set of average behaviors that may arise in an equilibrium typically depends on the network. The largest set (in the set inclusion sense) is achieved by a network that consists of a large number of copies of a large complete graph. The smallest set (in the set inclusion sense) is achieved on a lattice-type network. It consists of a single outcome that corresponds to a novel version of risk dominance that is appropriate for games with random utility.
    Date: 2021–08
  9. By: Gustavo Bergantiños (ECOSOT, Universidade de Vigo); Juan D. Moreno-Ternero (Department of Economics, Universidad Pablo de Olavide;)
    Abstract: We take the axiomatic approach to uncover the structure of the revenue-sharing problem from broadcasting sports leagues. We formalize two notions of impartiality, depending on the stance one takes with respect to the revenue generated in the games involving each pair of teams. We show that the resulting two axioms lead towards two broad categories of rules, when combined with additivity and some other basic axioms. We complement those results strengthening the impartiality notions to consider axioms of order preservation.
    Keywords: resource allocation, broadcasting, sport leagues, axioms, impartiality
    JEL: D63 C71 Z20
    Date: 2021
  10. By: Basak, Debasmita
    Abstract: We consider a vertically related market where one quantity setting and another price setting downstream firm negotiate the terms of a two-part tariff contract with an upstream input supplier. In contrast to the traditional belief, we show that when bargaining is decentralised, the price setting firm produces a higher output and earns a higher profit than the quantity setting firm. And, when bargaining is centralised, both firms produce the same output whereas the profit is higher under the price setting firm than the quantity setting firm.
    Keywords: Bargaining; Bertrand; Cournot; Two-part tariffs; Vertical pricing; Welfare
    JEL: L13 L2 L22
    Date: 2021–09–04
  11. By: Jens L. Hougaard (Department of Food and Resource Economics, University of Copenhagen); Juan D. Moreno-Ternero (Department of Economics, Universidad Pablo de Olavide); Lars P. Osterdal (Department of Economics, Copenhagen Business School)
    Abstract: We study the optimal management of evolving hierarchies of revenue-generating agents. The initiator invests into expanding the hierarchy by adding another agent, who will bring revenues to the joint venture and who will invest herself into expanding the hierarchy further, and so on. The higher the investments (which are private information), the higher the probability of expanding the hierarchy. An allocation scheme specifies how revenues are distributed, as the hierarchy evolves. We obtain schemes that are socially optimal and initiator-optimal respectively. Our results have potential applications for blockchain, cryptocurrencies, social mobilization and multi-level marketing.
    Keywords: Optimal allocation schemes; Hierarchies; Management; Nash equilibrium; Blockchain.
    JEL: C70 L24 M52
    Date: 2021
  12. By: Seungjin Han; Alex Sam; Youngki Shin
    Abstract: A decision maker (DM) determines a set of reactions that receivers can choose before senders and receivers move in a generalized competitive signaling model with two-sided matching. The DM’s optimal design of the unique stronger monotone signaling equilibrium (unique D1 equilibrium) is equivalent to the choice problem of two threshold sender types, one for market entry and the other for pooling on the top. Our analysis sheds light on the impacts of a trade-off between matching efficiency and signaling costs, the relative heterogeneity of receiver types to sender types, and the productivity of the sender’s action on optimal equilibrium designing.
    Keywords: optimal equilibrium design; monotone signaling equilibrium; stronger monotone belief; Criterion D1
    JEL: D82 D86
    Date: 2021–09
  13. By: Jehiel, Philippe (Paris School of Economics); Mohlin, Erik (Department of Economics, Lund University)
    Abstract: We study learning in a decentralized pairwise adverse selection economy, where buyers have access to the quality of traded goods but not to the quality of non- traded goods. Buyers categorize ask prices in order to predict quality as a function of ask price. The categorization is endogenously determined so that outcomes that are observed more often are categorized more finely, and within each category beliefs reflect the empirical average. This leads buyers to have a very fine understanding of the relationship between qualities and ask prices for prices below the current market price, but only a coarse understanding above that price. We find that this induces a price cycle involving the Nash equilibrium price, and one or more higher prices.
    Keywords: Adverse selection; Bounded rationality; Categorization; Learning; Model misspecification; OTC markets
    JEL: C70 C73 D82 D83 D91
    Date: 2021–09–02
  14. By: Kunimoto, Takashi (School of Economics, Singapore Management University); Zhang, Cuiling (The Institute for Advanced Economic Research, Dongbei University of Finance and Eco- nomics)
    Abstract: This paper considers a bilateral-trade model with one-sided asymmetric information in which one agent (seller) initially owns an indivisible object and is fully informed of its value, while the other agent (buyer) intends to obtain the object whose value is unknown to himself. As Jehiel and Pauzner (2006) show that no mechanisms can generally result in efficient, voluntary bilateral trades, we aim to overturn this impossibility result by employing two-stage mechanisms (Mezzetti (2004)) in which first, the outcome (e.g., allocation of the goods) is determined, then the agents observe their own outcome-decision payoffs, and finally, transfers are made. We show that the generalized two-stage Groves mechanism induces efficient, voluntary bilateral trades. On the contrary, we also show by means of an example that the generalized two-stage Groves mechanism fails to achieve efficient, voluntary trades in a two-sided asymmetric information setup in which both parties have private information and each party’s valuation depends on the other’s information in the same way.
    Keywords: bilateral trades; one-sided asymmetric information; two-stage mechanisms
    JEL: C72 D78 D82
    Date: 2021–08–01
  15. By: Fujisawa, Chieko; Kasuga, Norihiro
    Abstract: We develop an advertising strategy for durable goods firms applying a dual time-period model while considering three-stage game in a Cournot competition. We assume that firms employ two advertising approaches; one is online advertising, which escalates consumers' willingness to purchase goods and the other is conventional mass media advertising, including television and radio, which presents a limited 'evoked set' of goods. The term evoked set implies that consumers only consider a small group of brands prior to making a purchase. As firms understand the character of each advertisement, sales strategy is devised to target a heterogeneous consumer through advertising. Should firms only choose one type of advertisement or a combination of the two kinds of ads available? In this model we assume that firms directly consider both types of advertising. Our analysis demonstrates that online advertisement raises the total number of consumer-product matches in the competitive equilibrium. We also show that firms combine the two types of advertisement to apply the differing effects of each format. Moreover, firms increase revenue through an appropriate mix of advertising strategy, although the cost of advertising might increase. Regarding the future direction of advertising, we anticipate that the combination of both online and conventional strategies will persist, maintaining the growth of a diverse product market.
    Keywords: Durable goods,Online media advertising,mass media advertising,targeting,media strategy
    JEL: D15 D43 L13 D82
    Date: 2021
  16. By: Aslan, Fatma; Haouel, Chourouk; Nemeslaki, Andras; Somogyi, Robert
    Abstract: We investigate the effect of direct network externalities on the long- run dynamics of two-sided platforms. Two-sided platforms have been widespread in the economy, acting as intermediaries connecting two dis- tinct groups of agents. A defining characteristic of the two-sidedness is the existence of indirect network externalities between the two sides. How- ever, direct externalities can also be important in one or both sides of the market. For instance, direct externalities include review systems where buyers on the platform benefit from other buyers' ratings and comments. We find that considering direct externalities changes the dynamics quali- tatively. For example, instead of saddle path dynamics, they can lead to unstable node dynamics and the collapse of a platform.
    Date: 2021

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