nep-gth New Economics Papers
on Game Theory
Issue of 2023‒02‒13
twenty-two papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Geometry of set functions in cooperative game theory By Dylan Laplace Mermoud
  2. Stable source connection and assignment problems as multi-period shortest path problems By Leanne Streekstra; Christian Trudeau
  3. Sequential competition and the strategic origins of preferential attachment By Antoine Mandel; Xavier Venel
  4. Bargaining over information structures By Kemal Kivanc Akoz; Arseniy Samsonov
  5. Dynamic Volunteer’s Dilemma with Procrastinators By Yixuan Shi
  6. Multi-battle contests over complementary battlefields By Daniel Graydon Stephenson
  7. Endogenous choice of price or quantity contract with upstream advertising By Qing Hu; Dan Li; Tomomichi Mizuno
  8. Industrial policy and global public goods provision: rethinking the environmental trade agreement By Andres, Pia-Katharina
  9. Extending the Characterization of Maximum Nash Welfare By Sheung Man Yuen; Warut Suksompong
  10. Stable streaming platforms: a cooperative game approach By Schlicher, L.; Dietzenbacher, Bas; Musegaas, Marieke
  11. Promises or Agreements? Moral commitments in bilateral communication By Di Bartolomeo Giovanni; Dufwenberg Martin; Papa Stefano; Passarelli Francesco
  12. Evolutionary finance: A model with endogenous asset payoffs By Igor V. Evstigneev; Thorsten Hens; Mohammad Javad Vanaei
  13. Cheap Talk, Monitoring and Collusion By David Spector
  14. Information disclosure under liability: an experiment on public bads By Julien Jacob; Eve-Angéline Lambert; Mathieu Lefebvre; Sarah van Driessche
  15. Estimating Income in a Tax Compliance Game. A Bayesian Persuasion Approach By Raphaela Hennigs
  16. Price vs Market Share with Royalty Licensing: Incomplete Adoption of a Superior Technology with Heterogeneous Firms By Luca Sandrini
  17. Repeated Trading: Transparency and Market Structure By Ayca Kaya; Santanu Roy
  18. Feedback and Contagion through Distressed Competition By Hui Chen; Winston Wei Dou; Hongye Guo; Yan Ji
  19. Proportional Fairness in Obnoxious Facility Location By Haris Aziz; Alexander Lam; Bo Li; Fahimeh Ramezani; Toby Walsh
  20. Bounding Comparative Statics under Diagonal Dominance By Jordan Norris; Charles Johnson; Ilya Spitkovsky
  21. The Social Construction of Ignorance: Experimental Evidence By Ivan Soraperra; Joël van der Weele; Marie Claire Villeval; Shaul Shalvi
  22. A responsibility value for digraphs By Rosa van den Ende; Dylan Laplace Mermoud

  1. By: Dylan Laplace Mermoud
    Abstract: They are many unexplored links between cooperative transferable utility games and convex, discrete or combinatorial geometry. In this paper, we investigate some of these links, such as the ones between cores of convex games and generalized permutohedra, also named polymatroids or base polyhedra. Another link that we investigate is the one between the resonance hyperplane arrangement and the set of sets of preimputations which are effective for a given coalition. These bridges can give interpretation and intuition to cooperative game theory, as well as bring new results and tools from other fields into the study of cooperative games.
    Date: 2023–01
  2. By: Leanne Streekstra (Research Centre of Quantitative Social and Management Sciences, Budapest University of Technology and Economics); Christian Trudeau (Department of Economics, University of Windsor)
    Abstract: We extend the familiar shortest path problem by supposing that agent shave demands over multiple periods. This potentially allows agents to combine their paths if their demands are complementary; for instance if one agent only needs a connection to the source in the summer while the other requires it only in the winter. We not only show that the resulting cost sharing problem always generates a totally balanced game, regardless of the number of agents and periods, the cost structure or the demand profile, but that all totally balanced games are representable as MSP problems. We then exploit the fact that the model encompasses many well-studied problems to obtain or reobtain balancedness and total-balancedness results for source-connection problems, market problems and minimum coloring problems.
    Keywords: Shortest path; Demand over multiple periods; Cooperative game; Core; Total-balancedness; Source-conenction; Assignment
    JEL: C71 D63
    Date: 2022–09
  3. By: Antoine Mandel (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 - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - 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); Xavier Venel (LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma])
    Abstract: We analyze whether random network formation processes, such as preferential attachment, can emerge as the outcome of strategic behaviour. We represent network formation as an extensive game in which players sequentially form links as they enter the network. In this setting, we investigate under which conditions subgame perfect equilibria of the game are observationally equivalent with random network formation process. We put forward two structural conditions that are necessary in this respect. First, players must have some form of imperfect information as randomization is purposeful only if its realization is not perfectly observed by the other players. Second, there must be some form of competition between a player and its successors: a player has incentives to reduce the information available to its successors only to the extent that their objectives are in opposition. Accordingly, we put forward a class of games where players compete with their predecessors and their successors for the costs and benefits induced by link formation and show that subgame perfect equilibria of this game are observationally equivalent with random network formation process. In particular, when linkage costs are inversely proportional to the degree of a node, equilibrium play induces a preferential attachment process. This provides a positive answer to the question of the existence of strategic foundations for preferential attachment. However the very specific conditions requiredfor the observational equivalence to hold suggest that preferential attachment can be explained by strategic considerations only in a limited number of situations.
    Keywords: Game theory, Socio-economic networks, Endogenous network formation, Preferential attachment, Extensive games
    Date: 2022–11–15
  4. By: Kemal Kivanc Akoz (Faculty of Economic Sciences, HSE University); Arseniy Samsonov (Research Centre of Quantitative Social and Management Sciences, Budapest University of Technology and Economics)
    Abstract: How transparent are informational institutions if their founders have to agree on the design? We analyze a model where several agents bargain over persuasion of a single receiver. We characterize the existence of anagreement that is beneficial for all agents relative to some fixed benchmark information structure, when the preferences of agents are state-independent, and provide sufficient conditions for general preferences. We further show that a beneficial agreement exists if, for every coalition of a fixed size, there is a belief that generates enough surplus for its members. Next, we concentrate on agent-partitional environments, where for each agent there is a state where the informed decision of the receiver benefits her the most. In these environments, we define endorsement rules that fully reveal all such agent-states. Endorsement rules are Pareto efficient when providing information at all agent-states generates enough surplus, and they correspond to a Nash Bargaining solution when the environment is also symmetric. We provide two political economic applications of our model. In a running example, we discuss the implication of our model to bargaining of authoritarian elites over media policy. The last section applies the model to an electoral campaign in a multiparty democracy.
    Keywords: Persuasion; Bargaining solution; Efficiency
    JEL: C71 D82
    Date: 2023–01
  5. By: Yixuan Shi
    Abstract: We study a dynamic volunteering dilemma game in which two players choose to volunteer or wait given there have not been any volunteering actions in the past. The players can be procrastinators and the benefits of volunteering arrive later than the costs. We fully characterise the stationary Strotz-Pollak equilibria. When the cost of volunteering is suf- ficiently small or agents’ present-bias parameters are sufficiently close, there always exists an equilibrium in which both players randomise. This equilibrium features stochastic delay and the delay is exacerbated if one or both agents become more present-biased. However, if the agents differ significantly in their present-bias parameters, this difference may act as a ‘natural’ coordination device and the unique stationary equilibrium predicts that only the less severe procrastinator volunteers, this may result in an even quicker provision compared with the case of two exponential discounters.
    Keywords: Dynamic Volunteer’s dilemma, Present bias, Hyperbolic discounting, Strotz-Pollak equilibrium; Time inconsistency;
    JEL: D82 D83 H26
    Date: 2022–11
  6. By: Daniel Graydon Stephenson (Department of Economics, VCU School of Business)
    Abstract: This paper studies Blotto contests with divisible complementary prizes. Each agent distributes a fixed budget over multiple battlefields. Each battlefield has a single prize which is divided among the competi- tors in proportion to a power function of the corresponding investment levels. Prizes exhibit constant sub-unitary elasticity of substitution. Such contests are shown to have pure strategy Nash equilibria under arbitrarily sensitive battlefield success functions. In contrast, conven- tional Blotto and Tullock contests have no pure strategy Nash equi- libria under sufficiently sensitive battlefield success functions. These results suggest that divisible complementary prizes can help stabilize the distribution of resources in strategic conflicts.
    JEL: C70 C62 D74 Q34
  7. By: Qing Hu (Kushiro Public University of Economics); Dan Li (School of Management, Xi’an Polytechnic University); Tomomichi Mizuno (Graduate School of Economics, Kobe University)
    Abstract: We investigate a supply chain comprising a manufacturer engaged in advertising and two retailers who compete with differentiated products. We examine the endogenous choice between competing on quantity or price for the retailers. Our analysis reveals that, depending on the level of product substitutability, the range of possible outcomes is varied and includes Cournot, Bertrand, and Cournot-Bertrand under informative advertising. This result contradicts the established understanding that firms tend to engage in Cournot competition as their dominant strategy. Furthermore, we find that under persuasive advertising, Cournot or Bertrand outcomes may be optimal, but Cournot-Bertrand never arises as an equilibrium.
    Keywords: Exporting; endogenous competition mode, advertising, vertical relationship
    JEL: D43 L13 M21
    Date: 2023–01
  8. By: Andres, Pia-Katharina
    Abstract: Countries around the world increase the downstream cost of low carbon technologies using anti-dumping duties and local content requirements, while simultaneously blaming inadequate efforts to address climate change on the economic cost of doing so. This paper presents a 2-country, 2-period strategic model of trade in a clean technology in the presence of differential country-level production costs and imperfect competition. If the difference in production cost is large enough and learning-by-doing allows the laggard country to catch up, then in the absence of production subsidies remaining in autarky during Stage 1 of the game can be welfare-improving for both countries. This result is strengthened when both countries use consumer subsidies. When countries choose their policy mixes, the Nash Equilibrium involves both trade and production subsidies on the part of the laggard country. The analysis suggests that an environmental trade agreement is most likely to be beneficial if production subsidies for clean technology are explicitly permitted.
    JEL: R14 J01 J1
    Date: 2023–01–09
  9. By: Sheung Man Yuen; Warut Suksompong
    Abstract: In the allocation of indivisible goods, the maximum Nash welfare rule has recently been characterized as the only rule within the class of additive welfarist rules that satisfies envy-freeness up to one good. We extend this characterization to the class of all welfarist rules.
    Date: 2023–01
  10. By: Schlicher, L.; Dietzenbacher, Bas (RS: GSBE other - not theme-related research, QE Math. Economics & Game Theory); Musegaas, Marieke (Dept. of Advanced Computing Sciences, RS: FSE DACS Mathematics Centre Maastricht, RS: FSE DACS)
    Abstract: Problem definition: Streaming platforms such as Spotify are popular media services where content creators may offer their content. Because these platforms operate in a highly competitive market, content creators may leave the platform and join elsewhere. This paper studies conditions under which content creators have no incentives to leave the platform and thus stability can be preserved. Methodology/results: We introduce a stylized model for streaming platform situations and associate these situations with a cooperative game. We focus on the (non)emptiness of the core to analyze the stability of the streaming platforms. It turns out that both stable and unstable streaming platforms exist. We show that for streaming platforms operating in a market where users have completely opposite streaming behavior, stability cannot always be preserved. However, in markets where users are more similar in their streaming behavior, stability can be preserved. We further analyze the stability of streaming platforms by means of numerical experiments. Our results indicate that stability of streaming platforms generally is a delicate matter. Managerial implications: Streaming platforms are more likely to be stable in markets where users are similar in their streaming behavior. To avoid that content creators leave the platform, it is therefore recommended to focus on particular market segments where these similarities occur.
    JEL: C71
    Date: 2023–01–26
  11. By: Di Bartolomeo Giovanni; Dufwenberg Martin; Papa Stefano; Passarelli Francesco
    Abstract: Messages may trigger moral incentives to honor promises or agreements in a game with pre-play bilateral communication. We hypothesize that individuals’ inclination to keep a promise is highest if the counterpart requited the promise. We interpret this as an inclination to honor agreements. We report supporting results from an experiment.
    Date: 2022–10
  12. By: Igor V. Evstigneev (University of Manchester - Economics, School of Social Sciences); Thorsten Hens (University of Zurich - Department of Banking and Finance; Norwegian School of Economics and Business Administration (NHH); Swiss Finance Institute); Mohammad Javad Vanaei (University of Manchester)
    Abstract: Evolutionary Finance (EF) explores financial markets as evolving biological systems. Investors pursuing diverse investment strategies compete for the market capital. Some "survive" and some "become extinct". A central goal is to identify evolutionary stable (in one sense or another) investment strategies. The problem is analyzed in a framework combining stochastic dynamics and evolutionary game theory. Most of the models currently considered in EF assume that asset payoffs are exogenous and depend only on the underlying stochastic process of states of the world. The present work develops a model where the payoffs are endogenous: they depend on the share of total market wealth invested in the asset.
    Date: 2022–12
  13. By: David Spector (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - 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, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - 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: Many collusive agreements involve the exchange of self-reported sales data between competitors, which use them to monitor compliance with a target market share allocation. Such communication may facilitate collusion even if it is unverifiable cheap talk and the underlying information becomes publicly available with a delay. The exchange of sales information may allow firms to implement incentive-compatible market share reallocation mechanisms after unexpected swings, limiting the recourse to price wars. Such communication may allow firms to earn profits that could not be earned in any collusive, symmetric pure-strategy equilibrium without communication.
    Date: 2022–03
  14. By: Julien Jacob (BETA - Bureau d'Économie Théorique et Appliquée - AgroParisTech - UNISTRA - Université de Strasbourg - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Eve-Angéline Lambert (BETA - Bureau d'Économie Théorique et Appliquée - AgroParisTech - UNISTRA - Université de Strasbourg - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Mathieu Lefebvre (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique); Sarah van Driessche (BETA - Bureau d'Économie Théorique et Appliquée - AgroParisTech - UNISTRA - Université de Strasbourg - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)
    Abstract: We experimentally investigate the impact of information disclosure on managing common harms that are caused jointly by a group of liable agents. Subjects interact in a public bad setting and must choose ex ante how much to contribute in order to reduce the probability of causing a common damage. If a damage occurs, subjects bear a part of the loss according to the liability-sharing rule in force. We consider two existing rules: a per capita rule and a proportional rule. Our aim is to analyze the relative impact of information disclosure under each rule. We show that information disclosure increases contributions only under a per capita rule. This result challenges the classical results regarding the positive effects of information disclosure, since we show that this impact may depend upon the legal context. We also show that while a proportional rule leads to higher contributions than a per capita one, the positive effect of disclosure on a per capita rule makes it as efficient as a proportional rule without information disclosure.
    Keywords: Information disclosure, Common harms, Environmental Regulation, Liability Sharing Rules, Public Bads, Multiple Tortfeasors
    Date: 2023
  15. By: Raphaela Hennigs
    Abstract: This paper studies the tax authority’s problem of how to estimate a tax payer’s income in a tax compliance game. The tax authority’s choice of how to estimate income is modelled using the Bayesian persuasion framework and assuming that income can be estimated arbitrarily precisely. I show that the tax authority can use income estimates as a commitment device: ex-post, the tax authority has an incentive to audit a tax payer if his income is estimated to be high. This allows the tax authority to increase tax compliance by strategically overestimating low income. If the probability with which low income is falsely estimated to be high is strictly positive, the tax authority audits a low income tax payer with a strictly positive probability. Anticipating to be audited with a sufficiently high probability, the tax payer prefers to report low and high income to avoid being audited and fined.
    Keywords: tax audits, tax compliance, information design, Bayesian persuasion
    JEL: D82 D83 H26
    Date: 2022–11
  16. By: Luca Sandrini (Research Centre of Quantitative Social and Management Sciences, Budapest University of Technology and Economics)
    Abstract: This article shows that the usual result of full adoption of a superior technology induced by pure royalty licensing may not hold when firms have different production technologies. By modeling a licensing game with an external innovator offering per-unit royalty contracts to downstream firms, this article shows that full adoption of the innovation occurs only if i) the new technology is sufficiently more efficient than the best one available in the market or ii) if the firms have similar efficiency levels. Moreover, I disentangle two distinct forces that influence the innovator's choice: a price effect (PE) and a market share effect (MSE). The former highlight the asymmetry in willingness to pay for the new technology. The inefficient firms, which benefit the most from the cost-reducing innovation, are willing to pay a higher price than their efficient rivals to become licensees. The latter illustrates the innovator's aim to maximize the volume of royalties collected by licensing to many firms. When PE dominates MSE, the patent holder sets a higher royalty rate and attracts fewer, less efficient firms. Otherwise, if MSE dominates, the patent holder lowers the royalty rate and attracts more firms to reach as many consumers as possible. From a policy perspective, I show that royalty licensing improves consumer surplus and that the positive effect increases with the number of licensees.
    Keywords: Innovation; Licensing; Royalties; Price Effect; Market Share Effect
    JEL: L13 L24 O31
    Date: 2023–01
  17. By: Ayca Kaya (University of Miami); Santanu Roy (Southern Methodist University)
    Abstract: We analyze the effect of transparency of past trading volumes in markets where an informed long-lived seller can repeatedly trade with short-lived uninformed buyers. Transparency allows buyers to observe previously sold quantities. In markets with intra-period monopsony (single buyer each period), transparency reduces welfare if the ex-ante expected quality is low, but improves welfare if the expected quality is high. The effect is reversed in markets with intra-period competition (multiple buyers each period). This discrepancy in the efficiency implications of transparency is explained by how buyer competition affects the seller's ability to capture rents, which, in turn, influences market screening.
    Keywords: Repeated sales, adverse selection, transparency, competition, market efficiency
    JEL: D82 C73 D61
    Date: 2023–01
  18. By: Hui Chen; Winston Wei Dou; Hongye Guo; Yan Ji
    Abstract: Firms tend to compete more aggressively in financial distress; the intensified competition in turn reduces profit margins, pushing themselves further into distress and adversely affecting other firms. To study such feedback and contagion effects, we incorporate strategic competition into a dynamic model with long-term defaultable debt, which generates various peer interactions like predation and self-defense. The feedback effect imposes an additional source of financial distress costs incurred for raising leverage, which helps explain the negative profitability-leverage relation across industries. Owing to the contagion effect, in a decentralized equilibrium, leverage is excessively high from an industry perspective, compromising industry's financial stability.
    JEL: C73 D43 G12 L13 O33
    Date: 2023–01
  19. By: Haris Aziz; Alexander Lam; Bo Li; Fahimeh Ramezani; Toby Walsh
    Abstract: We consider the obnoxious facility location problem (in which agents prefer the facility location to be far from them) and propose a hierarchy of distance-based proportional fairness concepts for the problem. These fairness axioms ensure that groups of agents at the same location are guaranteed to be a distance from the facility proportional to their group size. We consider deterministic and randomized mechanisms, and compute tight bounds on the price of proportional fairness. In the deterministic setting, not only are our proportional fairness axioms incompatible with strategyproofness, the Nash equilibria may not guarantee welfare within a constant factor of the optimal welfare. On the other hand, in the randomized setting, we identify proportionally fair and strategyproof mechanisms that give an expected welfare within a constant factor of the optimal welfare.
    Date: 2023–01
  20. By: Jordan Norris; Charles Johnson; Ilya Spitkovsky (Division of Social Science)
    Abstract: A core purpose of economic modeling is to conduct comparative static analyzes. Often one is interested in its qualitative features, such as if the e ect of a shock is positive or above one. Yet, except in highly-stylized models, the theoretically implied relationships are intractable, and empirically demanding, requiring complete identication of the model. We derive new bounds on comparative statics that are more tractable and feasible under partial identi cation. We require only that the Jacobian is diagonally dominant | intuitively, there is limited feedback in the model. We demonstrate application in two canonical models: a network game and a model of oligopoly competition. JEL Codes: C3, D85
    Date: 2023–01
  21. By: Ivan Soraperra; Joël van der Weele; Marie Claire Villeval (GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - ENS Lyon - École normale supérieure - Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - Université de Lyon - CNRS - Centre National de la Recherche Scientifique); Shaul Shalvi
    Abstract: We experimentally study the social transmission of \inconvenient" information about the externalities generated by one's own decision. In the laboratory, we pair uninformed decision makers with informed senders. Compared to a setting where subjects can choose their information directly, we find that social interactions increase selfi sh decisions. On the supply side, senders suppress almost 30 percent of \inconvenient" information, driven by their own preferences for information and their beliefs about the decision maker's preferences. On the demand side, about one-third of decision makers avoids senders who transmit inconvenient information (\shooting the messenger"), which leads to assortative matching between information-suppressing senders and information-avoiding decision makers. Having more control over information generates opposing effects on behavior: sel sh decision makers remain ignorant more often and donate less, while altruistic decision makers seek out informative senders and give more. We discuss applications to information sharing in social networks and to organizational design.
    Keywords: Social interactions, Information avoidance, Assortative matching, Ethical behavior, experiment
    Date: 2023
  22. By: Rosa van den Ende; Dylan Laplace Mermoud
    Abstract: There is an increasing need to hold players responsible for negative or positive impact that take place elsewhere in a value chain or a network. For example, countries or companies are held more and more responsible for their indirect carbon emissions. We introduce a responsibility value that allocates the total impact of the value chain among the players, taking into account their direct impact and their indirect impact through the underlying graph. Moreover, we show that the responsibility value satisfies a set of natural yet important properties.
    Date: 2023–01

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