nep-gth New Economics Papers
on Game Theory
Issue of 2022‒05‒09
twenty papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Impacts of Public Information on Flexible Information Acquisition By Takashi Ui
  2. Inducing Social Optimality in Games via Adaptive Incentive Design By Chinmay Maheshwari; Kshitij Kulkarni; Manxi Wu; Shankar Sastry
  3. The Irreversible Pollution Game By Raouf Bouccekine; Weihua Ruan; Benteng Zou
  4. Best-response dynamics in combinatorial auctions with item bidding By Dütting, Paul; Kesselheim, Thomas
  5. Collusion Between Non-differentiated Two-Sided Platforms By Martin Peitz; Lily Samkharadze
  6. How Does Group-Decision Making Affect Subsequent Individual Behavior? By Philipp Dörrenberg; Christoph Feldhaus
  7. Signaling, Screening, and Core Stability By Yusuke Kamishiro; Rajiv Vohra; Roberto Serrano
  8. Axioms for the optimal stable rules and fair-division rules in a multiple-partners job market By Gerard Domènech Gironell; Marina Núñez Oliva
  9. A characterization of the family of Weighted priority values By Sylvain Béal; Sylvain Ferrières; Adriana Navarro-Ramos; Philippe Solal
  10. Optimal accuracy of unbiased Tullock contests with two heterogeneous players By Sahm, Marco
  11. Hierarchical Bayesian Persuasion: Importance of Vice Presidents By Majid Mahzoon
  12. Stability of heteroclinic cycles: a new approach By Telmo Peixe; Alexandre A. Rodrigues
  13. On Maximum Weighted Nash Welfare for Binary Valuations By Warut Suksompong; Nicholas Teh
  14. The Impact of Product Differentiation on the Channel Structure in a Manufacturer-Driven Supply Chain By Angelika Endres-Fröhlich
  15. Data Collection by an Informed Seller By Smolin, Alex; Ichihashi, Shota
  16. Budget-Constrained Auctions with Unassured Priors By Zhaohua Chen; Xiaotie Deng; Jicheng Li; Chang Wang; Mingwei Yang
  17. Approximate Group Fairness for Clustering By Bo Li; Lijun Li; Ankang Sun; Chenhao Wang; Yingfan Wang
  18. Effective risk aversion in thin risk-sharing markets By Anthropelos, Michail; Kardaras, Constantinos; Vichos, Georgios
  19. The Global Minimum Tax Raises More Revenues than You Think, or Much Less By Eckhard Janeba; Guttorm Schjelderup
  20. Agglomeration bonus and endogenous group formation By François Bareille; Matteo Zavalloni; Davide Viaggi

  1. By: Takashi Ui
    Abstract: Interacting agents receive public information at no cost and flexibly acquire private information at a cost proportional to entropy reduction. When a policymaker provides more public information, agents acquire less private information, thus lowering information costs. Does more public information raise or reduce uncertainty faced by agents? Is it beneficial or detrimental to welfare? To address these questions, we examine the impacts of public information on flexible information acquisition in a linear-quadratic-Gaussian game with arbitrary quadratic material welfare. More public information raises uncertainty if and only if the game exhibits strategic complementarity, which can be harmful to welfare. However, when agents acquire a large amount of information, more provision of public information increases welfare through a substantial reduction in the cost of information. We give a necessary and sufficient condition for welfare to increase with public information and identify optimal public information disclosure, which is either full or partial disclosure depending upon the welfare function and the slope of the best response.
    Date: 2022–04
  2. By: Chinmay Maheshwari; Kshitij Kulkarni; Manxi Wu; Shankar Sastry
    Abstract: How can a social planner adaptively incentivize selfish agents who are learning in a strategic environment to induce a socially optimal outcome in the long run? We propose a two-timescale learning dynamics to answer this question in both atomic and non-atomic games. In our learning dynamics, players adopt a class of learning rules to update their strategies at a faster timescale, while a social planner updates the incentive mechanism at a slower timescale. In particular, the update of the incentive mechanism is based on each player's externality, which is evaluated as the difference between the player's marginal cost and the society's marginal cost in each time step. We show that any fixed point of our learning dynamics corresponds to the optimal incentive mechanism such that the corresponding Nash equilibrium also achieves social optimality. We also provide sufficient conditions for the learning dynamics to converge to a fixed point so that the adaptive incentive mechanism eventually induces a socially optimal outcome. Finally, we demonstrate that the sufficient conditions for convergence are satisfied in a variety of games, including (i) atomic networked quadratic aggregative games, (ii) atomic Cournot competition, and (iii) non-atomic network routing games.
    Date: 2022–04
  3. By: Raouf Bouccekine (Rennes School of Business); Weihua Ruan (Purdue University Northwest); Benteng Zou (DEM, Université du Luxembourg)
    Abstract: We study a 2-country differential game with irreversible pollution. Irreversibil- ity is of a hard type: above a certain threshold level of pollution, the self-cleaning capacity of Nature drops to zero. Accordingly, the game includes a non-concave fea- ture, and we characterize both the cooperative and non-cooperative versions with this general non-LQ property. We deliver full analytical results for the existence of Markov Perfect Equilibria. We first demonstrate that when pollution costs are equal across players (symmetry), irreversible pollution regimes are more frequently reached than under cooperation. Second, we study the implications of asymmetry in the pollution cost. We find far nontrivial results on the reachability of the ir- reversible regime. However, we unambiguously prove that, for the same total cost of pollution, provided the irreversible regime is reached in both the symmetric and asymmetric cases, long-term pollution is larger in the symmetric case, reflecting more intensive free-riding under symmetry.
    Keywords: Differential games, Irreversible pollution, Non-concave pollution decay, Asymmetric pollution cost, Markov Perfect Equilibria.
    JEL: C72 C61 Q53
    Date: 2022
  4. By: Dütting, Paul; Kesselheim, Thomas
    Abstract: In a combinatorial auction with item bidding, agents participate in multiple single-item second-price auctions at once. As some items might be substitutes, agents need to strategize in order to maximize their utilities. A number of results indicate that high social welfare can be achieved this way, giving bounds on the welfare at equilibrium. Recently, however, criticism has been raised that equilibria of this game are hard to compute and therefore unlikely to be attained. In this paper, we take a different perspective by studying simple best-response dynamics. Often these dynamics may take exponentially long before they converge or they may not converge at all. However, as we show, convergence is not even necessary for good welfare guarantees. Given that agents’ bid updates are aggressive enough but not too aggressive, the game will reach and remain in states of high welfare after each agent has updated his bid at least once.
    Keywords: algorithmic game theory; combinatorial auctions; item bidding; best-response dynamics
    JEL: J1
    Date: 2020–10–01
  5. By: Martin Peitz; Lily Samkharadze
    Abstract: Platform competition can be intense when offering non-differentiated services. However, competition is somewhat relaxed if platforms cannot set negative prices. If platforms collude they may be able to implement the outcome that maximizes industry profits. In an infinitely repeated game with perfect monitoring, this is feasible if the discount factor is sufficiently large. When this is not possible, under some condition, a collusive outcome with one-sided rent extraction along the equilibrium path can be sustained that leads to higher profits than the non-cooperative outcome.
    Keywords: Two-sided markets, tacit collusion, cartelization, price structure, platform competition
    JEL: L41 L13 D43
    Date: 2022–01
  6. By: Philipp Dörrenberg; Christoph Feldhaus
    Abstract: Do groups and individuals behave differently in dictator games with varying deservingness of the recipient? Does the involvement in group-decision making affect the decisions of group members in subsequent individual decisions? We address these questions using a controlled dictator-game experiment and find the following main results. First, groups and individuals are not different w.r.t. their dictator-game decisions and recipient deservingness does not have a different effect on groups than on individuals. Second, participants who were previously part of a group decision process are more generous in a subsequent individual-level decision than participants who previously made individual decisions. We exploit the chat protocols of group discussions to shed light on the mechanism behind this result. Consistent with moral balancing, we show that the effect of group-decision making on subsequent individual decisions is driven by subjects who intent to make good for the initial group decision.
    Keywords: group-decision making, dictator game, recipient deservingness, moral balancing
    JEL: C91 C92 D91
    Date: 2022
  7. By: Yusuke Kamishiro; Rajiv Vohra; Roberto Serrano
    Abstract: This paper provides a noncooperative approach to core stability in an economy with incomplete information. The analysis covers general exchange economies, although our tightest results hold when effective coalitions consist of at most two players, as in matching. We study the perfect Bayesian equilibria of an extensive form mechanism that extends the one used by Serrano and Vohra (1997) to implement the core of a complete information economy. This leads to a version of the core that we refer to as the sequential core, which allows for information to be transmitted among the agents during the process of coalition formation. Such information flows include proposals that can be viewed as signaling devices and/or screening contracts. The same result is obtained in a model of infinite-horizon coalitional bargaining for stationary PBE. Equilibrium refinements are then used to provide justifications for the coarse core and the fine core.
    Date: 2022
  8. By: Gerard Domènech Gironell (Universitat de Barcelona); Marina Núñez Oliva (Universitat de Barcelona)
    Abstract: In the multiple-partners job market, introduced in (Sotomayor, 1992), each firm can hire several workers and each worker can be hired by several firms, up to a given quota. We show that, in contrast to what happens in the simple assignment game, in this extension, the firms-optimal stable rules are neither valuation monotonic nor pairwise monotonic. However, we show that the firms-optimal stable rules satisfy a weaker property, what we call firmcovariance, and that this property characterizes these rules among all stable rules. This property allows us to shed some light on how firms can (and cannot) manipulate the firms-optimal stable rules. In particular, we show that firms cannot manipulate them by constantly over-reporting their valuations. Analogous results hold when focusing on the workers. Finally, we extend to the multiple-partners market a known characterization of the fair-division rules on the domain of simple assignment games.
    Keywords: Assignment game, stable rules, fair division.
    JEL: C78 D78
    Date: 2022
  9. By: Sylvain Béal (CRESE EA3190, Univ. Bourgogne Franche-Comté, F-25000 Besançon, France); Sylvain Ferrières (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne, France); Adriana Navarro-Ramos (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 introduce a new family of values for TU-games with a priority structure. This family both contains the Priority value recently introduced by Béal et al. (2021) and the Weighted Shapley values (Kalai and Samet, 1987). Each value of this family is called a Weighted priority value and is constructed as follows. A strictly positive weight is associated with each agent and the agents are partially ordered according to a binary relation. An agent is a priority agent with respect to a coalition if it is maximal in this coalition with respect to the partial order. A Weighted priority value distributes the dividend of each coalition among the priority agents of this coalition in proportion to their weights. We provide an axiomatic characterization of the family of the Weighted Shapley values without the additivity axiom. To this end, we borrow the Priority agent out axiom from Béal et al. (2021), which is used to axiomatize the Priority value. We also reuse, in our domain, the principle of Super weak differential marginality introduced by Casajus (2018) to axiomatize the Positively weighted Shapley values (Shapley, 1953a). We add a new axiom of Independence of null agent position which indicates that the position of a null agent in the partial order does not affect the payoff of the other agents. Together with Efficiency, the above axioms characterize the Weighted Shapley values. Finally, we show that this axiomatic characterization holds on the subdomain where the partial order is structured by levels. This entails an alternative characterization of the Weighted Shapley values.
    Keywords: Differential marginality, Priority value, Shapley value, Superweak differiential marginality, Weighted Shapley value
    JEL: C71
    Date: 2022–05
  10. By: Sahm, Marco
    Abstract: I characterize the optimal accuracy level r of an unbiased Tullock contest between two players with heterogeneous prize valuations. The designer maximizes the winning probability of the strong player or the winner's expected valuation by choosing a contest with an all-pay auction equilibrium (r ≥ 2). By contrast, if she aims at maximizing the expected aggregate effort or the winner's expected effort, she will choose a contest with a pure-strategy equilibrium, and the optimal accuracy level r
    Keywords: Tullock Contest,Heterogeneous Valuations,Accuracy,Discrimination,Optimal Design,All-Pay Auction
    JEL: C72 D72
    Date: 2022
  11. By: Majid Mahzoon
    Abstract: We study strategic information transmission in a hierarchical setting where information gets transmitted through a chain of agents up to a decision maker whose action is of importance to every agent. This situation could arise whenever an agent can communicate to the decision maker only through a chain of intermediaries, for example, an entry-level worker and the CEO in a firm, or an official in the bottom of the chain of command and the president in a government. Each agent can decide to conceal part or all the information she receives. Proving we can focus on simple equilibria, where the only player who conceals information is the first one, we provide a tractable recursive characterization of the equilibrium outcome, and show that it could be inefficient. Interestingly, in the binary-action case, regardless of the number of intermediaries, there are a few pivotal ones who determine the amount of information communicated to the decision maker. In this case, our results underscore the importance of choosing a pivotal vice president for maximizing the payoff of the CEO or president.
    Date: 2022–04
  12. By: Telmo Peixe; Alexandre A. Rodrigues
    Abstract: This paper analyses the stability of cycles within a heteroclinic network lying in a three-dimensional manifold formed by six cycles, for a one-parameter model developed in the context of game theory. We show the asymptotic stability of the network for a range of parameter values compatible with the existence of an interior equilibrium and we describe an asymptotic technique to decide which cycle (within the network) is visible in numerics. The technique consists of reducing the relevant dynamics to a suitable one-dimensional map, the so called \emph{projective map}. Stability of the fixed points of the projective map determines the stability of the associated cycles. The description of this new asymptotic approach is applicable to more general types of networks and is potentially useful in computational dynamics.
    Date: 2022–04
  13. By: Warut Suksompong; Nicholas Teh
    Abstract: We consider the problem of fairly allocating indivisible goods to agents with weights representing their entitlements. A natural rule in this setting is the maximum weighted Nash welfare (MWNW) rule, which selects an allocation maximizing the weighted product of the agents' utilities. We show that when agents have binary valuations, a specific version of MWNW is resource- and population-monotone, satisfies group-strategyproofness, and can be implemented in polynomial time.
    Date: 2022–04
  14. By: Angelika Endres-Fröhlich (Paderborn University)
    Abstract: We study the impact of product differentiation on different distribution systems in a supply chain. Our market is characterized by an asymmetric supply chain with two retailers and three manufacturers that each produce one differentiated good. We determine that a non-exclusive distribution system is a Nash equilibrium for all degrees of product differentiation between the three goods. Furthermore, we assess the welfare implications of various distribution systems. We identify that the non-exclusive equilibrium channel structure provides the highest social welfare and highest consumer surplus for all degrees of product differentiation. Aside from that, we find a strong incentive for the manufacturers to form an exclusive selling cartel for close substitutes, which would cause a Pareto improvement for all firms but harm overall welfare.
    Keywords: product differentiation; endogenous markets; supply chains
    JEL: D21 D47 L22
    Date: 2022–04
  15. By: Smolin, Alex; Ichihashi, Shota
    Abstract: A seller faces a consumer with an uncertain value for the product. The seller has imperfect private information about the value and requests additional data to set the price. The consumer can decline any request. The consumer’s willingness to provide data depends on his belief about the seller’s type which in turn depends on the request. We show that the type uncertainty limits the scope of data collection: All equilibrium payoffs are spanned by fully pooling equilibria in which the seller collects the same data regardless of the type. The seller’s private information lowers efficiency and profits, but benefits the consumer by fueling his skepticism and preventing excessive data collection. Having less private information may enable the seller to collect more data directly from the consumer and may lower the overall consumer welfare.
    Keywords: consumer privacy; data collection; information design; mechanism design; price discrimination
    JEL: D42 D82 D83
    Date: 2022–04–19
  16. By: Zhaohua Chen; Xiaotie Deng; Jicheng Li; Chang Wang; Mingwei Yang
    Abstract: In today's online advertising markets, it is common for an advertiser to set a long-period budget. Correspondingly, advertising platforms adopt budget control methods to ensure that any advertiser's payment is within her budget. Most budget control methods rely on value distributions of advertisers. However, due to the complex environment advertisers stand in and privacy issues, the platform hardly learns their true priors. Therefore, it is essential to understand how budget control auction mechanisms perform under unassured priors. This paper gives a two-fold answer. First, we propose a bid-discount method barely studied in the literature. We show that such a method exhibits desirable properties in revenue-maximizing and computation when fitting into first-price auction. Second, we compare this mechanism with another four in the prior manipulation model, where an advertiser can arbitrarily report a value distribution to the platform. These four mechanisms include the optimal mechanism satisfying budget-constrained IC, first-price/second-price mechanisms with the widely-studied pacing method, and an application of bid-discount in second-price mechanism. We consider three settings under the model, depending on whether the reported priors are fixed and advertisers are symmetric or not. We show that under all three cases, the bid-discount first-price auction we introduce dominates the other four mechanisms concerning the platform's revenue. For the advertisers' side, we show a surprising strategic-equivalence result between this mechanism and the optimal auction. Extensive revenue dominance and strategic relationships among these mechanisms are also revealed. Based on these findings, we provide a thorough understanding of prior dependency in repeated auctions with budgets. The bid-discount first-price auction itself may also be of further independent research interest.
    Date: 2022–03
  17. By: Bo Li; Lijun Li; Ankang Sun; Chenhao Wang; Yingfan Wang
    Abstract: We incorporate group fairness into the algorithmic centroid clustering problem, where $k$ centers are to be located to serve $n$ agents distributed in a metric space. We refine the notion of proportional fairness proposed in [Chen et al., ICML 2019] as {\em core fairness}, and $k$-clustering is in the core if no coalition containing at least $n/k$ agents can strictly decrease their total distance by deviating to a new center together. Our solution concept is motivated by the situation where agents are able to coordinate and utilities are transferable. A string of existence, hardness and approximability results is provided. Particularly, we propose two dimensions to relax core requirements: one is on the degree of distance improvement, and the other is on the size of deviating coalition. For both relaxations and their combination, we study the extent to which relaxed core fairness can be satisfied in metric spaces including line, tree and general metric space, and design approximation algorithms accordingly.
    Date: 2022–03
  18. By: Anthropelos, Michail; Kardaras, Constantinos; Vichos, Georgios
    Abstract: We consider thin incomplete financial markets, where traders with heterogeneous preferences and risk exposures have motive to behave strategically regarding the demand schedules they submit, thereby impacting prices and allocations. We argue that traders relatively more exposed to the market portfolio tend to behave in a more risk tolerant manner. Noncompetitive equilibrium prices and allocations result as an outcome of a game among traders. General sufficient conditions for existence and uniqueness of such equilibrium are provided, with extensive analysis of two-trader transactions. Even though strategic behavior causes inefficient social allocations, traders with sufficiently high risk tolerance and/or high initial exposure to tradable securities obtain more utility gain in the noncompetitive equilibrium, when compared to the competitive one.
    Keywords: Nash equilibrium; effective risk aversion; noncompetitive risk sharing; price impact; thin markets
    JEL: F3 G3
    Date: 2020–10–01
  19. By: Eckhard Janeba; Guttorm Schjelderup
    Abstract: The OECD’s proposal for a global minimum tax (GMT) of 15% aims for a reversal of a decades-long race to the bottom of corporate tax rates driven by competition over real investments and profit shifting to low-tax jurisdictions. We study the revenue effects of the GMT by focusing on the induced strategic tax setting effects. The direct effect of the GMT is a reduction in profit shifting, which has a positive effect on revenues in high-tax countries as their tax base grows, and makes higher taxes attractive. A secondary effect, however, is that the value of attracting real foreign investments increases, which intensifies tax competition. We argue that the revenue effects of the GMT depend on the instruments governments use to attract firms. With endogenous corporate tax rates, revenues in non-havens increase if initially tax competition among non-havens is fierce. By contrast, when governments compete via lump sum subsidies, the revenue gains from less profit shifting are exactly offset by higher subsidies.
    Keywords: global minimum tax, tax competition, OECD BEPS, Pillar II
    JEL: F23 F55 H25 H73
    Date: 2022
  20. By: François Bareille (UMR PSAE - Paris-Saclay Applied Economics - AgroParisTech - Université Paris-Saclay - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Matteo Zavalloni (Department of Agricultural and Food Sciences (DISTAL) - Università di Bologna); Davide Viaggi (Department of Agricultural and Food Sciences (DISTAL) - Università di Bologna)
    Abstract: Agglomeration bonus schemes are envisioned to incentivize the connectivity of habitat conservation across landowners. Assuming full cooperation among landowners at the landscape scale, the bulk of the literature theoretically finds that agglomeration bonus schemes are more cost effective in achieving biodiversity conservation than spatially homogenous payments. However, it may be rational for landowners not to cooperate all together but, rather, to cooperate within smaller groups. Here, we analyze the cost effectiveness of agglomeration bonus schemes when such partial cooperation is allowed, that is, when cooperation is endogenously chosen. We introduce a spatially explicit ecological-economic model within a coalition formation game to assess how landowners form stable coalition structures and how this affects biodiversity conservation under a wide range of (i) degrees of spatial cost autocorrelation, (ii) bonuses and flat-rate payments, (iii) species dispersal rates, and (iv) coordination costs. We find that agglomeration bonus schemes are more cost effective than homogenous payments only for low public expenditures. This condition is not identified if full cooperation is assumed. We find, however, that full cooperation never emerges and hence that such an assumption leads to an overestimation of the cost effectiveness of agglomeration bonus schemes. Moreover, we find that the cost effectiveness of agglomeration bonus schemes increases when the spatial cost autocorrelation and species dispersal rate decrease. Finally, coordination costs do not affect the cost effectiveness of the agglomeration bonus scheme but they have implications for its design because of their impact on coalition formation.
    Abstract: Les systèmes de primes d'agglomération sont conçus pour encourager la connectivité de la conservation des habitats entre les propriétaires fonciers. Dans l'hypothèse d'une coopération totale entre les propriétaires fonciers à l'échelle du paysage, l'essentiel de la littérature montre théoriquement que les systèmes de primes d'agglomération sont plus rentables pour la conservation de la biodiversité que les paiements spatialement homogènes. Cependant, il peut être rationnel pour les propriétaires fonciers de ne pas coopérer tous ensemble, mais plutôt de coopérer au sein de groupes plus petits. Nous analysons ici la rentabilité des systèmes de primes d'agglomération lorsqu'une telle coopération partielle est autorisée, c'est-à-dire lorsque la coopération est choisie de manière endogène. Nous introduisons un modèle éco-économique spatialement explicite dans un jeu de formation de coalition pour évaluer comment les propriétaires terriens forment des structures de coalition stables et comment cela affecte la conservation de la biodiversité sous une large gamme de (i) degrés d'autocorrélation spatiale des coûts, (ii) primes et paiements forfaitaires, (iii) taux de dispersion des espèces, et (iv) coûts de coordination. Nous constatons que les systèmes de primes d'agglomération sont plus rentables que les paiements homogènes uniquement lorsque les dépenses publiques sont faibles. Cette condition n'est pas identifiée si l'on suppose une coopération totale. Nous constatons cependant qu'une coopération totale n'apparaît jamais et qu'une telle hypothèse conduit à une surestimation de la rentabilité des systèmes de primes d'agglomération. En outre, nous constatons que la rentabilité des systèmes de primes d'agglomération augmente lorsque l'autocorrélation des coûts spatiaux et le taux de dispersion des espèces diminuent. Enfin, les coûts de coordination n'affectent pas le rapport coût-efficacité du système de primes d'agglomération, mais ils ont des implications pour sa conception en raison de leur impact sur la formation de coalitions.
    Keywords: Biodiversity conservation,Collective incentive,Environmental subsidies,Green club
    Date: 2022–02–09

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