nep-gth New Economics Papers
on Game Theory
Issue of 2024‒03‒04
twenty-two papers chosen by
Sylvain Béal, Université de Franche-Comté

  1. Equitable Solutions in Game Representations: An Extension of the Shapley Value By Pradeep Dubey
  2. Information-Constrained Coordination of Economic Behavior By Guy Aridor; Rava Azeredo da Silveira; Michael Woodford
  3. On Interim Rationalizable Monotonicity By Ritesh Jain; Michele Lombardi
  4. The Impact of the Menstrual Cycle on Bargaining Behavior By Lozano, Lina; Riedl, Arno; Rott, Christina
  5. Tournament Auctions By Luca Anderlini; GaOn Kim
  6. Rebate rules in reward-based crowdfunding: Introducing the bid-cap rule By Fabian Gerstmeier; Yigit Oezcelik; Michel Tolksdorf
  7. Sequential Creation of Surplus and the Shapley Value By Mikel Álvarez-Mozos; Inés Macho-Stadler; David Pérez-Castrillo
  8. Information Design with Costly State Verifi cation By Lily Ling Yang
  9. Cooperative games with diversity constraints By Sylvain Béal; Marc Deschamps; Mostapha Diss; Rodrigue Tido Takeng
  10. Optimal consumption and Investment under Relative Performance Criteria with Epstein-Zin Utility By Dianetti, Jodi; Riedel, Frank; Stanza, Lorenzo
  11. Putting eggs in one basket: insights from a correlation inequality By Pradeep Dubey; Siddhartha Sahi; Guanyang Wang
  12. Revisiting ‘Growth and Inequality in Public Good Provision’—Reproducing and Generalizing Through Inconvenient Online Experimentation By Roggenkamp, Hauke C.
  13. Commitment vs. noncommitment behaviors in natural resource conflicts: A case study of groundwater resources By Mabel Tidball; Julia de Frutos Cachorro; Guiomar Martín-Herrán
  14. The Economics of Information in a World of Disinformation: A Survey Part 2: Direct Communication By Joseph E. Stiglitz; Andrew Kosenko
  15. Private labels and platform competition By Saruta, Fuyuki
  16. Deliberately Ignoring Unfairness: Responses to Uncertain Inequality in the Ultimatum Game By Konstantin Offer; Dorothee Mischkowski; Zoe Rahwan; Christoph Engel
  17. Negative Emission Technologies and Climate Cooperation By Michela Boldrini; Valentina Bosetti; Salvatore Nunnari
  18. Contracting with a Learning Agent By Guru Guruganesh; Yoav Kolumbus; Jon Schneider; Inbal Talgam-Cohen; Emmanouil-Vasileios Vlatakis-Gkaragkounis; Joshua R. Wang; S. Matthew Weinberg
  19. Coordinating Resource Allocation during Product Transitions Using a Multifollower Bilevel Programming Model By Rahman Khorramfar; Osman Ozaltin; Reha Uzsoy; Karl Kempf
  20. Stay positive or go negative? Memory imperfections and messaging strategy By Li, Xiaolin; Singh Rao, Raghunath; Narasimhan, Om; Gao, Xing
  21. The Importance of Social Status in a Rent-Seeking Society By J. Atsu Amegashie
  22. Political Competition and Strategic Voting in Multi-Candidate Elections By Bernhardt, Dan; Krasa, Stefan; Squintani, Francesco

  1. By: Pradeep Dubey
    Abstract: We show that any cooperative game can be represented by an assignment of costly facilities to players, in which it is intuitively obvious how to allocate the total cost in an equitable manner. This equitable solution turns out to be the Shapley value of the game, and thus provides as an alternative justication of the value. Game representations also open the door for extending the Shapley value to situations where not all coalitions can form, provided those that can constitute a quasi-algebra; or, more generally, a hierarchy; or, still more generally, have full span.
    Date: 2024
  2. By: Guy Aridor; Rava Azeredo da Silveira; Michael Woodford
    Abstract: We analyze a coordination game with information-constrained players. The players' actions are based on a noisy compressed representation of the game's payoffs in a particular case, where the compressed representation is a latent state learned by a variational autoencoder (VAE). Our generalized VAE is optimized to trade off the average payoff obtained over a distribution of possible games against a measure of the congruence between the agent's internal model and the statistics of its environment. We apply our model to the coordination game in the experiment of Frydman and Nunnari (2023), and show that it offers an explanation for two salient features of the experimental evidence: both the relatively continuous variation in the players' action probabilities with changes in the game payoffs, and the dependence of the degree of stochasticity of players' choices on the range of game payoffs encountered on different trials. Our approach also provides an account of the way in which play should gradually adjust to a change in the distribution of game payoffs that are encountered, offering an explanation for the history-dependent play documented by Arifovic et al. (2013).
    JEL: C60 C73 C92 D89
    Date: 2024–02
  3. By: Ritesh Jain; Michele Lombardi
    Abstract: Interim Rationalizable Monotonicity, due to Bergemann and Morris (2008a) and Oury and Tercieux (2012), fully characterizes the class of social choice functions that are implementable in interim rationalizable strategies by a mechanism that has a pure strategy Bayes-Nash equilibrium
    JEL: C79 D82
    Date: 2022–05
  4. By: Lozano, Lina (New York University, Abu Dhabi); Riedl, Arno (Maastricht University); Rott, Christina (Vrije Universiteit Amsterdam)
    Abstract: We investigate experimentally how the menstrual cycle affects bargaining behavior and bargaining outcomes of women. Female participants negotiate in an unstructured bilateral bargaining game with asymmetric information about the allocation of a surplus ('pie size'). We find that the menstrual cycle affects bargaining behavior and that the effects depend on the information players have. Players who are informed about the pie size are less compromising during ovulation and receive higher payoffs conditional on reaching an agreement. Uninformed players achieve higher final payoffs during ovulation, which is mainly driven by higher agreement rates.
    Keywords: bargaining, asymmetric information, menstrual cycle, biological factors
    JEL: C78 C91 D87 J16
    Date: 2024–01
  5. By: Luca Anderlini (Department of Economics, Georgetown University); GaOn Kim (EIEF)
    Abstract: We examine “tournament” second-price auctions in which N bidders compete for the right to participate in a second stage and contend against bidder N +1. When the first N bidders are committed so that their bids cannot be changed in the second stage, the analysis yields some unexpected results. The first N bidders consistently bid above their values in equilibrium. When bidder N + 1 is sufficiently stronger than the first N, overbidding leads to an increase in expected revenue in comparison to the standard second-price auction when N is large.
    Keywords: Tournament Auctions, Overbidding, Revenue Equivalence
    JEL: C70 C72 C79
    Date: 2024–02–14
  6. By: Fabian Gerstmeier; Yigit Oezcelik; Michel Tolksdorf
    Abstract: We study the efficacy of rebates in reward-based crowdfunding, where a project is only realized when a funding goal is met, and only those who pledge at least a reservation price receive a reward. We propose and experimentally test two rebate rules against the all-or-nothing model. Firstly, we adapt the proportional rebate rule from threshold public good games to our rewardbased setting. Secondly, we develop the novel bid-cap rule. Here, pledges must only be paid up to a cap, which is determined ex-post such that the provision point is exactly met. Theoretically, the bid-cap rule induces weakly less variance in payments compared with the proportional rebate rule. In our experiment, both rebate rules induce higher pledges and increase the project realization rate in comparison to the all-or-nothing model. Further, we can confirm that the variance of payments is lower under the bid-cap rule compared with the proportional rebate rule
    Keywords: Crowdfunding, laboratory experiment, provision point mechanism, rebates
    JEL: C72 C92 H41
    Date: 2023–05
  7. By: Mikel Álvarez-Mozos; Inés Macho-Stadler; David Pérez-Castrillo
    Abstract: We introduce the family of games with intertemporal externalities, where two disjoint sets of players play sequentially. Coalitions formed by the present cohort generate worth today. Moreover, today’s partition of players exerts an externality on the future; the worth of a coalition formed by future players is influenced by this externality. We adapt the classic Shapley axioms and study their implications in our class of games. They do not suffice to single out a unique solution. We introduce two values using the interpretation of the Shapley value as the players’ expected contributions to coalitions: the one-coalition externality value and the naive value. We state a relationship between these values and the Shapley value of an associated game in characteristic function form. Our main results characterize the two values by adding one additional property to the classic Shapley axioms. A property of equal treatment of contributions leads to characterizing the one-coalition externality value. A property of equal treatment of externalities characterizes the naive value
    Keywords: shapley value, Externalities
    JEL: C71 D62
    Date: 2024–02
  8. By: Lily Ling Yang
    Abstract: We study a persuasion problem when the receiver has the ability to probabilistically verify the state at a cost. The sender wants to convince the receiver to accept a project but the receiver is only willing to accept the project when the quality is above a threshold. The optimal disclosure policy balances between influencing the receiver's decisions to accept and to verify the quality. The optimal disclosure is deterministic and involves at most three messages, each consisting of an action recommendation and a verification recommendation. In the optimal disclosure, the action recommendation has a cutoff structure while the verification recommendation has a negative assortative structure. Specifically, the optimal disclosure recommends acceptance when the quality is above a threshold. When the quality is below this threshold, rejection without verification is recommended. Above this threshold, verification is not recommended when the quality lies in the middle range of the interval. The optimal disclosure reveals more information compared to the case where verification is exogenous.
    Keywords: Bayesian persuasion, Information design, Costly information acquisition, Costly state veri cation, Product recommendation
    JEL: D82 D83
    Date: 2024–02
  9. By: Sylvain Béal (Université de Franche-Comté, CRESE, UR3190, F-25000 Besançon, France); Marc Deschamps (Université de Franche-Comté, CRESE, UR3190, F-25000 Besançon, France); Mostapha Diss (Université de Franche-Comté, CRESE, UR3190, F-25000 Besançon, France); Rodrigue Tido Takeng (Université de Caen, CREM, UMR6211, F-14000 Caen, France)
    Abstract: A cooperative game with diversity constraints is given by a cooperative game, a coalition structure which partitions the set of players into communities, and a vector of integers specifying, for each community, the minimal number of its members that a coalition must possess to be considered as diverse. We provide axioms for a value on the class of such co- operative games with diversity constraints. Some combinations of axioms characterize two values inspired by the Shapley value (Shapley, 1953) and the Owen value (Owen, 1977) for games with a coalition structure. More specifically, the Diversity Owen value is character- ized as the Owen value of the diversity-restricted game with a coalition structure, where the diversity-restricted game assigns a null worth to a coalition if it does not meet the diversity requirements or its original worth otherwise. Similarly, the Diversity Shapley value is char- acterized as the Shapley value of the diversity-restricted game (without coalition structure). Some of our axiomatic characterizations can be adapted to the class of simple games by replacing the Additivity axiom by the Transfer axiom (Dubey, 1975).
    Keywords: Cooperative game; diversity constraints, axiomatic characterization, Owen Value, Shapley value
    JEL: D71 D72
    Date: 2024–02
  10. By: Dianetti, Jodi (Center for Mathematical Economics, Bielefeld University); Riedel, Frank (Center for Mathematical Economics, Bielefeld University); Stanza, Lorenzo (Center for Mathematical Economics, Bielefeld University)
    Abstract: We consider the strategic interaction of traders in a continuous-time financial market with Epstein-Zin-type recursive intertemporal preferences and performance concerns. We derive explicitly an equilibrium for the finite player and the mean-field version of the game, based on a study of geometric backward stochastic differential equations of Bernoulli type that describe the best replies of traders. Our results show that Epstein-Zin preferences can lead to substantially different equilibrium behavior.
    Keywords: Mean field games, portfolio choice, recursive utility, stochastic differential utility, BSDEs
    Date: 2024–02–19
  11. By: Pradeep Dubey; Siddhartha Sahi; Guanyang Wang
    Abstract: We give examples of situations – stochastic production, military tactics, corporate merger – where it is beneficial to concentrate risk rather than to diversify it, i.e., to put all eggs in one basket. The examples admit a dual interpretation: as optimal strategies of a single player (the “principal†) or, alternatively, as dominant strategies in a non-cooperative game with multiple players (the “agents†). The key mathematical result can be formulated in terms of a convolution structure on the set of increasing functions on a Boolean lattice (the lattice of subsets of a finite set). This result generalizes the well-known Harris inequality from statistical physics and discrete mathematics; we give a simple self-contained proof of this result, and then prove a further generalization based on game-theoretic ideas.
    Date: 2024
  12. By: Roggenkamp, Hauke C. (Univerisity of St. Gallen)
    Abstract: I revisit the dynamic public goods game developed by Gächter et al. (2017) to study cooperation under dynamic interdependencies. Collecting data from both a convenient (students) and an inconvenient (general population) sample, I not only reproduce some of the authors' original observations but also test their novel game's generalizability. Appending a charitable dictator game, I find no correlations between behavior in the charitable context and the dynamic game. This applies to students and the general population sample alike. Because the study of inexperienced general population samples raises methodological challenges, such as fatigue and dropouts, this research approaches them. In doing so, I provide simple solutions to run reliable interactive experiments online. Furthermore, this article showcases the use of literate programming and version control which I argue are convenient tools to make pre-registrations more credible and flexible.
    Date: 2024–02–07
  13. By: Mabel Tidball (CEE-M - Centre d'Economie de l'Environnement - Montpellier - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - UM - Université de Montpellier); Julia de Frutos Cachorro (UB - Universitat de Barcelona); Guiomar Martín-Herrán (IMUVA - Instituto de Investigación en Matemáticas - UVa - Universidad de Valladolid [Valladolid])
    Abstract: Abstract: We examine the problem of natural resource exploitation when an exceptional extraction of a resource (groundwater) is needed that is devoted to a different use than its regular use. The study applies a two-stage Stackelberg game to examine the strategic behavior of players who compete for water, with the leader (public resource manager), with varying degrees of environmental and public health concerns; the manager of the new (nonregular) resource use, who only intervenes in the second stage of the game; and the follower, who is a regular (agricultural) resource user. We examine the crucial resource of groundwater, introducing two types of Stackelberg equilibria (open-loop and feedback) that can arise depending on agents' commitment behavior, comparing the extraction behaviors of the leader and agricultural user for the two equilibria and the effects on the final state of the resource and agents' profits. Unexpectedly, we demonstrate that situations can occur in which noncommitment strategies could be more favorable than commitment strategies in terms of the final aquifer stock and the regular user's profits.
    Date: 2023
  14. By: Joseph E. Stiglitz; Andrew Kosenko
    Abstract: The paper surveys the recent work on economics of information with endogenous information structures where individuals can directly communicate information with each other. We consider the theoretical work on cheap talk, Bayesian persuasion, and information design, and review the implications of information control and information abundance for mis and disinformation. The relationship between information and market power is particularly important when social media can amplify and maintain harmful fictions that lead to polarization and undermine not only markets, but democratic discourse. We review both the “rational” decision-making paradigm, as well as departures from it, such as cases where decision makers can choose what to know, can allocate their attention in different ways or have behavioral biases that influence their information processing. We note some important connections to legal and media studies and highlight key messages in nontechnical language.
    JEL: D82 D86 D9
    Date: 2024–01
  15. By: Saruta, Fuyuki
    Abstract: This study examines the degree and manner by which first-party selling by a platform affects the profits of a third-party seller and a competing platform. After developing a model in which a third-party seller distributes goods through two competing platforms, with only one platform able to have a private label, we analyze first-party selling effects in both monopoly and duopoly platform cases. Our findings demonstrate the following. In a monopoly case, a platform consistently reduces the seller fee when introducing a private label. In a duopoly case, the two platforms will jointly raise or lower fees upon private label introduction. Additionally, first-party selling can either positively or negatively affect the competing platform's profit. Results suggest that competition among platforms might upset the influence of first-party selling on commission fees. Consequently, platforms might opt for first-party selling as a strategy to weaken commission fee competition and retail competition.
    Keywords: First-party selling; Platform competition; Marketplaces; Agency contracts; Wholesale contracts
    JEL: D21 L13 L22
    Date: 2023–12–27
  16. By: Konstantin Offer (Max Planck Institute for Human Development, Center for Adaptive Rationality (ARC), Lentzeallee 94, 14195 Berlin, Germany); Dorothee Mischkowski (Max Planck Institute for Research on Collective Goods, Bonn and Leiden University, The Netherlands); Zoe Rahwan (Max Planck Institute for Human Development, Center for Adaptive Rationality (ARC), Lentzeallee 94, 14195 Berlin, Germany); Christoph Engel (Max Planck Institute for Research on Collective Goods)
    Abstract: Why do people punish experienced unfairness if it induces costs for both the punisher and punished person(s) without any direct material benefits for the punisher? Economic theories of fairness propose that punishers experience disutility from disadvantageous inequality and punish in order to establish equality in outcomes. We tested these theories in a modified Ultimatum Game (N = 1, 370) by examining whether people avoid the urge to reject unfair offers, and thereby punish the proposer, by deliberately blinding themselves to unfairness. We found that 53% of participants deliberately ignored whether they had received an unfair offer. Among these participants, only 6% of unfair offers were rejected. In contrast, participants who actively sought information rejected 39% of unfair offers. Averaging these rejection rates to 21%, no significant difference to the rejection rate by participants who were directly informed about unfairness was found––in line with economic theories of fairness. We interpret these findings as evidence for sorting behavior: People who want to punish experienced unfairness seek information about it, while those who are unwilling to punish deliberately ignore it.
    Date: 2024–02
  17. By: Michela Boldrini; Valentina Bosetti; Salvatore Nunnari
    Abstract: Negative Emissions Technologies (NETs) — a range of methods to remove carbon dioxide from the atmosphere— are a crucial innovation in meeting temperature targets set by international climate agreements. However, mechanisms which undo the adverse consequences of short-sighted actions (as NETs) can fuel substitution effects and crowd out virtuous behaviors (e.g., mitigation efforts). For this reason, the impact of NETs on environmental preservation is an open question among scientists and policy-makers. We model this problem through a novel restorable common-pool resource game and use a laboratory experiment to exogenously manipulate key features of NETs and assess their consequences. We show that crowding out only emerges when NETs are surely available and cheap. The availability of NETs does not allow experimental communities to either conserve the common resource for longer or accrue higher earnings and makes the earnings distribution more unequal.
    Keywords: climate crisis, environmental sustainability, carbon dioxide removal, common-pool resource, free-rider problem, laboratory experiment
    JEL: C92 H41 Q55
    Date: 2024
  18. By: Guru Guruganesh; Yoav Kolumbus; Jon Schneider; Inbal Talgam-Cohen; Emmanouil-Vasileios Vlatakis-Gkaragkounis; Joshua R. Wang; S. Matthew Weinberg
    Abstract: Many real-life contractual relations differ completely from the clean, static model at the heart of principal-agent theory. Typically, they involve repeated strategic interactions of the principal and agent, taking place under uncertainty and over time. While appealing in theory, players seldom use complex dynamic strategies in practice, often preferring to circumvent complexity and approach uncertainty through learning. We initiate the study of repeated contracts with a learning agent, focusing on agents who achieve no-regret outcomes. Optimizing against a no-regret agent is a known open problem in general games; we achieve an optimal solution to this problem for a canonical contract setting, in which the agent's choice among multiple actions leads to success/failure. The solution has a surprisingly simple structure: for some $\alpha > 0$, initially offer the agent a linear contract with scalar $\alpha$, then switch to offering a linear contract with scalar $0$. This switch causes the agent to ``free-fall'' through their action space and during this time provides the principal with non-zero reward at zero cost. Despite apparent exploitation of the agent, this dynamic contract can leave \emph{both} players better off compared to the best static contract. Our results generalize beyond success/failure, to arbitrary non-linear contracts which the principal rescales dynamically. Finally, we quantify the dependence of our results on knowledge of the time horizon, and are the first to address this consideration in the study of strategizing against learning agents.
    Date: 2024–01
  19. By: Rahman Khorramfar; Osman Ozaltin; Reha Uzsoy; Karl Kempf
    Abstract: We study the management of product transitions in a semiconductor manufacturing firm that requires the coordination of resource allocation decisions by multiple, autonomous Product Divisions using a multi-follower bilevel model to capture the hierarchical and decentralized nature of this decision process. Corporate management, acting as the leader, seeks to maximize the firm's total profit over a finite horizon. The followers consist of multiple Product Divisions that must share manufacturing and engineering resources to develop, produce and sell products in the market. Each Product Division needs engineering capacity to develop new products, and factory capacity to produce products for sale while also producing the prototypes and samples needed for the product development process. We model this interdependency between Product Divisions as a generalized Nash equilibrium problem at the lower level and propose a reformulation where Corporate Management acts as the leader to coordinate the resource allocation decisions. We then derive an equivalent single-level reformulation and develop a cut-and-column generation algorithm. Extensive computational experiments evaluate the performance of the algorithm and provide managerial insights on how key parameters and the distribution of decision authority affect system performance.
    Date: 2024–01
  20. By: Li, Xiaolin; Singh Rao, Raghunath; Narasimhan, Om; Gao, Xing
    Abstract: This paper studies the optimal mix of message content in elections while explicitly accounting for voters' memory imperfections. We build an analytical model of a political contest between two candidates facing an election with an electorate consisting of supporters, opponents, and undecided voters. The candidates take decisions on advertising sequence and content (positive vs. negative). Our model explicitly considers the role of memory processes, in particular decay (the idea that memories fade with time) and rehearsal (the idea that accessing a memory eases its recall, ) that crucially affect how effective ads are in influencing choice. The model yields several interesting insights: (a) when both candidates have low initial support, they invest only in positive messages; (b) when both candidates are endowed with high initial support, their messaging strategies take a “pulsing” shape involving negative advertising accompanied by positive advertising; (c) when one candidate has low initial support while the other has high initial support, the former adopts a “pulsing” strategy while the latter adopts only positive advertising. Furthermore, we show that a candidate with low initial support facing a candidate with high initial support responds with a messaging strategy bunched with negative content towards the end of the election cycle. Our model's predictions are shown to find empirical support in a dataset assembled from 2016 U.S. Senate races.
    Keywords: political advertising; memory models; persuasion; game theory
    JEL: L81
    Date: 2022–12–01
  21. By: J. Atsu Amegashie
    Abstract: Status-seeking exists in all societies but different societies value status differently. How does the importance of social status affect the mode of status-seeking? I consider a game in which status can be achieved through productive effort that increases wealth or through a contest in which unproductive (rent-seeking) effort is used to redistribute wealth. Contestants are identical and there is a constraint on total effort. The number of contestants, the security of property rights, and the opportunity cost of unproductive activities in terms of productive activities (i.e., when the constraint binds or does not bind) determine whether an increase in the importance of status leads to an increase or decrease in productive effort (economic output). When the constraint on total effort does not bind, an increase in the importance of status leads to an increase in rent-seeking effort, regardless of the security of property rights. When the contestants differ by their taste for status, status-seeking can have far-reaching effects as a few people become more status-conscious and increase their status-seeking effort, this causes other relatively less status-conscious people to respond. When the contestants have different productive abilities, there exists an equilibrium in which rent-seeking effort is independent of productive ability.
    Keywords: contest, productive effort, property rights, rent-seeking, status-seeking
    JEL: C72 D72
    Date: 2024
  22. By: Bernhardt, Dan (Department of Economics, University of Illinois and Department of Economics, University of Warwick,); Krasa, Stefan (Department of Economics, University of Illinois); Squintani, Francesco (Department of Economics, University of Warwick)
    Abstract: We develop a model of strategic voting in a spatial setting with multiple candidates when voters have both expressive and instrumental concerns. The model endogenizes the strategic coordination of voters, yet is flexible enough to allow the analysis of political platform competition by policy-motivated candidates. We characterize all strategic voting equilibria in a three-candidate setting. Highlighting the utility of our approach, we analyze a setting with two mainstream and a spoiler candidate, showing that the spoiler can gain from entering, even though she has no chance of winning the election and reduces the winning probability of her preferred mainstream candidate.
    Date: 2024

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