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on Game Theory |
| By: | Ohnishi, Kazuhiro |
| Abstract: | This study investigates a quantity-setting duopoly model in which two partially cooperating firms coexist. The following three-stage game is considered. In the first stage, each owner decides whether to hire a manager. In the second stage, the owners who hired managers select incentive parameters for them. In the third stage, the managers or, in their absence, the owners simultaneously and independently choose the firms’ outputs. The study adopts subgame perfection as an equilibrium concept and solves the game by backward induction. The study demonstrates that, in the subgame-perfect equilibrium, both firms hire managers. |
| Keywords: | Managerial delegation; Mixed duopoly; Cournot model; Partially cooperating firm |
| JEL: | C72 D21 D43 L13 |
| Date: | 2026–04–15 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:128718 |
| By: | Falmagne, Guillaume |
| Abstract: | Symmetric 2x2 games are a cornerstone of game theory and its applications in biology, economics, and social sciences, yet no unified visual overview of their full parameter space exists in the literature. I present a minimal but exhaustive phase space of all symmetric 2x2 games in a two-dimensional payoff plane, leveraging symmetries and using parametrizations consistent with the cooperation and Prisoner's Dilemma literature. Within this phase space, I superimpose the boundaries of all standard strategic properties (Nash equilibria, Pareto efficiency, maximin strategies, and social optimum) across all 12 ordinal game classes but also considering real-valued payoffs. I highlight how the strategic challenges of games in each region originate from their unique combination of these standard properties. This unified representation reveals the continuous relationships between game archetypes: the phase space indeed situates well-known games (Prisoner's Dilemma, Stag Hunt, Hawk-Dove, (anti-)coordination) alongside understudied (Second Best, Harmony) regions. It thereby provides an immediate reading of any symmetric 2x2 game's strategic properties, and makes explicit how they shift as payoffs vary within and across ordinal classes. I then review each ordinal class in detail, covering its history, defining characteristics, and within-class variations. This work, and in particular the phase space visual, is intended as both a reference tool for experienced researchers and a pedagogical entry point. |
| Date: | 2026–04–18 |
| URL: | https://d.repec.org/n?u=RePEc:osf:socarx:tgh9y_v1 |
| By: | Volker Nocke; Nicolas Schutz |
| Abstract: | We develop a potential games approach to study multiproduct-firm pricing games.We introduce the new concept of transformed potential and characterize the classes of demand systems that give rise to pricing games admitting such a potential. The resulting demand systems may contain nests (of closer substitutes) or baskets (of products that are purchased jointly), or combinations thereof. These demand systems allow for flexible substitution patterns, and can feature product complementarities arising from joint purchases and substitution away from the outside option. Combining the potential games approach with a competition-in-utility approach, we derive powerful results on existence of pure-strategy Nash equilibria. |
| Keywords: | Multiproduct firms, potential game, oligopoly pricing, complementary goods, joint purchases, nests, equilibrium existence, equilibrium uniqueness |
| JEL: | L13 D43 |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2025_644_v3 |
| By: | Burkhard C. Schipper (Department of Economics, University of California Davis) |
| Abstract: | Heifetz, Meier, and Schipper (2013) introduced dynamic games with unawareness consisting of a partially ordered set of games in extensive form. Here, we study the normal form of dynamic games with unawareness. The generalized normal form associated with a dynamic game with unawareness consists of a partially ordered set of games in normal form. We characterize strong rationalizability (resp., prudent rationalizability) in dynamic games with unawareness by iterated conditional strict (resp., weak) dominance in the associated generalized normal form. We also show that the analogue to iterated admissibility for dynamic games with unawareness depends on the extensive form. This is because, under unawareness, a player's information set not only determines which nodes she considers possible but also which game tree(s) she is aware of. |
| Keywords: | Awareness, unknown unknowns, extensive form, normal form, strong rationalizabity, extensive-form rationalizability, prudent rationalizability, iterated conditional dominance, iterated admissibility |
| JEL: | C72 D83 |
| Date: | 2026–04–29 |
| URL: | https://d.repec.org/n?u=RePEc:cda:wpaper:380 |
| By: | Solomon Polachek; Kenneth Romano; Ozlem Tonguc |
| Abstract: | This study examines how large language models (LLMs) respond to varying stake sizes in the Dictator and Ultimatum games using the high-stakes design introduced by Andersen et al. (2011). We test ten leading LLMs chosen for their accessibility, prominence, and differences in reasoning capabilities. Results reveal substantial variation across models: Only 5 of 10 models exhibit strategic behavior by offering more in the Ultimatum Game (UG) than in the Dictator Game (DG). Relative to humans, 4 models are consistently more generous, 2 consistently less, and 4 vary with stake size. Only 1 model shows a monotonic decline in UG offers as stakes increase; the remaining 9 are non-monotonic or stable. Unlike humans, most models reduce UG offers when endowed with wealth. Prompting for "human-like" decisions generally increases generosity in the UG. These findings are important for evaluating whether LLMs can serve as realistic proxies for human subjects in behavioral experiments and highlight key limitations and future directions for model development. |
| Keywords: | Ultimatum Game, Dictator Game, fairness, payoff stakes, artificial intelligence |
| JEL: | D01 C72 C90 |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:crm:wpaper:26110 |
| By: | Yves Zenou |
| Abstract: | This paper reviews the theoretical and empirical foundations of peer and network effects, aiming to bridge insights from both literatures. We first examine the main identification challenges in linear-in-means models-reflection, correlated effects, and sorting-and show how introducing explicit network structures can help address them. We also review reduced-form strategies based on within-school cohort composition, exposure to peers' shocks, random assignment, and exogenous variation in network links. The analysis then develops the microfoundations of peer effects through linear-quadratic network games, linking equilibrium behavior to network centrality and highlighting the role of key players. Using this framework, we discuss how structural models of network formation and individual effort choices can resolve endogeneity concerns. The paper concludes with recent advances on non-linear and multiplex interactions, where individuals respond to specific peers and operate across multiple, interdependent layers. |
| Keywords: | Social interactions; Identification; Network games; Centrality; Multiplex networks; Non-linearities. |
| JEL: | A14 C57 D85 Z13 |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:crm:wpaper:25118 |
| By: | Ohnishi, Kazuhiro |
| Abstract: | This paper explores a Cournot duopoly model involving two firms that engage in partial cooperation. The paper reevaluates the effectiveness of using ambient charges as a policy tool to control industrial nonpoint-source pollution. The findings suggest that when the level of cooperation between the firms is relatively low, increasing ambient charges can serve as an effective means to reduce pollution. By analyzing the strategic interactions between the firms, the paper highlights how limited cooperation influences the success of environmental policies. These insights contribute to a better understanding of regulatory approaches in industries where firms have interdependent pollution outcomes. |
| Keywords: | Ambient charge; Cournot duopoly; Environmental regulation; partially cooperating firms; Pollution |
| JEL: | D21 L13 L20 |
| Date: | 2026–03–01 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:128241 |
| By: | Zhang, Chuyuan; Lee, Sang-Ho |
| Abstract: | This study considers a vertically related market where an upstream firm supplies an intermediate good to competing downstream firms that may adopt environmental corporate social responsibility (ECSR). When downstream firm owners, guided by common ownership, appoint green managerial delegation contract, we investigate strategic interaction between common ownership and ECSR, demonstrating that downstream firms may engage in ECSR, which can reduce intermediate prices, while common ownership may increase market competition through ECSR. Our analysis shows that Cournot firms adopt ECSR only when common ownership is sufficiently high or product substitutability is sufficiently low, whereas Bertrand firms always adopt ECSR. Cournot competition can yield higher welfare than Bertrand competition when the degree of common ownership is sufficiently high (low) and product substitutability is sufficiently low (high). As environmental damage increases, Cournot competition yields much higher welfare than Bertrand competition. Finally, we compare outcomes under discriminatory input prices and mandatory ECSR guidelines, and discuss the policy implications. |
| Keywords: | Common ownership; Environmental corporate social responsibility; Green managerial delegation; Vertically related market |
| JEL: | D43 L2 L21 L44 |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:128009 |
| By: | Appelbaum, Elie; Melatos, Mark |
| Abstract: | We model equilibrium carbon emissions and welfare in an imperfectly competitive two-country world in which countries strategically choose carbon taxes to maximize national welfare. Each country trades off total national surplus and the cost of global carbon emissions, but differs in its degree of concern about global emissions (CAE) and in its carbon efficiency (CE). We show that CAEs and CEs influence the strategic interaction between countries and, hence, Nash equilibrium carbon taxes, emissions and welfare. Our simulations demonstrate that there is no clear-cut relationship between equilibrium emissions and welfare. While an increase in one country’s CAE reduces global emissions -and global welfare - individual country emissions and welfare may rise or fall. Moreover, an increase in a country’s CE does not guarantee lower emissions or higher welfare nationally or globally. Our results suggest that international trade can reduce global emissions; consumers can access more carbon-efficient sources of production. |
| Keywords: | Optimal carbon taxes, carbon emissions, strategic carbon taxes, best-reply functions, carbon efficiency, emission aversion. |
| JEL: | F12 F13 F18 Q54 Q55 Q58 |
| Date: | 2025–11–21 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:128066 |
| By: | Galdino, Manoel (Universidade de São Paulo) |
| Abstract: | When and why would a hegemon prefer consensus to majority rule in an international organization? I argue that consensus can be a technology of hegemonic power rather than a constraint upon it. In a formal model, a hegemon privately observes the value of cooperation and uses Bayesian persuasion to influence weaker states' entry decisions. Under majority rule, weak states can bypass the hegemon, eliminating any screening problem. Under unanimity, weak states must include the hegemon in every bargaining coalition without knowing its type, creating a screening cutoff at which their behavior changes discretely. This generates an upward jump in the hegemon's value function---a non-convexity that Bayesian persuasion exploits. The institutional comparison has a single-crossing property: there is a unique prior threshold, in closed form, above which the hegemon prefers unanimity and below which majority can dominate by making entry easier. The mechanism reframes institutional design as a trade-off between informational leverage under unanimity and easier participation under majority, providing a distributive explanation for consensus rules in organizations like the GATT/WTO. |
| Date: | 2026–04–23 |
| URL: | https://d.repec.org/n?u=RePEc:osf:socarx:ca8vj_v1 |
| By: | GHOSH, Arghya; HODAKA, Morita; SATO, Susumu |
| Abstract: | Firms compete in both product and labor markets by making decisions about hiring, training, and poaching workers. We develop a theoretical model in which firm-sponsored training links product and labor market competition. Changes in labor, product, or overall market power influence firms' incentives to invest in training, which can lead to clear-cut welfare improvements benefiting all relevant parties. The distinction between under- vs. overinvestment in training, a unique feature that emerges from the interaction between the two markets, plays a critical role in determining whether or not such welfare improvements are possible, enriching welfare and policy implications. |
| Keywords: | product market competition, oligopoly, market power, labor mobility, training, welfare, antitrust implications |
| JEL: | D21 L13 L40 M50 |
| Date: | 2026–03 |
| URL: | https://d.repec.org/n?u=RePEc:hit:hitcei:2025-04 |
| By: | Friedrich, Thomas |
| Abstract: | The transfer space is a biochemical model of enzymatic cooperation and complementation. A substrate is transferred from a source to a sink; together they form an ensemble, a unity of two. Benefit (b) and cost (c) of this substrate are two sides of the same coin but their size and size relation are decided by local conditions in source and sink. Both have linear cost and saturating benefit functions; both contribute to the ensemble´s total net profit. A transfer changes the productivity of each single party and the ensemble in a non-linear way. As the parties are independent of each other, they are orthogonal and form the transfer space of the ensemble. The cost and benefit functions of each party intercept at one point (b=c) and thus cut the transfer space into four subspaces or areas (top-down view). In area I source is cost dominated and wants to get rid of the substrate while sink is benefit dominated and wants to take this substrate. I interpreted this as mutual cooperation at free will (R, in two-player games). In area II both parties are cost dominated and in area III both parties are benefit dominated. In these areas one party has to force or deceive the other party either to take (II, source forces sink) or to give (III, sink forces source) substrate. Exploitation of a cooperating party is called defect; T and S in two-player games. Finally, everywhere in the transfer space the behavioural alternative is not to transfer substrate (area I to IV). This corresponds to mutual defection (P) in two-player games. In the transfer space several symmetric and asymmetric two-player games coexist. Their local outcomes are different hierarchies of rational transfers based on mutual self-interest (cooperation), transfers through force and deception (exploitation), and inaction (mutual defect) within a global transfer space. |
| Keywords: | Concepts: source, sink, ensemble, superadditivity, subadditivity, transfer space; Games: Prisoner's Dilemma, Wise Exploitation, Stag Hunt, Snow-Drift, Hawk-Dove, Deadlock, Assurance, Battle of the Sexes, Dictator, Ultimatum, Chicken |
| JEL: | Z00 |
| Date: | 2026–03–17 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:128388 |
| By: | Margherita Comola (RITM - Réseaux Innovation Territoires et Mondialisation - Université Paris-Saclay, 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 nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Agnieszka Rusinowska (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 nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Marie Claire Villeval (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - UL2 - Université Lumière - Lyon 2 - UJM - Université Jean Monnet - Saint-Étienne - UJM EPE - Université Jean Monnet (EPSCPE) - EM - EMLyon Business School - CNRS - Centre National de la Recherche Scientifique, IZA - Forschungsinstitut zur Zukunft der Arbeit - Institute of Labor Economics) |
| Abstract: | We experimentally investigate targeting decisions in a setting where a human player competes for influence in a network against a computerized opponent with opposing views, whose targeting choice is revealed before the player acts. By varying network structure, opponent influence, and nodes opinion heterogeneity, we find that players typically adopt best-response strategies based on relative influence. However, they sometimes deviate – for example, by erroneously targeting central nodes or by avoiding the opponent's target. Targeting is also affected by affinity and opposition biases, the strength of which depends on the initial opinion distribution. Targeting the center, avoiding the competitor's target, or selecting nodes based on their initial opinions when these are not best responses generates significant efficiency losses. |
| Keywords: | Network, Influence, Targeting, Competition, Experiment |
| Date: | 2026–04–12 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-04706311 |
| By: | Jeon, Doh-Shin; Drugov, Mikhail |
| Abstract: | This paper studies the incentives of a subscription-funded platform that offers both proprietary and third-party content to bias its recommendations about which con tent users should consume. Consistent with Netflix’s practice, we consider fixed-fee bargaining between the platform and a content provider, which eliminates any static incentive to bias recommendations. However, our dynamic model identifies two dis tinct incentives to bias recommendations: improving the platform’s future bargain ing position and increasing users’ expected surplus. The former favors first-party content, while the latter favors the ex ante superior content. As a result, biased recommendations may lead to either self-preferencing or third-party preferencing. |
| JEL: | D83 L42 |
| Date: | 2026–04–29 |
| URL: | https://d.repec.org/n?u=RePEc:tse:wpaper:131694 |
| By: | Santiago Hermo |
| Abstract: | How does collective bargaining shape the labor market response to economic shocks? I use novel Argentine administrative data to uncover the network of firms linked by collective bargaining and show that positive product-demand shocks to firms within a bargaining unit raise wages at other non-shocked firms in the same unit. Heterogeneous wage and employment responses indicate that propagation operates via collectively bargained wage floors. I develop and estimate a structural model where wage floors are determined in bargaining equilibrium. The model shows that the network shapes the bite of wage floors, which in turn determines the magnitude of shock propagation. |
| Keywords: | collective bargaining, unions, wage floors, monopsony power, trade shocks, shock propagation, rent-sharing |
| JEL: | J51 J52 J42 F16 |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:crm:wpaper:25157 |