Games

15 pages, 289 KiB

Open AccessArticle

Equilibrium Coalition Structures in Three-Player Symmetric Games

by Jingyi Shen and Chen Qu

Games 2025, 16(3), 30; https://doi.org/10.3390/g16030030 - 5 Jun 2025

In symmetric games with externalities across coalitions, we investigate how three players form coalitions using two solutions:

n^{*}

, which is a focal prediction of coalition structure in a class of noncooperative coalitional bargaining games, and equilibrium binding agreements, which represent the [...] Read more.

In symmetric games with externalities across coalitions, we investigate how three players form coalitions using two solutions:

n^{*}

, which is a focal prediction of coalition structure in a class of noncooperative coalitional bargaining games, and equilibrium binding agreements, which represent the cooperative blocking approach. We find that the coarsest equilibrium coalition structure (based on the latter notion) is never finer than

n^{*}

, and we provide a sufficient and necessary condition for these two solutions to generate the same coalition structure (i.e., the two solutions coincide if and only if the first coalition to form in

n^{*}

is not a two-player coalition or a particular condition about average coalitional worths is satisfied). In symmetric games with more than three players, we demonstrate through a series of examples that any relationship between these two solutions is possible. We also discuss symmetric games with positive externalities or equal division in which these two solutions coincide. Full article

13 pages, 836 KiB

Open AccessFeature PaperArticle

The Raiffa–Kalai–Smorodinsky Solution as a Mechanism for Dividing the Uncertain Future Profit of a Partnership

by Yigal Gerchak and Eugene Khmelnitsky

Games 2025, 16(3), 29; https://doi.org/10.3390/g16030029 - 4 Jun 2025

Abstract

Establishing a partnership necessitates agreeing on how to divide future profits or losses. We consider parties who wish to contract on the division of uncertain future profits. We propose to divide profits according to the Raiffa–Kalai–Smorodinsky (K-S) solution, which is the intersection point [...] Read more.

Establishing a partnership necessitates agreeing on how to divide future profits or losses. We consider parties who wish to contract on the division of uncertain future profits. We propose to divide profits according to the Raiffa–Kalai–Smorodinsky (K-S) solution, which is the intersection point of the feasible region’s boundary and the line connecting the disagreement and ideal points. It is the only function which satisfies invariance to linear transformations, symmetry, strong Pareto optimality, and monotonicity. We formulate the general problem of designing a contract which divides uncertain future profit between the partners and determines shares of each partner. We first focus on linear and, later, non-linear contracts between two partners, providing analytical and numerical solutions for various special cases in terms of the utility functions of the partners, their beliefs, and the disagreement point. We then generalize the analysis to any number of partners. We also consider a contract which is partially based on the parties’ financial contribution to the partnership, which have a positive impact on profit. Finally, we address asymmetric K-S solutions. K-S solutions are seen to be a useful predictor of the outcome of negotiations, similar to Nash’s bargaining solution. Full article

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39 pages, 3987 KiB

Open AccessArticle

The Impact of Gifts and Shared Experiences on an Investor-Manager Relationship

by Maximilian Olaf Hoyer and Frans van Winden

Games 2025, 16(3), 28; https://doi.org/10.3390/g16030028 - 4 Jun 2025

Abstract

This paper experimentally investigates the relationship between an investor and a project manager. Project managers choose from a pool of projects, the success probabilities of which are uncertain. Investors can change projects, but also have to change project managers if they want to [...] Read more.

This paper experimentally investigates the relationship between an investor and a project manager. Project managers choose from a pool of projects, the success probabilities of which are uncertain. Investors can change projects, but also have to change project managers if they want to do so. An additional joint project or a voluntary money transfer precedes their interaction. We hypothesize that investors favor projects of managers with whom they share positive experiences at that stage, even though these experiences do not provide any information about the subsequent project’s success probability. Interaction through a voluntary transfer plays a clear and significant role in the investors’ decision-making via bonding, whereas the influence of merely sharing a positive or negative experience proves more complex. Full article

(This article belongs to the Section Behavioral and Experimental Game Theory)

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12 pages, 218 KiB

Open AccessArticle

Match Stability with a Costly and Flexible Number of Positions

by James Gilmore and David Porter

Games 2025, 16(3), 27; https://doi.org/10.3390/g16030027 - 21 May 2025

Abstract

One of the main goals of two-sided matching mechanisms is to pair two groups of agents in a stable manner. Stability means that no pair of agents has an incentive to deviate from their assigned match. The outcome of such a match can [...] Read more.

One of the main goals of two-sided matching mechanisms is to pair two groups of agents in a stable manner. Stability means that no pair of agents has an incentive to deviate from their assigned match. The outcome of such a match can have significant consequences for the participants involved. Most existing research in this field assumes that the quotas of organizations are fixed and externally determined, which may not always be realistic. We introduce the concept of slot stability, which considers the possibility that organizations may want to adjust their quotas after the match process. To address this issue, we propose an algorithm that generates both stable and slot-stable matches by using flexible, endogenous quotas. Full article

37 pages, 498 KiB

Open AccessArticle

A General Model of Bertrand–Edgeworth Duopoly

by Blake A. Allison and Jason J. Lepore

Games 2025, 16(3), 26; https://doi.org/10.3390/g16030026 - 19 May 2025

Abstract

This paper studies a class of two-player all-pay contests with externalities that encompass a general version of duopoly price competition. This all-pay contest formulation puts little restriction on production technologies, demand, and demand rationing. There are two types of possible equilibria: In the [...] Read more.

This paper studies a class of two-player all-pay contests with externalities that encompass a general version of duopoly price competition. This all-pay contest formulation puts little restriction on production technologies, demand, and demand rationing. There are two types of possible equilibria: In the first type of equilibrium, the lower bound to pricing is the same for each firm, and the probability of any pricing tie above this price is zero. Each firm’s equilibrium expected profit is their monopoly profit at the lower bound price. In the second type of equilibrium, one firm prices at the lower bound of the other firm’s average cost and other firm prices according to a non-degenerate mixed strategy. This type of equilibrium can only occur if production technologies are sufficiently different across firms. We derive necessary and sufficient conditions for the existence of pure strategy equilibrium and use these conditions to demonstrate the fragility of deterministic outcomes in pricing games. Full article

36 pages, 447 KiB

Open AccessFeature PaperArticle

Procedural Information as a “Game Changer” in School Choice

by Yoan Hermstrüwer

Games 2025, 16(3), 25; https://doi.org/10.3390/g16030025 - 12 May 2025

Abstract

This article explores the impact of procedural information on the behavior of students under two school admission procedures commonly used in the US, the EU, and other jurisdictions: the Gale–Shapley mechanism and the Boston mechanism. In a lab experiment, I compare the impact [...] Read more.

This article explores the impact of procedural information on the behavior of students under two school admission procedures commonly used in the US, the EU, and other jurisdictions: the Gale–Shapley mechanism and the Boston mechanism. In a lab experiment, I compare the impact of information about the mechanism, information about individually optimal application strategies, and information about both. I find that strategic and full information increases truth-telling and stability under the Gale–Shapley mechanism. Under the Boston mechanism, however, the adoption of equilibrium strategies remains unaffected. Contrary to the prevailing assumptions in matching theory, the Boston mechanism improves perceived fairness. These results underscore the importance of procedural transparency and suggest that eliminating justified envy may not be sufficient to foster fairness and mitigate litigation risks. Full article

(This article belongs to the Section Behavioral and Experimental Game Theory)

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21 pages, 901 KiB

Open AccessFeature PaperArticle

Mobility Comparisons: Theoretical Definitions and People’s Perceptions

by Michele Bernasconi, Giulio Cinquanta, Valentino Dardanoni and Vincenzo Prete

Games 2025, 16(3), 24; https://doi.org/10.3390/g16030024 - 8 May 2025

Abstract

Comparing mobility is an important but controversial issue. In this paper, we argue that in a specific and relevant case, there exists a univocal and non-controversial definition of greater (exchange) mobility that allows for unambiguous comparisons. We conducted a questionnaire experiment to investigate [...] Read more.

Comparing mobility is an important but controversial issue. In this paper, we argue that in a specific and relevant case, there exists a univocal and non-controversial definition of greater (exchange) mobility that allows for unambiguous comparisons. We conducted a questionnaire experiment to investigate whether people’s perceptions of social mobility align with this definition, and we found that people’s choices are broadly in line with the theoretical predictions. Full article

(This article belongs to the Section Behavioral and Experimental Game Theory)

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7 pages, 202 KiB

Open AccessArticle

The Role of Reputation in Sequel Production

by Khac Minh Duc Do and Dmitriy Knyazev

Games 2025, 16(3), 23; https://doi.org/10.3390/g16030023 - 8 May 2025

Abstract

This paper develops a simple model of sequel production for experience goods, showing how reputation shapes a producer’s incentives. Producers differ in productivity, which determines how much effort they invest. A sequel is made only if the previous installment exceeds a quality threshold, [...] Read more.

This paper develops a simple model of sequel production for experience goods, showing how reputation shapes a producer’s incentives. Producers differ in productivity, which determines how much effort they invest. A sequel is made only if the previous installment exceeds a quality threshold, capturing the idea that consumers base future consumption on past success. Although high-productivity producers create higher-quality originals and sequels, the conditioning on successful originals still makes sequels, on average, worse than their predecessors. This aligns with evidence of sequel underperformance in media markets. Full article

(This article belongs to the Special Issue Applications of Game Theory to Industrial Organization)

21 pages, 4424 KiB

Open AccessFeature PaperArticle

New Categories of Conditional Contribution Strategies in the Public Goods Game

by Klaudia Schäffer, Adrienn Král and Ádám Kun

Games 2025, 16(3), 22; https://doi.org/10.3390/g16030022 - 6 May 2025

Abstract

Human cooperation is ubiquitous and instinctive. We are among the most cooperative species on Earth. Still, research mostly focuses on why we cooperate, instead of understanding why some of us do not do so. The public goods game can be used to map [...] Read more.

Human cooperation is ubiquitous and instinctive. We are among the most cooperative species on Earth. Still, research mostly focuses on why we cooperate, instead of understanding why some of us do not do so. The public goods game can be used to map human cooperation as well as to study free riding. We acquired data through an online, unincentivized questionnaire which prompted respondents to choose how much of an initial endowment to contribute to a common pool. The respondents contributed, on average, 54% of their initial endowment to the common pool. The usual categorization scheme of the elicited conditional contribution pattern discerns unconditional free riders who do not contribute irrespective of the contributions of others and calls everyone a conditional cooperator who correlates their contribution with that of the others. However, someone consistently offering less than the others should not be called a cooperator. Consequently, based on the conditional contribution patterns among our respondents, we suggest a recategorization of contribution patterns into the following categories: unconditional cooperator (1.5%), unconditional free rider (10.6%), perfect conditional cooperator (42.6%), hump-shaped contributor (0.7%), V-shaped contributor (0.4%), conditional cooperator (16.6%), conditional free rider (13.6%), conditional contributor (6.4%), negative conditional contributor (0%), and others (7.6%). We only call someone a cooperator if the respondent at least matches others’ contribution, and call everyone consistently offering less a free rider. Furthermore, we found no difference between the contributions of women and men. No correlation of contribution with age, educational attainment, and size of the residential settlement was found. Students’ contributions were not different from non-students’ contributions. We found a significant correlation of the contribution to the common pool with hypercompetitive orientation (negative correlation) and the self-assessed willingness to take risks in general (positive correlation). Full article

(This article belongs to the Section Behavioral and Experimental Game Theory)

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46 pages, 527 KiB

Open AccessArticle

Strategic Complementarities in a Model of Commercial Media Bias

by Anna Kerkhof and Johannes Münster

Games 2025, 16(3), 21; https://doi.org/10.3390/g16030021 - 23 Apr 2025

Abstract

Media content is an important privately supplied public good. While it has been shown that contributions to a public good crowd out other contributions in many cases, the issue has not been thoroughly studied for media markets yet. We show that in a [...] Read more.

Media content is an important privately supplied public good. While it has been shown that contributions to a public good crowd out other contributions in many cases, the issue has not been thoroughly studied for media markets yet. We show that in a standard model of commercial media bias, qualities of media content are strategic complements, whereby investments into quality can crowd in further investments and engage competitors in a race to the top. Therefore, financially strong public service media can mitigate commercial media bias: the content of commercial media can be more in line with the preferences of the audience and less advertiser-friendly in a dual (mixed public and commercial) media system than in a purely commercial media market. Full article

(This article belongs to the Special Issue Mass Media Industries: The Economic Games)

28 pages, 832 KiB

Open AccessFeature PaperArticle

Two-Tier Marketplace with Multi-Resource Bidding and Strategic Pricing for Multi-QoS Services

by Samira Habli, Rachid El-Azouzi, Essaid Sabir, Mandar Datar, Halima Elbiaze and Mohammed Sadik

Games 2025, 16(2), 20; https://doi.org/10.3390/g16020020 - 21 Apr 2025

Abstract

Fog computing introduces a new dimension to the network edge by pooling diverse resources (e.g., processing power, memory, and bandwidth). However, allocating resources from heterogeneous fog nodes often faces limited capacity. To overcome these limitations, integrating fog nodes with cloud resources is crucial, [...] Read more.

Fog computing introduces a new dimension to the network edge by pooling diverse resources (e.g., processing power, memory, and bandwidth). However, allocating resources from heterogeneous fog nodes often faces limited capacity. To overcome these limitations, integrating fog nodes with cloud resources is crucial, ensuring that Service Providers (SPs) have adequate resources to deliver their services efficiently. In this paper, we propose a game-theoretic model to describe the competition among non-cooperative SPs as they bid for resources from both fog and cloud environments, managed by an Infrastructure Provider (InP), to offer paid services to their end-users. In our game model, each SP bids for the resources it requires, determining its willingness to pay based on its specific service demands and quality requirements. Resource allocation prioritizes the fog environment, which offers local access with lower latency but limited capacity. When fog resources are insufficient, the remaining demand is fulfilled by cloud resources, which provide virtually unlimited capacity. However, this approach has a weakness in that some SPs may struggle to fully utilize the resources allocated in the Nash equilibrium-balanced cloud solution. Specifically, under a nondiscriminatory pricing scheme, the Nash equilibrium may enable certain SPs to acquire more resources, granting them a significant advantage in utilizing fog resources. This leads to unfairness among SPs competing for fog resources. To address this issue, we propose a price differentiation mechanism among SPs to ensure a fair allocation of resources at the Nash equilibrium in the fog environment. We establish the existence and uniqueness of the Nash equilibrium and analyze its key properties. The effectiveness of the proposed model is validated through simulations using Amazon EC2 instances, where we investigate the impact of various parameters on market equilibrium. The results show that SPs may experience profit reductions as they invest to attract end-users and enhance their quality of service QoS. Furthermore, unequal access to resources can lead to an imbalance in competition, negatively affecting the fairness of resource distribution. The results demonstrate that the proposed model is coherent and that it offers valuable information on the allocation of resources, pricing strategies, and QoS management in cloud- and fog-based environments. Full article

(This article belongs to the Section Non-Cooperative Game Theory)

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28 pages, 768 KiB

Open AccessArticle

Procedurally Fair Co-Determination with Endogeneous Value Uncertainty: An Experiment

by Werner Güth, Ludivine Martin, Tibor Neugebauer and Sotiria Xanalatou

Games 2025, 16(2), 19; https://doi.org/10.3390/g16020019 - 21 Apr 2025

Abstract

We present an experimental test of a procedurally fair co-determination mechanism where group members reduce their value uncertainty before submitting bids for a joint project. The results suggest a relatively efficient mechanism, with unprofitable projects being largely rejected and profitable ones accepted. Repeated [...] Read more.

We present an experimental test of a procedurally fair co-determination mechanism where group members reduce their value uncertainty before submitting bids for a joint project. The results suggest a relatively efficient mechanism, with unprofitable projects being largely rejected and profitable ones accepted. Repeated interactions tended to enhance the efficiency, while uncertain information reduced it. The subjects invested surprisingly little search effort to reduce the uncertainty about the costs and benefits, and appeared to trade off search costs against higher bids. Full article

(This article belongs to the Section Behavioral and Experimental Game Theory)

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16 pages, 5600 KiB

Open AccessArticle

Cultural Dissemination on Evolving Networks: A Modified Axelrod Model Based on a Rewiring Process

by Yuri Perez, Fabio Henrique Pereira and Pedro Henrique Triguis Schimit

Games 2025, 16(2), 18; https://doi.org/10.3390/g16020018 - 17 Apr 2025

Abstract

In this paper, we investigate the classical Axelrod model of cultural dissemination under an adaptive network framework. Unlike the original model, we place agents on a complex network, where they cut connections with any agent that does not share at least one cultural [...] Read more.

In this paper, we investigate the classical Axelrod model of cultural dissemination under an adaptive network framework. Unlike the original model, we place agents on a complex network, where they cut connections with any agent that does not share at least one cultural trait. This rewiring process alters the network topology, and key parameters—such as the number of traits, the neighborhood search range, and the degree-based preferential attachment exponent—also influence the distribution of cultural traits. Unlike conventional Axelrod models, our approach introduces a dynamic network structure where the rewiring mechanism allows agents to actively modify their social connections based on cultural similarity. This adaptation leads to network fragmentation or consolidation depending on the interaction among model parameters, offering a framework to study cultural homogeneity and diversity. The results show that, while long-range reconnections can promote more homogeneous clusters in certain conditions, variations in the local search radius and preferential attachment can lead to rich and sometimes counterintuitive dynamics. Extensive simulations demonstrate that this adaptive mechanism can either increase or decrease cultural diversity, depending on the interplay of network structure and cultural dissemination parameters. These findings have practical implications for understanding opinion dynamics and cultural polarization in social networks, particularly in digital environments where rewiring mechanisms are analogous to recommendation systems or user-driven connection adjustments. Full article

(This article belongs to the Section Learning and Evolution in Games)

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6 pages, 190 KiB

Open AccessArticle

Von Neumann–Morgenstern Hypergraphs

by Stefano Vannucci

Games 2025, 16(2), 17; https://doi.org/10.3390/g16020017 - 15 Apr 2025

Abstract

A simple hypergraph H with vertex set X and edge set

E

is representable by Von Neumann–Morgenstern (VNM)-stable sets—or VNM—if there exists an irreflexive simple digraph D with vertex set X such that each edge of H is a VNM-stable set of D [...] Read more.

A simple hypergraph H with vertex set X and edge set

E

is representable by Von Neumann–Morgenstern (VNM)-stable sets—or VNM—if there exists an irreflexive simple digraph D with vertex set X such that each edge of H is a VNM-stable set of D. It is shown that a simple hypergraph H is VNM if and only if each edge of H is a maximal clique of the conjugation graph of H. A related algorithm that identifies finite VNM hypergraphs is also provided. Full article

19 pages, 392 KiB

Open AccessArticle

Analysis of the Competition of the South-Eastern Railway of Peru Through a Timetable Auction

by Augusto Aliaga-Miranda, Luis Ricardo Flores-Vilcapoma, Christian Efrain Raqui-Ramirez, José Luis Claudio-Pérez, Yadira Yanase-Rojas and Jovany Pompilio Espinoza-Yangali

Games 2025, 16(2), 16; https://doi.org/10.3390/g16020016 - 7 Apr 2025

Abstract

Our research analyzes the design of an auction model for railway transportation on the South-East Railway of Peru, managed by Ferrocarril Transandino S.A. (Fetransa) and operated by PeruRail. Initially, the regulatory framework aimed to promote competition in railway transportation through timetable auctions and [...] Read more.

Our research analyzes the design of an auction model for railway transportation on the South-East Railway of Peru, managed by Ferrocarril Transandino S.A. (Fetransa) and operated by PeruRail. Initially, the regulatory framework aimed to promote competition in railway transportation through timetable auctions and infrastructure access. However, the concession has resulted in a vertically integrated structure that favors PeruRail, which faces minimal direct competition, controls high-demand time slots, and hinders the entry of other operators due to strategic and structural access barriers. To address these distortions, we propose reforming the auction mechanism to neutralize these advantages and enhance competition. In this revised framework, the track usage fee will serve as the competitive factor, with the highest bid above a minimum base rate securing the allocation. Additionally, we propose the implementation of asymmetric tariffs to compensate for the higher costs faced by operators with fewer economies of scale, technological optimizations to facilitate equitable access to time slots, and stricter oversight mechanisms to ensure transparency in timetable allocation. These measures aim to balance the market and safeguard competition through a more equitable and efficient auction design. Full article

(This article belongs to the Special Issue Applications of Game Theory to Industrial Organization)

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8 pages, 215 KiB

Open AccessArticle

Biased-Manager Hiring in a Market with Network Externalities and Product Compatibility

by Shih-Hao Huang, Chien-Shu Tsai, Jen-Yao Lee and Su-Ching Tsai

Games 2025, 16(2), 15; https://doi.org/10.3390/g16020015 - 21 Mar 2025

Abstract

This paper studies biased-manager hiring in a market with network externalities and product compatibility. We show that the aggressivity of a biased manager has a non-linear relationship with product compatibility; however, since both owners want to hire aggressive managers, product compatibility is irrelevant [...] Read more.

This paper studies biased-manager hiring in a market with network externalities and product compatibility. We show that the aggressivity of a biased manager has a non-linear relationship with product compatibility; however, since both owners want to hire aggressive managers, product compatibility is irrelevant to the type of manager the owner hires. In Cournot competition, product compatibility is crucial in alleviating the “prisoner’s dilemma” due to the net network effect of network externalities with product compatibility. In Bertrand competition, the “prisoner’s dilemma” is resolved when the augmented net network effect of product compatibility is large. Full article

(This article belongs to the Section Applied Game Theory)

17 pages, 530 KiB

Open AccessArticle

Greenwashing Risks in Environmental Quality Competition: Detection and Deterrence

by Arka Mukherjee and Subhadip Ghosh

Games 2025, 16(2), 14; https://doi.org/10.3390/g16020014 - 11 Mar 2025

Abstract

The rising prevalence of greenwashing by firms has emerged as a major concern for regulatory authorities over the past decade. This paper examines the impact of regulation on firms’ strategic decisions regarding greenwashing and environmental quality in an oligopolistic market. We model two [...] Read more.

The rising prevalence of greenwashing by firms has emerged as a major concern for regulatory authorities over the past decade. This paper examines the impact of regulation on firms’ strategic decisions regarding greenwashing and environmental quality in an oligopolistic market. We model two firms that compete on environmental quality and greenwashing levels, operating under the oversight of a regulatory authority. The authority’s policy instruments include a detection mechanism and fines imposed on firms engaging in greenwashing. Using a differential game-theoretical framework, we examine the effectiveness of regulatory interventions like detection and penalties in reducing greenwashing behavior and enhancing environmental quality. Additionally, we discuss the post-detection trajectories of both firms, providing insights into the effects on consumer perceptions and market competition. We find that while regulation can reduce greenwashing as expected, it may also reduce firms’ environmental quality efforts. Indeed, when penalties are sufficiently high, the marginal returns on investment in greenwashing exceed those from actual green quality improvements. Full article

(This article belongs to the Special Issue Applications of Differential Games and Related Models in Mathematics and Economics)

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25 pages, 808 KiB

Open AccessArticle

Sharing Price Announcements

by Maarten Janssen and Vladimir Karamychev

Games 2025, 16(2), 13; https://doi.org/10.3390/g16020013 - 10 Mar 2025

Abstract

We present a simple model where, before competing in prices, firms announce which prices they intend to choose. Deviating from these announcements involves a cost. We show that sharing pricing intentions results in prices being set above their competitive levels. All equilibria result [...] Read more.

We present a simple model where, before competing in prices, firms announce which prices they intend to choose. Deviating from these announcements involves a cost. We show that sharing pricing intentions results in prices being set above their competitive levels. All equilibria result in prices that are higher than in the absence of announcements. When the deviation cost of not sticking to the price announcement is high, the unique equilibrium market outcome is asymmetric, as with price leadership. When this cost is low, a symmetric equilibrium exists with even higher prices. Product differentiation is a key ingredient to these results. Full article

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37 pages, 427 KiB

Open AccessArticle

Structured Equilibria for Dynamic Games with Asymmetric Information and Dependent Types

by Nasimeh Heydaribeni and Achilleas Anastasopoulos

Games 2025, 16(2), 12; https://doi.org/10.3390/g16020012 - 3 Mar 2025

Abstract

We consider a dynamic game with asymmetric information where each player privately observes a noisy version of a (hidden) state of the world V, resulting in dependent private observations. We study the structured perfect Bayesian equilibria (PBEs) that use private beliefs in [...] Read more.

We consider a dynamic game with asymmetric information where each player privately observes a noisy version of a (hidden) state of the world V, resulting in dependent private observations. We study the structured perfect Bayesian equilibria (PBEs) that use private beliefs in their strategies as sufficient statistics for summarizing their observation history. The main difficulty in finding the appropriate sufficient statistic (state) for the structured strategies arises from the fact that players need to construct (private) beliefs on other players’ private beliefs on V, which, in turn, would imply that one needs to construct an infinite hierarchy of beliefs, thus rendering the problem unsolvable. We show that this is not the case: each player’s belief on other players’ beliefs on V can be characterized by her own belief on V and some appropriately defined public belief. We then specialize this setting to the case of a Linear Quadratic Gaussian (LQG) non-zero-sum game, and we characterize structured PBEs with linear strategies that can be found through a backward/forward algorithm akin to dynamic programming for the standard LQG control problem. Unlike the standard LQG problem, however, some of the required quantities for the Kalman filter are observation-dependent and, thus, cannot be evaluated offline through a forward recursion. Full article

(This article belongs to the Section Learning and Evolution in Games)

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