Games

20 pages, 336 KiB

Open AccessArticle

Spatial Competition Across Borders: The Role of Patients’ Mobility and Institutional Settings

by Laura Levaggi and Rosella Levaggi

Games 2025, 16(3), 31; https://doi.org/10.3390/g16030031 - 5 Jun 2025

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Health care systems rely on geographical boundaries that secure financial stability and adequate planning. Quality differences across regions often arise for efficiency reasons, causing patient flows if mobility is free. In this paper, a theoretical spatial competition model is developed to study the [...] Read more.

Health care systems rely on geographical boundaries that secure financial stability and adequate planning. Quality differences across regions often arise for efficiency reasons, causing patient flows if mobility is free. In this paper, a theoretical spatial competition model is developed to study the role of patients’ mobility on quality setting and to draw policy implications on its use as an instrument to reduce disparities, in a setting where regions differ in efficiency, costs, and market structure. From the analysis, it emerges that the institutional setting matters and a trade-off may appear between equity (in terms of quality difference across patients) and welfare (finding an allocation that maximizes social benefits). In a centralized setting, it is optimal to regulate mobility and increase the quality gap, while allowing free mobility calls for a refined quality setting, in which, depending on a balance between costs and benefits, the quality gap may be either increased or decreased. In decentralization the gap is generally lower, compared to centralization: the different consideration of benefits from local quality provision results in higher quality levels where the market structure is vertically integrated. Full article

(This article belongs to the Section Applied Game Theory)

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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

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Abstract

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

Viewed by 136

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

Viewed by 222

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

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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

Viewed by 168

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

Viewed by 331

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

Viewed by 458

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

Viewed by 273

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

Viewed by 470

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

Viewed by 571

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)

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Games, Volume 16, Issue 3 (June 2025) – 11 articles

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