Games

15 pages, 467 KB

Open AccessArticle

Monopoly, Multi-Product Quality, Consumer Heterogeneity, and Market Segmentation

by Amit Gayer

Games 2025, 16(5), 49; https://doi.org/10.3390/g16050049 - 10 Sep 2025

This paper introduces a novel ratio-based framework for analyzing how consumer heterogeneity translates into product differentiation in vertically structured monopoly markets. We consider a monopolist facing a continuum of consumers and a strictly convex production cost function and identify conditions under which the [...] Read more.

This paper introduces a novel ratio-based framework for analyzing how consumer heterogeneity translates into product differentiation in vertically structured monopoly markets. We consider a monopolist facing a continuum of consumers and a strictly convex production cost function and identify conditions under which the heterogeneity of preferences, measured by the length of the consumer type interval, maps into a corresponding range of offered qualities. The analysis shows that this mapping depends on the curvature of the marginal cost function: under linear costs, the relationship is proportional; under convex costs, heterogeneity expands faster than segmentation; and under concave costs, the reverse occurs. These findings offer a new lens for understanding endogenous market granularity in monopoly settings and have potential applicability in markets with vertically differentiated goods. We also show that under partial market coverage, this proportionality breaks down - even in the linear case - revealing a critical asymmetry in equilibrium structure. Full article

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

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11 pages, 260 KB

Open AccessOpinion

The Agentic Perspective in Experimental Economics

by Arturo Macías

Games 2025, 16(5), 48; https://doi.org/10.3390/g16050048 - 8 Sep 2025

Viewed by 47

Abstract

Mainstream experimental economics is characterized by its focus on theory testing and “treatment effects” on aggregate outcomes. The “agentic” alternative is concerned with the econometric specification of individual behavior. In this essay, first, a literature review of agentic experimental economics is provided, and [...] Read more.

Mainstream experimental economics is characterized by its focus on theory testing and “treatment effects” on aggregate outcomes. The “agentic” alternative is concerned with the econometric specification of individual behavior. In this essay, first, a literature review of agentic experimental economics is provided, and a stylized workflow is proposed to produce and validate econometric models of individual behavior based on experimental data: (i) create a baseline (“optimal”) behavioral benchmark (by analytical means or reinforcement learning) for the considered multi-agent game, (ii) conduct experiments with human subjects, (iii) use the experimental results to characterize the structure of the deviations from the baseline behavior, and (iv) re-run the experiment with artificial agents calibrated in the previous step, and compare the outcomes with those of the human experiment. Two papers have been selected to illustrate the successful use of the proposed workflow. Finally, the relations between agent-based and experimental economics are discussed after deep learning has “tamed” the curse of dimensionality. Full article

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

21 pages, 324 KB

Open AccessFeature PaperArticle

Asymptotic Thresholds for (a:b) Minimum-Degree Games

by Adnane Fouadi, Mourad El Ouali and Anand Srivastav

Games 2025, 16(5), 47; https://doi.org/10.3390/g16050047 - 8 Sep 2025

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Abstract

We investigate the

(a : b)

Maker–Breaker subgraph game played on the edge set of the complete graph

K_{n}

, where

n, a, b \in N

, and Maker’s objective is to construct a member of a prescribed [...] Read more.

We investigate the

(a : b)

Maker–Breaker subgraph game played on the edge set of the complete graph

K_{n}

, where

n, a, b \in N

, and Maker’s objective is to construct a member of a prescribed family of graphs H, while Breaker aims to prevent this. In our study, Breaker moves first, and H is taken to be either the family of connected spanning subgraphs or the family of spanning subgraphs with minimum-degree at least

k = k (n)

. For the

(a : b)

minimum-degree-k game, we determine the asymptotically optimal threshold bias across a wide range of values for a. For the

(a : b)

connectivity game, we resolve an open problem posed by Hefetz et al. (2012) by identifying the exact leading term in the asymptotic behavior of the threshold bias when

a = c ln n

. Full article

(This article belongs to the Section Algorithmic and Computational Game Theory)

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17 pages, 415 KB

Open AccessArticle

Dividend Representations for Two Influence Assessments

by Yu-Hsien Liao

Games 2025, 16(5), 46; https://doi.org/10.3390/g16050046 - 4 Sep 2025

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Abstract

This paper establishes dividend-based representations for two influence assessments. First, we define a system of min-dividends derived from the minimal-influence evaluation via a unique linear decomposition using unanimity-type spanning models. Building on this, we further construct a pair of internal and external min-dividends [...] Read more.

This paper establishes dividend-based representations for two influence assessments. First, we define a system of min-dividends derived from the minimal-influence evaluation via a unique linear decomposition using unanimity-type spanning models. Building on this, we further construct a pair of internal and external min-dividends satisfying Completeness and Balancedness conditions, through which we express the stable min-value as the net difference of internal gains and external losses. We then demonstrate that the minimal self-stable value can be represented as accumulated average min-dividends across all coalitions they have participated in. Furthermore, the proposed expression also is adopted to analyze the stability of the minimal self-stable value. These results extend the classical notion of dividends into a minimal-influence-based framework with potential applications in fair resource allocation and responsibility apportionment. Full article

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17 pages, 2567 KB

Open AccessArticle

Optimal Vaccination Strategies to Reduce Endemic Levels of Meningitis in Africa

by Alfredo Martinez, Jonathan Machado, Eric Sanchez and Igor V. Erovenko

Games 2025, 16(5), 45; https://doi.org/10.3390/g16050045 - 1 Sep 2025

Viewed by 336

Abstract

Meningococcal meningitis is a deadly acute bacterial infection caused by the Neisseria meningitidis bacterium that affects the membrane covering the brain and spinal cord. The World Health Organization launched the “Defeating bacterial meningitis by 2030” initiative in 2018, which relies on recent discoveries [...] Read more.

Meningococcal meningitis is a deadly acute bacterial infection caused by the Neisseria meningitidis bacterium that affects the membrane covering the brain and spinal cord. The World Health Organization launched the “Defeating bacterial meningitis by 2030” initiative in 2018, which relies on recent discoveries of cheap and effective vaccines. Here, we consider one important factor—human behavior—which is often neglected by immunization campaigns. We constructed a game-theoretic model of meningitis in the meningitis belt, where individuals make selfish rational decisions whether to vaccinate based on the assumed costs and the vaccination decisions of the entire population. We identified conditions when individuals should vaccinate, and we found the optimal (equilibrium) population vaccination rate. We conclude that voluntary compliance significantly reduces the endemic levels of meningitis if the cost of vaccination relative to the cost of the disease is sufficiently low, but it does not eliminate the disease. We also performed uncertainty and sensitivity analysis on our model. Full article

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64 pages, 2160 KB

Open AccessFeature PaperArticle

Test Me If You Can—Providing Optimal Information for Consumers Through a Novel Certification Mechanism

by Ulrike Vollstädt, Patrick Imcke, Franziska Brendel and Christiane Ehses-Friedrich

Games 2025, 16(5), 44; https://doi.org/10.3390/g16050044 - 29 Aug 2025

Viewed by 345

Abstract

Certifiers such as Stiftung Warentest (Germany), Which? (UK), and Consumer Reports (US) reduce asymmetric information between buyers and sellers by providing credible information about product quality. However, due to their limited testing capacities, they face a set selection problem and test only a [...] Read more.

Certifiers such as Stiftung Warentest (Germany), Which? (UK), and Consumer Reports (US) reduce asymmetric information between buyers and sellers by providing credible information about product quality. However, due to their limited testing capacities, they face a set selection problem and test only a subset of all available product models. We show theoretically that, under any current mechanism to select product models for testing, buyers always end up buying suboptimal product models, unless all product models which would be sold under complete information (or all but the overall cheapest one) happen to be tested. Instead, we propose a novel mechanism based on voluntary disclosure, but with the same testing capacity, which always yields the maximum possible consumer surplus and thus weakly dominates any current mechanism. Furthermore, we confirm in a controlled laboratory experiment that our mechanism significantly increases consumer surplus. Full article

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20 pages, 593 KB

Open AccessArticle

The Power of Passivity in the Hirshleifer Contest Under Small Noise

by Guang-Zhen Sun

Games 2025, 16(5), 43; https://doi.org/10.3390/g16050043 - 29 Aug 2025

Viewed by 250

Abstract

Hirshleifer’s difference-form contest technology is a useful tool in the study of a class of conflict, especially military combats. We aim to highlight an important feature that the Hirshleifer contest model distinctively has, namely passivity (bidding zero effort) may stand as an effective [...] Read more.

Hirshleifer’s difference-form contest technology is a useful tool in the study of a class of conflict, especially military combats. We aim to highlight an important feature that the Hirshleifer contest model distinctively has, namely passivity (bidding zero effort) may stand as an effective choice in conflict even when the contest is highly deterministic (i.e., with small noise). For that purpose, we establish two propositions on the contest with

n \geq 2

risk-neutral contestants under small noise. The first proposition states that every contestant bids arbitrarily close to zero (if not bidding zero with positive probability at all) under sufficiently small noise. The second proposition, more strikingly, states that every contestant either bids arbitrarily close to the second-highest valuation (among all the contestants’ valuations), or simply remains passive with certainty under any sufficiently small noise. We further show that the first proposition holds for the contest between risk-averse individuals endowed with constant absolute risk aversion as well, and illustrate by an example how quickly polarization in bidding among contestants, as is predicted by the propositions, may emerge as the noise of the contest abates. These results help pave the way toward a complete characterization of the difference-form contest. Full article

(This article belongs to the Section Applied Game Theory)

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21 pages, 493 KB

Open AccessFeature PaperArticle

A Theoretical Analysis of Cooperation Incentives for Non-Mutually Dependent Sellers

by Lorenzo Ferrari, Werner Güth, Vittorio Larocca and Luca Panaccione

Games 2025, 16(5), 42; https://doi.org/10.3390/g16050042 - 27 Aug 2025

Viewed by 293

Abstract

This paper examines stochastic cooperation in markets with two sellers who exhibit one-sided dependency. The independent seller’s pricing influences the dependent seller’s demand, but not vice versa. We study the one-dimensional hybrid game class whose parameter is the exogenously given probability of cooperation. [...] Read more.

This paper examines stochastic cooperation in markets with two sellers who exhibit one-sided dependency. The independent seller’s pricing influences the dependent seller’s demand, but not vice versa. We study the one-dimensional hybrid game class whose parameter is the exogenously given probability of cooperation. In each game of this class, both sellers simultaneously choose prices that determine their endogenous threats, i.e., conflict profits. The sellers are aware of the cooperation probability but cannot condition prices on whether or not there is cooperation. We characterize the equilibrium prices and the sellers’ expected profits. Our main result shows that the independent seller earns higher expected profits when cooperation is more likely. In contrast, the dependent seller earns lower expected profits when the likelihood of cooperation is below a threshold that we characterize explicitly, and higher profits are earned thereafter. These findings suggest that, within our framework, antitrust concerns may be mitigated. Since dependent sellers can incur losses from cooperation, collusion attempts become less viable in markets with one-sided dependency. Full article

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23 pages, 380 KB

Open AccessArticle

Power Indices with Threats in Precoalitions

by Jochen Staudacher

Games 2025, 16(5), 41; https://doi.org/10.3390/g16050041 - 25 Aug 2025

Viewed by 447

Abstract

We investigate power indices for simple games with precoalitions which distribute power among players in an external and an internal step. We extend an existing approach which uses the Public Good index both on the external level in the quotient game as well [...] Read more.

We investigate power indices for simple games with precoalitions which distribute power among players in an external and an internal step. We extend an existing approach which uses the Public Good index both on the external level in the quotient game as well as on the internal level for measuring the leverage of players to threaten their peers through departing the precoalition. We replace the Public Good index in that model by five other efficient power indices, i.e., the Shapley–Shubik index, the Deegan–Packel index, the Johnston index and two indices based on null player free winning coalitions. Axiomatizations of the novel power indices with threat partitions are presented. We also propose a slight modification to the existing framework for threat power indices which guarantees that null players are always assigned zero power. Numerical results for all power indices combined with different threat partitions are presented and discussed. Full article

(This article belongs to the Section Cooperative Game Theory and Bargaining)

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Games, Volume 16, Issue 5 (October 2025) – 9 articles

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