Games

19 pages, 619 KB

Open AccessArticle

A Generalized Nash Equilibrium Approach to the Inverse Eigenvector Centrality Problem

by Mauro Passacantando and Fabio Raciti

Games 2026, 17(2), 20; https://doi.org/10.3390/g17020020 - 7 Apr 2026

Eigenvector-based centrality captures recursive notions of importance in networks. While the direct problem computes centrality from given edge weights, the inverse eigenvector centrality problem seeks edge weights that reproduce a prescribed centrality profile; for directed multigraphs, this inverse task is typically non-unique and [...] Read more.

Eigenvector-based centrality captures recursive notions of importance in networks. While the direct problem computes centrality from given edge weights, the inverse eigenvector centrality problem seeks edge weights that reproduce a prescribed centrality profile; for directed multigraphs, this inverse task is typically non-unique and depends on the admissible arc structure. We study the direct and inverse problems on directed multigraphs and derive an explicit linear characterization of the set of admissible edge-weight vectors that are compatible with a given centrality target. On this feasible set, we formulate a generalized Nash equilibrium problem with shared centrality constraints, in which multiple agents select edge weights to maximize economically interpretable payoffs that incorporate arc-level competition effects. We provide conditions under which the induced game admits a concave potential function, yielding equilibrium existence and, under standard strict concavity assumptions, uniqueness. Finally, we illustrate the model on an airport network where nodes represent airports and parallel arcs represent airline-specific routes, showing that equilibrium selection produces a feasible and interpretable weight configuration that preserves the prescribed centrality. Full article

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17 pages, 283 KB

Open AccessArticle

Monopoly and Endogenous Single Highest Quality

by Amit Gayer

Games 2026, 17(2), 19; https://doi.org/10.3390/g17020019 - 6 Apr 2026

Abstract

This paper analyzes a monopolistic market with a continuum of consumers in the linear case. Consumers are vertically differentiated by a one-dimensional preference for quality, and the monopolist is allowed to offer a menu of quality-price pairs. The analysis shows that, in the [...] Read more.

This paper analyzes a monopolistic market with a continuum of consumers in the linear case. Consumers are vertically differentiated by a one-dimensional preference for quality, and the monopolist is allowed to offer a menu of quality-price pairs. The analysis shows that, in the linear case, the monopolist’s optimal offer endogenously collapses to a single quality-price pair, where the quality equals the highest feasible level. In addition, welfare maximization is achieved if and only if the market is fully served in equilibrium. Full article

(This article belongs to the Special Issue Game Theory in Economics: Recent Advances in Spatial Competition)

22 pages, 445 KB

Open AccessArticle

by Timothy Flannery

Games 2026, 17(2), 18; https://doi.org/10.3390/g17020018 - 31 Mar 2026

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Abstract

Randomized response is a widely used survey technique for measuring stigmatized populations, but it may provide limited information in small samples. This paper introduces a method of elicitation through perfectly correlated questions, showing that correlation can substantially improve statistical performance and allow a [...] Read more.

Randomized response is a widely used survey technique for measuring stigmatized populations, but it may provide limited information in small samples. This paper introduces a method of elicitation through perfectly correlated questions, showing that correlation can substantially improve statistical performance and allow a dominant-strategy mechanism when either the interviewer or respondents hold symmetric beliefs. The framework also allows the interviewer to possess private information about the distribution of questions, further relaxing incentive constraints. Building on an existing survey design game framework, the paper introduces a novel efficiency-normalized comparison that holds statistical performance constant across mechanisms, enabling a direct comparison of incentives. The analysis characterizes incentive properties and estimation under correlated questions and randomized response, and identifies when it is optimal to ask respondents directly, use randomized response, or correlate questions. Full article

(This article belongs to the Special Issue Advancements in Social Choice and Mechanism Design)

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36 pages, 627 KB

Open AccessArticle

Cooperation or Confrontation? An Evolutionary Game Study on Content Clipping Authorization in Live Streaming E-Commerce Under Platform Regulation

by Feng Luo, Xinmiao Zhao and Tiantong Xu

Games 2026, 17(2), 17; https://doi.org/10.3390/g17020017 - 27 Mar 2026

Viewed by 236

Abstract

The rapid rise of live-streaming e-commerce has fostered a new “content clipping” model, in which secondary creators edit and republish anchors’ live-streaming content to promote product sales. While this model can expand market reach and enhance revenue, it also introduces copyright disputes, regulatory [...] Read more.

The rapid rise of live-streaming e-commerce has fostered a new “content clipping” model, in which secondary creators edit and republish anchors’ live-streaming content to promote product sales. While this model can expand market reach and enhance revenue, it also introduces copyright disputes, regulatory challenges, and profit-sharing conflicts among platforms, anchors, and secondary creators. This study develops a three-party evolutionary game model to examine strategic choices regarding platform regulation, anchor authorization, and secondary content creation. Results reveal that excessive regulation may undermine equilibrium and profitability, while appropriate authorization can balance risk and reward. Secondary creators’ participation is sensitive to commission rates and cost–benefit trade-offs. This research contributes to the literature by integrating copyright governance into live-streaming e-commerce game theory and offers actionable insights for designing regulatory mechanisms, optimizing authorization policies, and fostering sustainable multi-party collaboration. Full article

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

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28 pages, 7213 KB

Open AccessArticle

Platform Empowerment and Digital Inclusion in Industrial Clusters: A Complex Network Game Analysis with Performance Feedback

by Dingteng Wang, Chengwei Liu and Shuping Wang

Games 2026, 17(2), 16; https://doi.org/10.3390/g17020016 - 10 Mar 2026

Viewed by 322

Abstract

The digital divide between large enterprises and SMEs (Small and Medium-sized Enterprises) within industrial clusters poses a significant challenge to achieving collective digital transformation, exacerbated by the quasi-public goods, attributes of digital inclusion ecosystems, and the prevalence of free-riding behavior. This paper investigates [...] Read more.

The digital divide between large enterprises and SMEs (Small and Medium-sized Enterprises) within industrial clusters poses a significant challenge to achieving collective digital transformation, exacerbated by the quasi-public goods, attributes of digital inclusion ecosystems, and the prevalence of free-riding behavior. This paper investigates whether platform enterprises, as core actors occupying structural holes in cluster networks, can foster the co-construction of a digitally inclusive ecosystem. We developed a complex network public goods game model, incorporating performance feedback into a modified Fermi learning to capture firms’ adaptive decision-making based on historical and social aspirations. The model simulates strategic interactions on both small-world and scale-free networks, characteristic of industrial clusters. Numerical simulations reveal that: (1) The core driver of co-construction is the investment return coefficient; (2) Performance feedback amplifies individual rationality, accelerating the formation or collapse of cooperation depending on the investment return coefficient; (3) Platform empowerment—specifically, selectively connecting and incentivizing cooperative firms—effectively promotes ecosystem co-construction, with this strategy proving most impactful when investment returns are moderate. Furthermore, while this selective empowerment strategy benefits the cluster overall, its effect on the platform’s own revenue is network-dependent, showing a more pronounced decline in small-world structures. This study provides a novel analytical framework for understanding strategic interactions in digital inclusion and offers practical insights for policymakers and platform leaders in orchestrating collaborative digital transformation. Full article

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23 pages, 414 KB

Open AccessFeature PaperArticle

Measuring Pitcher Production Fairly in Baseball Using the Shapley Value

by Michael McBride

Games 2026, 17(2), 15; https://doi.org/10.3390/g17020015 - 10 Mar 2026

Viewed by 290

Abstract

This paper introduces fairer measures of individual pitcher performance in baseball using the Shapley Value from coalitional game theory. The paper’s key conceptual innovation is a novel two-stage procedure for constructing the coalitionary game value functions for runs allowed and outs recorded by [...] Read more.

This paper introduces fairer measures of individual pitcher performance in baseball using the Shapley Value from coalitional game theory. The paper’s key conceptual innovation is a novel two-stage procedure for constructing the coalitionary game value functions for runs allowed and outs recorded by a baseball team’s defense. This procedure enables the Shapley Value calculation to fairly divide credit for runs and out between different pitchers and between pitchers and fielders. It also results in two new statistics—Shapley Pitcher Runs (SPR) and Shapley Pitcher Outs (SPO)—that, unlike traditional pitching statistics, consistently satisfy several mathematical fairness axioms. A third statistic, called Shapley Run Average, provides a fairer measure of pitcher efficiency. I calculate these statistics for the 2022 Major League Baseball regular season and the 1955–2022 World Series championships. Using SPR and SPO as the standard for fairness, empirical analysis reveals that the traditional pitching statistics systematically and unfairly overcredit pitchers by 40–50%, with starting pitchers miscredited more severely than relievers. Analysis of SRA identifies efficient pitchers whose performance is obscured by conventional statistics and enables a reassessment of historic World Series performances. Overall, this work demonstrates another application of the Shapley Value to creating new performance measures in team sports. Full article

(This article belongs to the Section Applied Game Theory)

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12 pages, 270 KB

Open AccessEssay

Cooperation Collapse in the Harmony Game: Revisiting Scodel and Minas Through Evolutionary Game Theory

by Shade T. Shutters

Games 2026, 17(2), 14; https://doi.org/10.3390/g17020014 - 9 Mar 2026

Viewed by 449

Abstract

Between 1959 and 1962, Alvin Scodel, J. Sayer Minas, and colleagues conducted some of the earliest laboratory studies of strategic interaction using non-zero-sum games. Working at the margins of economics in the Journal of Conflict Resolution, they documented a striking pattern: subjects [...] Read more.

Between 1959 and 1962, Alvin Scodel, J. Sayer Minas, and colleagues conducted some of the earliest laboratory studies of strategic interaction using non-zero-sum games. Working at the margins of economics in the Journal of Conflict Resolution, they documented a striking pattern: subjects frequently chose options that reduced an opponent’s payoff by more than their own, even when mutual cooperation was both individually and collectively optimal. These results—especially the behavior observed in their so-called Game H4, a Harmony Game in which cooperation strictly dominated defection—anticipate a central insight of evolutionary game theory: what matters for adaptation is relative payoff, not absolute gain. This essay reinterprets the Scodel–Minas experiments through a Darwinian lens, arguing that they provide an early empirical challenge to Nash-equilibrium reasoning and to models that evaluate strategies solely in terms of absolute utility. By reconstructing the H4 payoff structure and embedding it within a simple evolutionary framework, I show how small levels of “competitive” behavior can destabilize cooperative equilibria that appear self-evident under standard assumptions. I then revisit three later “puzzles” in the evolution of cooperation—altruistic punishment, the fragility of “win–win” treaties, and rejections in ultimatum bargaining—to ask how differently they might have been framed had the Scodel–Minas findings been part of the canonical experimental literature. Rather than treating these phenomena as surprising anomalies, a historically informed, relative-payoff perspective suggests that they could have been recognized much earlier as natural expressions of an already documented pattern. Full article

(This article belongs to the Special Issue Evolution of Cooperation and Evolutionary Game Theory)

20 pages, 888 KB

Open AccessArticle

How to Sell Debt (But Not Money)

by Arup Daripa

Games 2026, 17(2), 13; https://doi.org/10.3390/g17020013 - 9 Mar 2026

Viewed by 347

Abstract

Multi-unit common value auctions in which bidders submit demand functions are used for a variety of purposes, including selling government debt (Treasury auctions) and allocating liquidity (repo auctions). Typically, either a discriminatory or a uniform-price format is used. In this paper, we consider [...] Read more.

Multi-unit common value auctions in which bidders submit demand functions are used for a variety of purposes, including selling government debt (Treasury auctions) and allocating liquidity (repo auctions). Typically, either a discriminatory or a uniform-price format is used. In this paper, we consider the incentive for participation by relatively uninformed bidders in the presence of more informed bidders under these formats. We characterize the equilibrium under a discriminatory auction and show that discriminatory pricing inhibits uninformed participation. In contrast, the equilibria we construct under a uniform pricing rule show that profitable uninformed participation can occur. The usefulness of widening participation in Treasury auctions makes the latter format a natural choice in these auctions, providing an explanation for the switch to the uniform-price format in US Treasury auctions. We also apply our results to repo auctions and show that a uniform-price format can reduce the ability of a central bank to steer interest rates. This sheds light on the reason for the switch away from the uniform-price format by several central banks in conducting repo auctions. We also consider the question of information aggregation and show that uniform-price auctions might fail to do so. The results also offer an explanation for the fact that the ECB, as well as several other central banks, prefer to allocate liquidity through a fixed-rate tender rather than either uniform-price or discriminatory auctions. Full article

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Games, Volume 17, Issue 2 (April 2026) – 8 articles

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