Games

18 pages, 315 KiB

Open AccessArticle

Fair Allocation in Crowd-Sourced Systems

by Mishal Assif, William Kennedy and Iraj Saniee

Games 2023, 14(4), 57; https://doi.org/10.3390/g14040057 - 15 Aug 2023

Viewed by 1625

In this paper, we address the problem of fair sharing of the total value of a crowd-sourced network system between major participants (founders) and minor participants (crowd) using cooperative game theory. We use the framework of a Shapley allocation which is regarded as [...] Read more.

In this paper, we address the problem of fair sharing of the total value of a crowd-sourced network system between major participants (founders) and minor participants (crowd) using cooperative game theory. We use the framework of a Shapley allocation which is regarded as a fundamental method of computing the fair share of all participants in a cooperative game when the values of all possible coalitions could be quantified. To quantify the value of all coalitions, we define a class of value functions for crowd-sourced systems which capture the contributions of the founders and the crowd plausibly and derive closed-form expressions for Shapley allocations to both. These value functions are defined for different scenarios, such as the presence of oligopolies or geographic spread of the crowd, taking network effects, including Metcalfe’s law, into account. A key result we obtain is that under quite general conditions, the crowd participants are collectively owed a share between

\frac{1}{2}

and

\frac{2}{3}

of the total value of the crowd-sourced system. We close with an empirical analysis demonstrating the consistency of our results with the compensation offered to the crowd participants in some public internet content sharing companies. Full article

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

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11 pages, 278 KiB

Open AccessArticle

Duopoly and Endogenous Single Product Quality Strategies

by Amit Gayer

Games 2023, 14(4), 56; https://doi.org/10.3390/g14040056 - 15 Aug 2023

Viewed by 1017

Abstract

This research paper investigates a duopolistic market characterized by vertical product differentiation. The study considers both product qualities and consumer preferences represented as one-dimensional intervals. The focus is on analyzing the equilibrium in a duopoly game with convex production costs. In this setting, [...] Read more.

This research paper investigates a duopolistic market characterized by vertical product differentiation. The study considers both product qualities and consumer preferences represented as one-dimensional intervals. The focus is on analyzing the equilibrium in a duopoly game with convex production costs. In this setting, each firm has the option to present a multi-product strategy consisting of quality–price pairs, and their profits are determined by the decisions made by consumers. The findings of the study reveal that, under typical consumer preference conditions, both firms tend to offer a single quality–price pair. Additionally, the market is shown to be fully served, and firm profits decrease as the index of product quality increases. A comparative analysis is also conducted with the case of a monopoly. Full article

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

10 pages, 261 KiB

Open AccessArticle

Asymmetric Reimbursement and Contingent Fees in Environmental Conflicts: Observable vs. Unobservable Contracts

by Sung-Hoon Park and Chad E. Settle

Games 2023, 14(4), 55; https://doi.org/10.3390/g14040055 - 28 Jul 2023

Viewed by 984

Abstract

We investigate the impact of observability of contracts between a plaintiff and his attorney on both the efficiency of the environmental conflict and the fairness of the resulting outcome from the environmental conflict. By including two specific game-theoretic models (an observable-contract game and [...] Read more.

We investigate the impact of observability of contracts between a plaintiff and his attorney on both the efficiency of the environmental conflict and the fairness of the resulting outcome from the environmental conflict. By including two specific game-theoretic models (an observable-contract game and an unobservable-contract game), we find two key results: (i) The unobservability of a contract may increase inefficiency of the environmental conflict in terms of legal efforts; however, (ii) the unobservability of a contract may increase the fairness of the outcome in terms of the plaintiff’s probability of winning the contest. Full article

(This article belongs to the Special Issue Fairness in Non-cooperative Strategic Interactions)

9 pages, 262 KiB

Open AccessCommunication

Stackelberg Social Equilibrium in Water Markets

by Harold Houba and Françeska Tomori

Games 2023, 14(4), 54; https://doi.org/10.3390/g14040054 - 11 Jul 2023

Viewed by 1215

Abstract

Market power in water markets can be modeled as simultaneous quantity competition on a river structure and analyzed by applying social equilibrium. In an example of a duopoly water market, we argue that the lack of backward induction logic implies that the upstream [...] Read more.

Market power in water markets can be modeled as simultaneous quantity competition on a river structure and analyzed by applying social equilibrium. In an example of a duopoly water market, we argue that the lack of backward induction logic implies that the upstream supplier foregoes profitable strategic manipulation of water to the downstream supplier. To incorporate backward induction, we propose the Stackelberg social equilibrium concept. We prove the existence of Stackelberg social equilibrium in duopoly water markets with an upstream–downstream river structure and derive it in the example of a duopoly market. Full article

(This article belongs to the Special Issue Game Theory with Applications to Economics)

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8 pages, 262 KiB

Open AccessArticle

Price and Quantity Competition under Vertical Pricing

by Debasmita Basak

Games 2023, 14(4), 53; https://doi.org/10.3390/g14040053 - 29 Jun 2023

Viewed by 1107

Abstract

We consider a vertically related market where one quantity-setting and another price-setting downstream firm negotiate the terms of a two-part tariff contract with an upstream input supplier. In contrast to the traditional belief, we show that the price-setting firm produces a higher output [...] Read more.

We consider a vertically related market where one quantity-setting and another price-setting downstream firm negotiate the terms of a two-part tariff contract with an upstream input supplier. In contrast to the traditional belief, we show that the price-setting firm produces a higher output and earns a higher profit than the quantity-setting firm when bargaining is decentralised. Additionally, both firms produce the same output, whereas the profit is higher under the price-setting firm than the quantity-setting firm when bargaining is centralised. Full article

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

6 pages, 256 KiB

Open AccessArticle

Evasion Differential Game of Multiple Pursuers and a Single Evader with Geometric Constraints in ℓ²

by Gafurjan Ibragimov, Marks Ruziboev, Ibroximjon Zaynabiddinov and Bruno Antonio Pansera

Games 2023, 14(4), 52; https://doi.org/10.3390/g14040052 - 29 Jun 2023

Viewed by 964

Abstract

We investigate a differential evasion game with multiple pursuers and an evader for the infinite systems of differential equations in ℓ². The control functions of the players are subject to geometric constraints. The pursuers’ goal is to bring the state of [...] Read more.

We investigate a differential evasion game with multiple pursuers and an evader for the infinite systems of differential equations in ℓ². The control functions of the players are subject to geometric constraints. The pursuers’ goal is to bring the state of at least one of the controlled systems to the origin of ℓ², while the evader’s goal is to prevent this from happening in a finite interval of time. We derive a sufficient condition for evasion from any initial state and construct an evasion strategy for the evader. Full article

(This article belongs to the Special Issue Applications of Differential Game and Its Related Theories in Mathematics and Economics)

10 pages, 268 KiB

Open AccessArticle

Power Indices under Specific Multicriteria Status

by Yu-Hsien Liao

Games 2023, 14(4), 51; https://doi.org/10.3390/g14040051 - 27 Jun 2023

Viewed by 717

Abstract

By considering the maximal efficacy among allocation vectors, we define two power indices under specific multicriteria conditions. Additionally, we introduce a reduction approach to the axiomatic framework for these power indices. Furthermore, we propose an alternative formulation that focuses on discrepancy mapping. Based [...] Read more.

By considering the maximal efficacy among allocation vectors, we define two power indices under specific multicriteria conditions. Additionally, we introduce a reduction approach to the axiomatic framework for these power indices. Furthermore, we propose an alternative formulation that focuses on discrepancy mapping. Based on reduction and discrepancy mapping, we also provide two dynamic procedures. Full article

(This article belongs to the Special Issue Advances in Game Theory, Multi-Agent Systems, and Computer Security)

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Games, Volume 14, Issue 4 (August 2023) – 7 articles

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