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Games, Volume 15, Issue 2 (April 2024) – 10 articles

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16 pages, 1716 KiB  
Article
The Evolution of Cooperation and Diversity under Integrated Indirect Reciprocity
by Tatsuya Sasaki, Satoshi Uchida, Isamu Okada and Hitoshi Yamamoto
Games 2024, 15(2), 15; https://doi.org/10.3390/g15020015 - 18 Apr 2024
Viewed by 546
Abstract
Indirect reciprocity is one of the major mechanisms driving the evolution of cooperation in human societies. There are two types of indirect reciprocity: upstream and downstream reciprocity. Cooperation in downstream reciprocity follows the pattern ‘You helped someone, and I will help you’, while [...] Read more.
Indirect reciprocity is one of the major mechanisms driving the evolution of cooperation in human societies. There are two types of indirect reciprocity: upstream and downstream reciprocity. Cooperation in downstream reciprocity follows the pattern ‘You helped someone, and I will help you’, while the direction of cooperation is reversed in upstream reciprocity, which follows the pattern ‘You helped me, and I will help someone else’. These two types of indirect reciprocity often occur in combination. However, upstream and downstream reciprocity have mostly been theoretically studied in isolation. In this study, we propose a new model that integrates both types of reciprocity. In particular, we apply the standard giving-game framework of indirect reciprocity and analyze the three-strategy model including reciprocal altruists, indiscriminate altruists, and free riders using evolutionary game theory. We show that the model allows reciprocal altruists and free riders to coexist stably in well-mixed populations. We also find that by accounting for inattention in the assessment rule, the stability of this mixed equilibrium can be strengthened to prevent the invasion of infamous indiscriminate altruists and can even be made globally stable. Full article
(This article belongs to the Section Cooperative Game Theory and Bargaining)
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23 pages, 832 KiB  
Article
Quid Pro Quo Diplomacy
by Matt Malis and Alastair Smith
Games 2024, 15(2), 14; https://doi.org/10.3390/g15020014 - 17 Apr 2024
Viewed by 251
Abstract
Political leaders value public demonstrations of support from foreign leaders and frequently make concessions in order to obtain them. We model the bargaining dynamics surrounding these exchanges and their impact on the recipient leader’s political survival, with a focus on top-level diplomatic visits [...] Read more.
Political leaders value public demonstrations of support from foreign leaders and frequently make concessions in order to obtain them. We model the bargaining dynamics surrounding these exchanges and their impact on the recipient leader’s political survival, with a focus on top-level diplomatic visits as a means of signaling international support. Our model addresses two interrelated questions; first, we consider how symbolic displays of support from one leader to another can be informative even when they are “purchased” with concessions, and second, we derive the equilibrium price and political impact of a visit under different bargaining protocols. The incentive to make a concession in exchange for a visit generally undermines a visit’s signaling value. We identify a diplomatic resource curse, where the existence of opportunities for diplomatic exchange can force leaders into accepting visit-for-concession deals that leave them worse off than if they were diplomatically isolated. Visits never occur when negotiations are fully transparent. Mutually beneficial quid pro quo diplomacy requires opacity in negotiations. Full article
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28 pages, 1953 KiB  
Article
Dynamic Awareness and Strategic Adaptation in Cybersecurity: A Game-Theory Approach
by Katarina Kostelić
Games 2024, 15(2), 13; https://doi.org/10.3390/g15020013 - 08 Apr 2024
Viewed by 391
Abstract
Awareness and human factors are becoming ever more important in cybersecurity, particularly in the context of small companies that may need more resources to deal with cybersecurity effectively. This paper introduces a theoretical framework for game analysis of the role of awareness in [...] Read more.
Awareness and human factors are becoming ever more important in cybersecurity, particularly in the context of small companies that may need more resources to deal with cybersecurity effectively. This paper introduces a theoretical framework for game analysis of the role of awareness in strategic interactions between the manager and a hacker. A computable approach is proposed based on Bayesian updating to model awareness in a cybersecurity context. The process of gaining awareness considers the manager’s perception of the properties of the hacker’s actions, game history, and common knowledge. The role of awareness in strategy choices and outcomes is analyzed and simulated, providing insights into decision-making processes for managers and highlighting the need to consider probabilistic assessments of threats and the effectiveness of countermeasures. The accuracy of the initial frequencies plays a significant role in the manager’s success, with aligned frequencies leading to optimal results. Inaccurate information on prior frequencies still outperforms complete uncertainty, emphasizing the value of any available intelligence. However, the results suggest that other awareness modeling approaches are necessary to enhance the manager’s agility and adaptiveness when the prior frequencies do not reflect the immediate attacker’s type, indicating the need for improved intelligence about cyber-attacks and examinations of different awareness modeling approaches. Full article
(This article belongs to the Special Issue Game Theory for Cybersecurity and Privacy)
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12 pages, 1648 KiB  
Article
Physics-Informed Graph Neural Operator for Mean Field Games on Graph: A Scalable Learning Approach
by Xu Chen, Shuo Liu and Xuan Di
Games 2024, 15(2), 12; https://doi.org/10.3390/g15020012 - 30 Mar 2024
Viewed by 588
Abstract
Mean-field games (MFGs) are developed to model the decision-making processes of a large number of interacting agents in multi-agent systems. This paper studies mean-field games on graphs (G-MFGs). The equilibria of G-MFGs, namely, mean-field equilibria (MFE), are challenging to solve [...] Read more.
Mean-field games (MFGs) are developed to model the decision-making processes of a large number of interacting agents in multi-agent systems. This paper studies mean-field games on graphs (G-MFGs). The equilibria of G-MFGs, namely, mean-field equilibria (MFE), are challenging to solve for their high-dimensional action space because each agent has to make decisions when they are at junction nodes or on edges. Furthermore, when the initial population state varies on graphs, we have to recompute MFE, which could be computationally challenging and memory-demanding. To improve the scalability and avoid repeatedly solving G-MFGs every time their initial state changes, this paper proposes physics-informed graph neural operators (PIGNO). The PIGNO utilizes a graph neural operator to generate population dynamics, given initial population distributions. To better train the neural operator, it leverages physics knowledge to propagate population state transitions on graphs. A learning algorithm is developed, and its performance is evaluated on autonomous driving games on road networks. Our results demonstrate that the PIGNO is scalable and generalizable when tested under unseen initial conditions. Full article
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39 pages, 480 KiB  
Article
Matching with Nonexclusive Contracts
by Daniel Ripperger-Suhler
Games 2024, 15(2), 11; https://doi.org/10.3390/g15020011 - 30 Mar 2024
Viewed by 612
Abstract
A variety of empirical papers document the coexistence of exclusive and nonexclusive contracts within a given market across a multitude of industries. However, the theoretical literature has not been able to generate a differentiable model with the coexistence of these contracts. I rectify [...] Read more.
A variety of empirical papers document the coexistence of exclusive and nonexclusive contracts within a given market across a multitude of industries. However, the theoretical literature has not been able to generate a differentiable model with the coexistence of these contracts. I rectify the gap in the literature by developing a theoretical model of two-sided matching, in which principals and agents choose between exclusive and nonexclusive contracts with cost-of-effort inefficiencies. I find that the coexistence of contracts relies on cost-sharing between principals, relative bargaining power, and an endogenous outside option. I also find that the pattern of contracts is monotonic with respect to the type distributions of principals and agents. Full article
(This article belongs to the Special Issue Industrial Organization and Organizational Economics)
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29 pages, 1297 KiB  
Article
Random Informative Advertising with Vertically Differentiated Products
by Rim Lahmandi-Ayed and Didier Laussel
Games 2024, 15(2), 10; https://doi.org/10.3390/g15020010 - 22 Mar 2024
Viewed by 525
Abstract
We study a simple model in which two vertically differentiated firms compete in prices and mass advertising on an initially uninformed market. Consumers differ in their preference for quality. There is an upper bound on prices since consumers cannot spend more on the [...] Read more.
We study a simple model in which two vertically differentiated firms compete in prices and mass advertising on an initially uninformed market. Consumers differ in their preference for quality. There is an upper bound on prices since consumers cannot spend more on the good than a fixed amount (say, their income). Depending on this income and on the ratio between the advertising cost and quality differential (relative advertising cost), either there is no equilibrium in pure strategies or there exists one of the following three types: (1) an interior equilibrium, where both firms have positive natural markets and charge prices lower than the consumer’s income; (2) a constrained interior equilibrium, where both firms have positive natural markets, and the high-quality firm charges the consumer’s income or (3) a corner equilibrium, where the low-quality firm has no natural market selling only to uninformed customers. We show that no corner equilibrium exists in which the high-quality firm would have a null natural market. At an equilibrium (whenever there exists one), the high-quality firm always advertises more, charges a higher price and makes a higher profit than the low-quality one. As the relative advertising cost goes to infinity, prices become equal and the advertising intensities converge to zero as well as the profits. Finally, the advertising intensities are, at least globally, increasing with the quality differential. Finally, in all cases, as the advertising parameter cost increases unboundedly, both prices converge increasingly towards the consumer’s income. Full article
(This article belongs to the Special Issue Game Theory in Economics: Recent Advances in Spatial Competition)
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23 pages, 570 KiB  
Article
Dynamic Vertical Foreclosure with Learning-by-Doing Production Technologies
by Frago Kourandi and Nikolaos Vettas
Games 2024, 15(2), 9; https://doi.org/10.3390/g15020009 - 29 Feb 2024
Viewed by 760
Abstract
Here, we study vertical foreclosure in a dynamic setup with learning-by-doing production technologies. There is a downstream monopoly and an upstream duopoly, where manufacturers produce differentiated products and can gain proficiency through the accumulation of their production. We study the dynamic interactions in [...] Read more.
Here, we study vertical foreclosure in a dynamic setup with learning-by-doing production technologies. There is a downstream monopoly and an upstream duopoly, where manufacturers produce differentiated products and can gain proficiency through the accumulation of their production. We study the dynamic interactions in the vertical chain when the monopolist sets the prices; we find that customer foreclosure may arise in equilibrium when the products are close substitutes and be welfare-enhancing. The rate of learning is lower than the social optimal and a social planner would tend to impose exclusivity more often compared to the downstream monopolist. Full article
(This article belongs to the Special Issue Industrial Organization and Organizational Economics)
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26 pages, 5292 KiB  
Article
Imitation Dynamics in Oligopoly Games with Heterogeneous Players
by Daan Lindeman and Marius I. Ochea
Games 2024, 15(2), 8; https://doi.org/10.3390/g15020008 - 28 Feb 2024
Viewed by 715
Abstract
We investigate the role and performance of imitative behavior in a class of quantity-setting, Cournot games. Within a framework of evolutionary competition between rational, myopic best-response and imitation heuristics with differential heuristics’ costs, we found that the equilibrium stability depends on the sign [...] Read more.
We investigate the role and performance of imitative behavior in a class of quantity-setting, Cournot games. Within a framework of evolutionary competition between rational, myopic best-response and imitation heuristics with differential heuristics’ costs, we found that the equilibrium stability depends on the sign of the cost differential between the unstable heuristic (Cournot best-response) and the stable one (imitation) and on the intensity of the evolutionary pressure. When this cost differential is positive (i.e., imitation is relatively cheaper vis a vis Cournot), most firms use this heuristic and the Cournot equilibrium is stabilized for market sizes for which it was unstable under Cournot homogeneous learning. However, as the number of firms increases (n=7), instability eventually sets in. When the cost differential is negative (imitation is more expensive than Cournot), complicated quantity fluctuations, along with the co-existence of heuristics, arise already for the triopoly game. Full article
(This article belongs to the Section Learning and Evolution in Games)
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10 pages, 368 KiB  
Article
Nash Equilibria in Two-Resource Congestion Games with Player-Specific Payoff Functions
by Fatima Khanchouche, Samir Sbabou, Hatem Smaoui and Abderrahmane Ziad
Games 2024, 15(2), 7; https://doi.org/10.3390/g15020007 - 26 Feb 2024
Viewed by 795
Abstract
In this paper, we examine the class of congestion games with player-specific payoff functions introduced by Milchtaich, I. (1996). Focusing on the special case of two resources, we give a short and simple method for identifying all Nash equilibria in pure strategies. We [...] Read more.
In this paper, we examine the class of congestion games with player-specific payoff functions introduced by Milchtaich, I. (1996). Focusing on the special case of two resources, we give a short and simple method for identifying all Nash equilibria in pure strategies. We also provide a computation algorithm based on our theoretical analysis. Full article
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15 pages, 408 KiB  
Article
A Model of Competing Gangs in Networks
by Alexis Poindron and Nizar Allouch
Games 2024, 15(2), 6; https://doi.org/10.3390/g15020006 - 21 Feb 2024
Viewed by 849
Abstract
Two groups produce a network good perceived by a third party, such as a police or military institution, as a ‘public bad’, referred to as ‘crime’ for simplicity. These two groups, considered mafias, are assumed to be antagonists, whether they are enemies or [...] Read more.
Two groups produce a network good perceived by a third party, such as a police or military institution, as a ‘public bad’, referred to as ‘crime’ for simplicity. These two groups, considered mafias, are assumed to be antagonists, whether they are enemies or competitors in the same market, causing harm to each other’s activities. This paper provides guidelines for the policymaker, typically the police, seeking to minimize overall crime levels by internalizing these negative externalities. One specific question is investigated: the allocation of resources for the police. In general, we recommend a balanced crackdown on both antagonists, but an imbalance in group sizes may lead the police to focus on the more criminal group. Full article
(This article belongs to the Section Applied Game Theory)
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