Games

15 pages, 373 KiB

Open AccessArticle

A Differential Game for Optimal Water Price Management

by Andrea Caravaggio, Luigi De Cesare and Andrea Di Liddo

Games 2023, 14(2), 33; https://doi.org/10.3390/g14020033 - 05 Apr 2023

Viewed by 1270

This article studies a leader–follower differential game with a finite horizon, where a single buyer reacts to the selling price set by an agency (water supplier). The Open-Loop Stackelberg equilibrium is calculated, assuming that the user demand is fully satisfied (that is, the [...] Read more.

This article studies a leader–follower differential game with a finite horizon, where a single buyer reacts to the selling price set by an agency (water supplier). The Open-Loop Stackelberg equilibrium is calculated, assuming that the user demand is fully satisfied (that is, the interior solution is considered), and the following different tariff schemes are analyzed: linear scheme, increasing block tariff, and convex tariff. Numerical simulations highlight how tariff convexity and seasonality in buyer’s preferences affect water price and demand, and the dynamics of the basin over time. The study shows that synchrony or asynchrony between basin recharge and buyer cyclical demand can dramatically affect the dynamics and basin levels observed at the end of the time period considered. Additionally, the presence of a large number of fluctuations in buyer preferences affects basin fluctuations, while natural recharge may help in maintaining acceptable levels of future water demands. Full article

(This article belongs to the Special Issue Game Theory Applications to Socio-Environmental Studies, Development Economics and Sustainability Research)

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15 pages, 418 KiB

Open AccessArticle

Measuring the Difficulties in Forming a Coalition Government

by Tobias Hiller

Games 2023, 14(2), 32; https://doi.org/10.3390/g14020032 - 31 Mar 2023

Cited by 1 | Viewed by 2079

Abstract

Electoral thresholds in the context of parliamentary elections are an instrument for preventing the fragmentation of parliaments and facilitate the formation of a coalition government. However, the clauses also introduce distortions and modify the equality of electoral votes in an election. In order [...] Read more.

Electoral thresholds in the context of parliamentary elections are an instrument for preventing the fragmentation of parliaments and facilitate the formation of a coalition government. However, the clauses also introduce distortions and modify the equality of electoral votes in an election. In order to decide to what extent these negative effects can be accepted, it is necessary to measure the difficulties in forming a coalition government and to quantify the effects of electoral thresholds on these difficulties. For this issue, we introduce a concept based on cooperative game theory which takes into account the distribution of seats in parliament and coalition statements of parties. Full article

(This article belongs to the Section Applied Game Theory)

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6 pages, 253 KiB

Open AccessArticle

Equivalent Modes of Reimbursement in Augmented Contests

by Chen Cohen, Roy Darioshi and Shmuel Nitzan

Games 2023, 14(2), 31; https://doi.org/10.3390/g14020031 - 31 Mar 2023

Viewed by 876

Abstract

This article presents an equivalence theorem in the context of Tullock’s augmented lottery contest with external or internal cost reimbursement. Three alternative modes of reimbursement are studied. The equivalence implies that, even though the augmented contest is vulnerable to framing biases, it is [...] Read more.

This article presents an equivalence theorem in the context of Tullock’s augmented lottery contest with external or internal cost reimbursement. Three alternative modes of reimbursement are studied. The equivalence implies that, even though the augmented contest is vulnerable to framing biases, it is strategically neutral. Full article

23 pages, 486 KiB

Open AccessArticle

Robust Satisfaction of Metric Interval Temporal Logic Objectives in Adversarial Environments

by Luyao Niu, Bhaskar Ramasubramanian, Andrew Clark and Radha Poovendran

Games 2023, 14(2), 30; https://doi.org/10.3390/g14020030 - 30 Mar 2023

Viewed by 1181

Abstract

This paper studies the synthesis of controllers for cyber-physical systems (CPSs) that are required to carry out complex time-sensitive tasks in the presence of an adversary. The time-sensitive task is specified as a formula in the metric interval temporal logic (MITL). CPSs that [...] Read more.

This paper studies the synthesis of controllers for cyber-physical systems (CPSs) that are required to carry out complex time-sensitive tasks in the presence of an adversary. The time-sensitive task is specified as a formula in the metric interval temporal logic (MITL). CPSs that operate in adversarial environments have typically been abstracted as stochastic games (SGs); however, because traditional SG models do not incorporate a notion of time, they cannot be used in a setting where the objective is time-sensitive. To address this, we introduce durational stochastic games (DSGs). DSGs generalize SGs to incorporate a notion of time and model the adversary’s abilities to tamper with the control input (actuator attack) and manipulate the timing information that is perceived by the CPS (timing attack). We define notions of spatial, temporal, and spatio-temporal robustness to quantify the amounts by which system trajectories under the synthesized policy can be perturbed in space and time without affecting satisfaction of the MITL objective. In the case of an actuator attack, we design computational procedures to synthesize controllers that will satisfy the MITL task along with a guarantee of its robustness. In the presence of a timing attack, we relax the robustness constraint to develop a value iteration-based procedure to compute the CPS policy as a finite-state controller to maximize the probability of satisfying the MITL task. A numerical evaluation of our approach is presented on a signalized traffic network to illustrate our results. Full article

(This article belongs to the Special Issue Game-Theoretic Analysis of Network Security and Privacy)

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11 pages, 1707 KiB

Open AccessArticle

Network Externalities and Downstream Collusion under Asymmetric Costs: A Note

by Jen-Yao Lee, Chen-Chia Fan and Chien-Shu Tsai

Games 2023, 14(2), 29; https://doi.org/10.3390/g14020029 - 30 Mar 2023

Viewed by 1241

Abstract

This paper considers the collusive stability of downstream competition in a vertical market with network externalities and cost asymmetry. A dynamic collusion game is constructed, and backward induction is employed to solve the subgame perfect Nash equilibrium. We show that larger network externalities [...] Read more.

This paper considers the collusive stability of downstream competition in a vertical market with network externalities and cost asymmetry. A dynamic collusion game is constructed, and backward induction is employed to solve the subgame perfect Nash equilibrium. We show that larger network externalities lead to less collusive incentive for an inefficient firm, while for an efficient firm, this depends on the efficiency gap. An increase in network externalities will destabilize the downstream collusion when the cost asymmetry is large and network externalities are relatively weak. Full article

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4 pages, 152 KiB

Open AccessEditorial

A Yin and Yang Perspective on the Trust Game: Trust and Reciprocity

by Frank Krueger

Games 2023, 14(2), 28; https://doi.org/10.3390/g14020028 - 23 Mar 2023

Viewed by 1295

Abstract

Trust and reciprocity are fundamental for the cohesion and stability of human society, as they are essential components of cooperative exchange [...] Full article

(This article belongs to the Special Issue A Yin and Yang Perspective on the Trust Game: Trust and Reciprocity)

3 pages, 162 KiB

Open AccessEditorial

Advances in the Theory and Applications of Contests and Tournaments: Introduction to the Special Issue

by Theofanis Tsoulouhas

Games 2023, 14(2), 27; https://doi.org/10.3390/g14020027 - 17 Mar 2023

Viewed by 1075

Abstract

The theory of relative performance evaluation has come a long way since its inception, so much so that it is now a major research branch in economic theory [...] Full article

(This article belongs to the Special Issue Advances in the Theory and Applications of Contests and Tournaments)

18 pages, 304 KiB

Open AccessArticle

Efficient Decentralized Leadership under Hybrid Work and Attachment to Regions

by Naoto Aoyama and Emilson Caputo Delfino Silva

Games 2023, 14(2), 26; https://doi.org/10.3390/g14020026 - 16 Mar 2023

Viewed by 1236

Abstract

Under the ‘new normal’ in the labor market, individuals can work remotely or in person, a hybrid work mode that became ubiquitous during the pandemic. This paper studies the efficiency of decentralized leadership in federations in which hybrid work is the modus operandi. [...] Read more.

Under the ‘new normal’ in the labor market, individuals can work remotely or in person, a hybrid work mode that became ubiquitous during the pandemic. This paper studies the efficiency of decentralized leadership in federations in which hybrid work is the modus operandi. Self-interested regional governments and a benevolent central government interact strategically in dynamic games in which there are provisions of federal and regional public goods and interregional income and fiscal transfers, the population is attached to regions and hybrid work creates a common labor market in the federation. In this setting, we first show that decentralized leadership is inefficient if the center controls income transfers only. This result provides an efficiency enhancing motivation for the center to additionally control earmarked transfers: we demonstrate that decentralized leadership is efficient whenever the center controls both income and earmarked transfers. However, this is not the only federal regime in which decentralized leadership is efficient. It is efficient in the absence of earmarked transfers if it is appropriately selective: when the regional governments commit to the provision of the federal public only and the center redistributes income across regions. Full article

(This article belongs to the Special Issue Game Theory Applications to Socio-Environmental Studies, Development Economics and Sustainability Research)

28 pages, 498 KiB

Open AccessArticle

Ad-Valorem Taxes, Prices and Content Diversification in the News Market

by Armando José Garcia Pires

Games 2023, 14(2), 25; https://doi.org/10.3390/g14020025 - 16 Mar 2023

Viewed by 1335

Abstract

In this paper, we look at two research questions. First, can lower ad-valorem taxes, on the selling of news and on the selling of advertising, conduce to lower prices in the media sector? Second, can lower ad-valorem taxes stimulate firms to increase the [...] Read more.

In this paper, we look at two research questions. First, can lower ad-valorem taxes, on the selling of news and on the selling of advertising, conduce to lower prices in the media sector? Second, can lower ad-valorem taxes stimulate firms to increase the diversity of content that they offer? The purpose of this work is to give tax political guidelines to policy makers for the media sector. This is important for a sector that has seen the reduction in payment subscriptions by readers (due to competition from free news from the Internet), and reduction of advertisement revenues due to competition from media giants like Google and Facebook. With this purpose we build on the Hoteling product competition model, which is the workhorse model in media economics. We show that ad-valorem taxes on the selling of advertising are preferable to ad-valorem taxes on the selling of news because the former conduce to reduction in prices of newspaper. However, both ad-valorem taxes on the selling of news and on the selling of advertisement reduces media diversity, because they reduce revenues that media firms can use to invest in media content. Full article

(This article belongs to the Special Issue Mass Media Industries: The Economic Games)

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25 pages, 13983 KiB

Open AccessArticle

Price Competition with Differentiated Products on a Two-Dimensional Plane: The Impact of Partial Cartel on Firms’ Profits and Behavior

by Stanislav Stoykov and Ivan Kostov

Games 2023, 14(2), 24; https://doi.org/10.3390/g14020024 - 15 Mar 2023

Viewed by 2365

Abstract

A numerical procedure capable of obtaining the equilibrium states of oligopoly markets under several assumptions is presented. Horizontal and vertical product differentiation were included by taking into account Euclidean distance in a two-dimensional space and quality characteristics of the product. Different quality preferences [...] Read more.

A numerical procedure capable of obtaining the equilibrium states of oligopoly markets under several assumptions is presented. Horizontal and vertical product differentiation were included by taking into account Euclidean distance in a two-dimensional space and quality characteristics of the product. Different quality preferences of consumers were included in the model. Firms implement two strategies in the market: profit maximization and market share maximization. Numerical discretization of a two-dimensional area was performed for computing the equilibrium prices which allows one to consider any market area and any location of the firms. Four scenarios of oligopoly markets were developed by combining both strategies from one side and competitive behavior and a partial cartel agreement from another side. The main differences between the scenarios are outlined. Profits, market shares and equilibrium prices are presented and compared. The influence of collusion, the existence of participants with a market share maximization strategy and consumer preferences on the firm’s profits and equilibrium prices were examined. Cases whereby firms prefer to leave the cartel were investigated. Best locations for the setting of a new store for profit maximization are shown and discussed. Full article

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2 pages, 173 KiB

Open AccessEditorial

The “Black Box” Method for Experimental Economics

by Heinrich H. Nax

Games 2023, 14(2), 23; https://doi.org/10.3390/g14020023 - 01 Mar 2023

Viewed by 1169

Abstract

How humans behave in repeated strategic interactions, how they learn, how their decisions adapt, and how their decision-making evolves is a topic of fundamental interest in behavioral economics and behavioral game theory [...] Full article

(This article belongs to the Special Issue Learning and Evolution in Games, 1st Edition)

13 pages, 377 KiB

Open AccessReview

Matrix-Based Method for the Analysis and Control of Networked Evolutionary Games: A Survey

by Xinrong Yang, Zhenping Geng and Haitao Li

Games 2023, 14(2), 22; https://doi.org/10.3390/g14020022 - 28 Feb 2023

Viewed by 1434

Abstract

In this paper, a detailed survey is presented for the analysis and control of networked evolutionary games via the matrix method. The algebraic form of networked evolutionary games is firstly recalled. Then, some existing results on networked evolutionary games are summarized. Furthermore, several [...] Read more.

In this paper, a detailed survey is presented for the analysis and control of networked evolutionary games via the matrix method. The algebraic form of networked evolutionary games is firstly recalled. Then, some existing results on networked evolutionary games are summarized. Furthermore, several generalized forms of networked evolutionary games are reviewed, including networked evolutionary games with time delay, networked evolutionary games with bankruptcy mechanism, networked evolutionary games with time-varying networks, and random evolutionary Boolean games. The computational complexity of general networked evolutionary games is still challenging, which limits the application of the matrix method to large-scale networked evolutionary games. Future works are finally presented in the conclusion. Full article

(This article belongs to the Special Issue Applications of Game Theory with Mathematical Methods)

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14 pages, 975 KiB

Open AccessArticle

The Impact of Order Effects on the Framing of Trust and Reciprocity Behaviors

by Davood Bayat, Hadi Mohamadpour, Huihua Fang, Pengfei Xu and Frank Krueger

Games 2023, 14(2), 21; https://doi.org/10.3390/g14020021 - 27 Feb 2023

Cited by 2 | Viewed by 1684

Abstract

Trust and reciprocity have paramount importance in cooperative relationships. The influence of psychological effects such as framing and anchoring on trust and reciprocity has been investigated; however, the impact of an order effect on them is still unexplored. The goal of our study [...] Read more.

Trust and reciprocity have paramount importance in cooperative relationships. The influence of psychological effects such as framing and anchoring on trust and reciprocity has been investigated; however, the impact of an order effect on them is still unexplored. The goal of our study was to examine how order impacts the framing of trust and reciprocity by manipulating framing and order as within- and between-subjects factors, respectively. Different groups of participants first completed two framings of the one-shot trust game (give vs. take frame) in a counterbalanced order (give first and then take second vs. take first then give second) in the role of trustors or trustees and rated the expectations of their counterparts’ decisions afterward. Our results revealed higher trust in the take than give frame in the first decision and a reverse outcome in the second decision due to strong anchoring. Reciprocity was higher in the give than take frame in the first decisions, and no difference in the second decisions was observed due to weak anchoring. Anchoring also caused an order effect in trust and reciprocity, with higher trust when the take frame was played first, and higher reciprocity when the give frame was played first. Our results contribute to our knowledge about situational factors that shape trust and reciprocity, highlighting the impact of the context of the decision environment in terms of the impact of the order on framing. Full article

(This article belongs to the Special Issue A Yin and Yang Perspective on the Trust Game: Trust and Reciprocity)

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19 pages, 912 KiB

Open AccessArticle

Deterrence, Backup, or Insurance: Game-Theoretic Modeling of Ransomware

by Tongxin Yin, Armin Sarabi and Mingyan Liu

Games 2023, 14(2), 20; https://doi.org/10.3390/g14020020 - 23 Feb 2023

Cited by 1 | Viewed by 1561

Abstract

In this paper, we present a game-theoretic analysis of ransomware. To this end, we provide theoretical and empirical analysis of a two-player Attacker-Defender (A-D) game, as well as a Defender-Insurer (D-I) game; in the latter, the attacker is assumed to be a non-strategic [...] Read more.

In this paper, we present a game-theoretic analysis of ransomware. To this end, we provide theoretical and empirical analysis of a two-player Attacker-Defender (A-D) game, as well as a Defender-Insurer (D-I) game; in the latter, the attacker is assumed to be a non-strategic third party. Our model assumes that the defender can invest in two types of protection against ransomware attacks: (1) general protection through a deterrence effort, making attacks less likely to succeed, and (2) a backup effort serving the purpose of recourse, allowing the defender to recover from successful attacks. The attacker then decides on a ransom amount in the event of a successful attack, with the defender choosing to pay ransom immediately, or to try to recover their data first while bearing a recovery cost for this recovery attempt. Note that recovery is not guaranteed to be successful, which may eventually lead to the defender paying the demanded ransom. Our analysis of the A-D game shows that the equilibrium falls into one of three scenarios: (1) the defender will pay the ransom immediately without having invested any effort in backup, (2) the defender will pay the ransom while leveraging backups as a credible threat to force a lower ransom demand, and (3) the defender will try to recover data, only paying the ransom when recovery fails. We observe that the backup effort will be entirely abandoned when recovery is too expensive, leading to the (worst-case) first scenario which rules out recovery. Furthermore, our analysis of the D-I game suggests that the introduction of insurance leads to moral hazard as expected, with the defender reducing their efforts; less obvious is the interesting observation that this reduction is mostly in their backup effort. Full article

(This article belongs to the Special Issue Game-Theoretic Analysis of Network Security and Privacy)

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15 pages, 909 KiB

Open AccessArticle

A Representation for Many Player Generalized Divide the Dollar Games

by Garrison W. Greenwood and Daniel Ashlock

Games 2023, 14(2), 19; https://doi.org/10.3390/g14020019 - 23 Feb 2023

Viewed by 1567

Abstract

Divide the dollar is a simplified version of a two player bargaining problem game devised by John Nash. The generalized divide the dollar game has

n > 2

players. Evolutionary algorithms can be used to evolve individual players for this generalized game but [...] Read more.

Divide the dollar is a simplified version of a two player bargaining problem game devised by John Nash. The generalized divide the dollar game has

n > 2

players. Evolutionary algorithms can be used to evolve individual players for this generalized game but representation—i.e., a genome plus a move or search operator(s)—must be carefully chosen since it affects the search process. This paper proposes an entirely new representation called a demand matrix. Each individual in the evolving population now represents a collection of n players rather than just an individual player. Players use previous outcomes to decide their choices (bids) in the current round. The representation scales linearly with the number of players and the move operator is a variant of an evolution strategy. The results indicate that this proposed representation for the generalized divide the dollar game permits the efficient evolution of large player populations with high payoffs and fair demand sets. Full article

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

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Games, Volume 14, Issue 2 (April 2023) – 15 articles

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