Equilibrium Of Game Research Articles

A Game-Theoretic Analysis of Joint Mobile Edge Caching and Peer Content Sharing

<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Mobile edge caching</i> allows edge devices to cache popular contents and deliver them to end-users directly, and hence can effectively alleviate the increasingly heavy backbone loads and improve the quality-of-service of end-users. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Peer content sharing</i> enables edge devices to share the cached contents with each other, and can further increase the caching capability and efficiency. While lots of research efforts have been made to edge caching or content sharing, it remains largely open to devise a joint caching and sharing framework and study the complicated technical and economic interplay between both technologies. In this paper, we propose a joint framework for mobile edge caching and peer content sharing, and focus on studying the strategic behaviors and interactions of edge devices in the joint framework. Specifically, we model their interactions as a non-cooperative game, where each edge device ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">player</i> ) can choose to be an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">agent</i> (who caches and shares contents with others) or a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">requester</i> (who doesn't cache but requests contents from other devices) of each content. We characterize the game equilibrium under a generic usage-based pricing scheme (for content sharing) and analyze its existence and uniqueness systematically. We further design a best response based iterative learning algorithm for players to update their behaviors and reach the equilibrium in a self-enforcing manner. Moreover, we analyze the Price of Anarchy (PoA) of the game equilibrium to measure the system performance degradation due to the selfish strategic behaviors of game players, based on which we further design a pricing scheme (for content sharing) to reduce such performance degradation. Simulations show that our framework can reduce the total system cost by up to 60%, comparing with the benchmark pure caching system without peer content sharing.

Bayesian inference for Quantal Response Equilibrium in normal-form games

This paper develops a framework for estimating Quantal Response Equilibrium models from experimental data using Bayesian techniques. Bayesian techniques offer some advantages over the more commonly-used maximum likelihood approach: (i) more favorable small-sample properties, and (ii) ease of handling unobservable heterogeneity. As Quantal Response Equilibrium is a non-linear model, I also discuss some issues with choosing appropriate priors.Of the twenty-nine models taken to the data, the selected model assumes between-game heterogeneity in choice precision parameter λ, and some dispersion around the Quantal Response Equilibrium. Some implications of this model are discussed.

Game Theory of Universal Health Coverage for Sustainable Development

1. Aklilu Endalamaw, Charles F Gilks, Fentie Ambaw, Tesfa Dejenie Habtewold and Yibeltal Assefa. (2022). Universal Health Coverage for Antiretroviral Treatment:A Review. Retrieved from Researchgate website: https://www.researchgate.net/publication/366504047_Universal_Health_Coverage_for_Antiretroviral_Treatment_A_Review#fullTextFileContent 2. Badia Leonardo and Marchioro Thomas. (2022). Game Theory a handbook of problems and exercises. Società Editrice Esculapio s.r.l . Italy. 3. Barachini Franz and Stary Christian. (2022). From digital twins to digital selves and beyond. Engineering and social models for a trans- humanist world. Springer. Switzlerland. 4. Elena Parilina, Puduru Viswanadha Reddy, Georges Zaccour. (2022). Theory and Applications of Dynamic Games. A Course on Noncooperative and Cooperative Games Played over Event Trees. Springer. 5. Eoghan Brady a, Andy E. Carmone a, Sarthak Dasb, Raphael Hurleya, Maria Theresa Martinez Vergarac, and Address Malata. (2020). Harnessing the Power of Networks of Care for Universal Health Coverage Retrieved from Researchgate website: https://www.researchgate.net/publication/346521559_Harnessing_the_Power_of_Networks_of_Care_for_Universal_Health_Coverage 6. Fan Bai. (2016). Uniqueness of Nash equilibrium in vaccination games. Retrieved from tandfonline website: https://www.tandfonline.com/doi/epdf/10.1080/17513758.2016.1213319?needAccess=true&role=button 7. Hossain Golam and Sabiruzzaman (2021). Health expenditure, universal health coverage and mortality of mother andchild in South East Asia. Retrieved from Researchgate website: https://www.researchgate.net/publication/348906783_Health_expenditure_universal_health_coverage_and_mortality_of_mother_and_child_in_South_East_Asia#fullTextFileContent 8. Icddr,b. (2011). Science to Accelerate Universal Health Coverage. Retrieved from Researchgate website: https://www.researchgate.net/publication/363761888_Science_to_Accelerate_Universal_Health_Coverage#fullTextFileContent 9. O. Orjingene a, Ugo Okoli a, A. Adetunji-Hassan b and M. Ganama. (2022). Universal Health Coverage: A Catalyst for Achieving 2030 Sustainable Development Goals. Retrieved from Researchgate website: https://www.researchgate.net/publication/363255711_Universal_Health_Coverage_A_Catalyst_for_Achieving_2030_Sustainable_Development_Goals#fullTextFileContent 10. Prince Agwu, Obinna Onwujekwe, Benjamin Uzochukwu, Modest Mulenga. (2021). Improving service delivery at primary healthcare facilities for achievingUniversal Health Coverage: Examining the effects of insecurity in such fa-cilities in Enugu State, Nigeria Retrieved from Researchgate website: https://www.researchgate.net/publication/351022237_universal-health-coverage-insecurity#fullTextFileContent 11. Sandhya Venkateswaran, Shruti Slaria3 and Sampriti Mukherjee. (2022). Political motivation as akey driver for universal health coverage. Retrieved from DOI: 10.3389/fpubh.2022.922578 12. Sheryl L. Changa, Mahendra Piraveenan, Philippa PattisoncandMikhail Prokopenko. (2020). Game theoretic modelling of infectious disease dynamics and intervention methods: a review Retrieved from tandfonline website: https://www.tandfonline.com/doi/epdf/10.1080/17513758.2020.1720322?needAccess=true&role=button 13. Talwalkar P. (2016). The Joy of Game Theory: An Introduction to Strategic Thinking. Create space independent publishing platform. Standford University. UK. 14. Tjemkes Brian and Oli Mihalache. (2021). Transformative Strategies: Strategic Thinking in the Age of Globalization, Disruption, Collaboration and Responsibility. Routledge.USA. 15. Universal Health Coverage (UHC) Index. (2023) Retieve from website https://ourworldindata.org/grapher/universal-health-coverage-index?country=BWA~GMB~YEM 16. Yanhao Lin. (2022). Applications of Game Theory in Microeconomics. Retrieve online from website https://drpress.org/ojs/index.php/EHSS/article/view/777 17. WHO. (2021). Tracking UHC 2021 Global Monitoring Report. Retrieve online from websitehttps://www.who.int/news-room/fact-sheets/detail/universal-health-coverage-(uhc)

Equilibrium refinement in finite action evidence games

Evidence games study situations where a sender persuades a receiver by selectively disclosing hard evidence about an unknown state of the world. Evidence games often have multiple equilibria. Hart et al. (Am Econ Rev 107:690-713, 2017) propose to focus on truth-leaning equilibria, i.e., perfect Bayesian equilibria where the sender discloses truthfully when indifferent, and the receiver takes off-path disclosure at face value. They show that a truth-leaning equilibrium is an equilibrium of a perturbed game where the sender has an infinitesimal reward for truth-telling. We show that, when the receiver’s action space is finite, truth-leaning equilibrium may fail to exist, and it is not equivalent to equilibrium of the perturbed game. To restore existence, we introduce a disturbed game with a small uncertainty about the receiver’s payoff. A purifiable truthful equilibrium is the limit of a sequence of truth-leaning equilibria in the disturbed games as the disturbances converge to zero. It exists and features a simple characterization. A truth-leaning equilibrium that is also purifiable truthful is an equilibrium of the perturbed game. Moreover, purifiable truthful equilibria are receiver optimal and give the receiver the same payoff as the optimal deterministic mechanism.

Pure-strategy equilibrium in Bayesian potential games with absolutely continuous information

We prove the existence of a pure-strategy Bayesian Nash equilibrium in Bayesian games with absolutely continuous information and a Bayesian potential that is upper semi-continuous in actions for any realization of the players' types. In particular, all Bayesian potential games with finitely many actions and absolutely continuous information possess a pure-strategy Bayesian Nash equilibrium.

A Collaborative Transit Signal Priority Method Considering Gaming among Traffic Participants

How to realize the game equilibrium between bus and nontransit vehicle is a hot topic in the field of transit signal priority (TSP). To this end, a collaborative transit signal priority (Co-TSP) method is proposed. The core of Co-TSP is a two-objective optimization problem which takes the expected delays of buses and the average delays of nontransit vehicles as the objectives. Different from previous studies, Co-TSP uses game theory to realize collaborative optimization, instead of transforming the problem into a single objective optimization problem by weighting. A finite state machine-based algorithm is developed to estimate the average delays of nontransit vehicles. The stochasticity of bus arrival time is also considered in the estimation of bus delays to improve the robustness. Candidate timing plans obtained by the nondominated sorting genetic algorithm (NSGA) are divided into three priority levels based on the delays of buses. The final timing plans can be picked intuitively from the candidates by rules representing expert knowledge and demands to control the priority level. Co-TSP guarantees theoretically by preliminary screening that the expected delays of bus after optimization must be no higher than that before optimization. Simulation experiments are conducted in Shanghai, China, to verify the performance. Results show that Co-TSP reduces the delays of buses by 27.7%∼41.0% and still performs well under low and high congestion levels, while the conventional TSP (CTSP) fails in some cases. Priority control proves to be effective at last. The research provides a new idea for the benefit allocation among participants at intersections.

Kdb-D2CFR: Solving Multiplayer imperfect-information games with knowledge distillation-based DeepCFR

Counterfactual regret minimization (CFR) is a popular method for finding approximate Nash equilibrium in imperfect-information games (IIG). However, CFR based methods for the IIG are either only designed for two-player IIGs or require much expert knowledge. In this paper, towards to solve the multiplayer IIG problem without utilizing much expert knowledge, we proposed a practical knowledge distillation based framework, which aims to transferring the knowledge from model of two-player IIG into the multiplayer one. By this framework, both of the training efficiency and performance is improved. To eliminate the requirement of expert knowledge, here we introduced a deep learning based CFR in the framework, by which the counterfactual value of CFR can be estimated in an end-to-end way without any expert knowledge and abstraction. We further propose kdb-DeepCFR and kdb-D2CFR based on DeepCFR and D2CFR respectively, which can effectively solve the strategy of multiplayer large-scale game problems. The extensive experiments conducted on 3-8 players poker games suggest that our method outperforms other baselines in the game performance.

Integrated demand-side management for multi-energy system based on non-cooperative game and multi-energy pricing

This paper proposes an integrated demand-side management (IDSM) approach based on non-cooperative game and multi-energy pricing strategy for a regional integrated energy system (RIES). On the demand side, the competition among multi-energy users was modeled as a non-cooperative energy consumption game, and the conditions to ensure the existence and uniqueness of the Nash equilibrium of the non-cooperative game were given. Considering the privacy of user information, a distributed multi energy consumption control algorithm based on dual theory and gradient descent method was designed to search for the optimal multi-energy consumption and the multi-energy daily retail price. In addition, for the energy supply side, the scheduling strategy of energy hub (EH) was proposed based on linear programming (LP) theory to optimize equipment operation. The results show that this approach can enable users and EH to coordinate optimization, so as to reduce the peak-to-average ratio (PAR) and energy cost of the system, and ensure the balance between supply and demand of multi-energy.

Can Carbon Trading Promote Low-Carbon Transformation of High Energy Consumption Enterprises?—The Case of China

This paper explores the effect of carbon trading on low-carbon transformation of high energy consumption enterprises in China. Based on the mechanism of interaction and restriction among high energy consumption enterprises, carbon verification agencies and the government, a tripartite evolutionary game model is constructed. The three-dimensional dynamic system is built to analyze the behavior patterns of the three parties. The evolution path of the tripartite game is visualized, and the low-carbon transformation states of high energy consumption enterprises in different situations are described. The results show that the high energy consumption enterprises, verification organization and the government cannot reach the optimal game equilibrium (low-carbon transformation, verification and supervision) temporarily when seeking their own interests. The corresponding measures should be taken with different situations of the tripartite game. No matter what strategy the government chooses, the low-carbon transformation could be promoted by carbon trading through carbon verification mechanism.

Spatial competition with demand uncertainty: A laboratory experiment

AbstractMotivated by recent research on product differentiation, we conduct laboratory experiments to study how demand uncertainty influences firms' incentives to differentiate. We ground our experiment on a discrete version of the standard location‐then‐price game introduced by Hotelling (1929), and we consider different levels of demand uncertainty. We first derive the game equilibrium assuming risk‐neutral firms, and obtain the standard prediction that a high level of demand uncertainty generates more differentiation. Second, we extend the analysis to consider non‐risk neutral firms and markets with asymmetric risk profiles. We show that the game equilibrium can differ substantially according to the attitude to risk. Third, we compare our predictions with the experimental data and find that demand uncertainty acts as a differentiation force in the context of both symmetric markets composed of risk‐neutral or risk‐lover subjects and asymmetric markets. We find support also for the agglomeration effect arising from demand uncertainty for sufficiently risk‐averse subjects. Overall, these results might explain the opposite product differentiation strategies frequently observed in markets with fast‐evolving tastes (i.e., minimum or maximum differentiation). Finally, the data confirm that subjects differentiate to relax price competition and provide evidence of a strong positive relationship between differentiation and prices.

Legal Framework for Rear-End Crashes in Mixed-Traffic Platooning: A Matrix Game Approach

Autonomous vehicles (AV) hold great potential to increase road safety, reduce traffic congestion, and improve mobility systems. However, the deployment of AVs introduces new liability challenges when they are involved in car accidents. A new legal framework should be developed to tackle such a challenge. This paper proposes a legal framework, incorporating liability rules to rear-end crashes in mixed-traffic platoons with AVs and human-propelled vehicles (HV). We leverage a matrix game approach to understand interactions among players whose utility captures crash loss for drivers according to liability rules. We investigate how liability rules may impact the game equilibrium between vehicles and whether human drivers’ moral hazards arise if liability is not designed properly. We find that compared to the no-fault liability rule, contributory and comparative rules make road users have incentives to execute a smaller reaction time to improve road safety. There exists moral hazards for human drivers when risk-averse AV players are in the car platoon.

Transient Impact from the Nash Equilibrium of a Permanent Market Impact Game

A large body of empirical literature has shown that market impact of financial prices is transient. However, from a theoretical standpoint, the origin of this temporary nature is still unclear. We show that an implied transient impact arises from the Nash equilibrium between a directional trader and one arbitrageur in a market impact game with fixed and permanent impact. The implied impact is the one that can be empirically inferred from the directional trader’s trading profile and price reaction to order flow. Specifically, we propose two approaches to derive the functional form of the decay kernel of the transient impact model, one of the most popular empirical models for transient impact, from the behavior of the directional trader at the Nash equilibrium. The first is based on the relationship between past order flow and future price change, while in the second we solve an inverse optimal execution problem. We show that in the first approach the implied kernel is unique, while in the second case infinite solutions exist and a linear kernel can always be inferred.

Environmental delegation versus sales delegation: a game-theoretic analysis

AbstractRecently, in their 2019 paper, Poyago-Theotoky and Yong consider a managerial Cournot duopoly with pollution externalities and emission taxes and propose an explicit environmental incentive in a managerial compensation contract. The authors compare several exogenous equilibria emerging in the symmetric sub-games in which the owner offers either the environmental delegation contract or the standard sales delegation contract: abatement and social welfare (resp. emission taxes) under environmental delegation are higher (resp. lower) than under sales delegation. The present work extends their model using a game-theoretic approach to analyse the asymmetric sub-games, in which only one firm adopts the environmental contract, and adds the contract decision stage. Results show that the environmental contract never emerges as the unique sub-game perfect Nash equilibrium of this non-cooperative managerial decision game. Indeed, if the green R&amp;D technology is efficient, the sales contract emerges as the unique Pareto-inefficient Nash equilibrium. Otherwise, if the green R&amp;D technology is inefficient, multiple Nash equilibria in pure strategies exist (coordination game). Our findings offer direct policy implications.

Generalization of the social coalitional equilibrium structure

We generalize the notion of Ichiishi (Econometrica 49(2):369–377, 1981)’s social coalitional equilibrium to a multi-layered coalition structure with parameters, in which agents can incorporate simultaneously multiple coalition structures with multiple independent coalition-deviation opportunities. For each opportunity, agents play a social coalitional equilibrium (SCE) game, called a sub-parametric SCE game, constrained by external environment (parameters and joint decisions of all other sub-parametric SCE games). The generalized social coalitional equilibrium (GSCE) concept is, therefore, considered to be a synthesis of the Nash equilibrium concept and the cooperative solution concept. We provide the definition of GSCE and give the proof of existence theorem. Through some applications to general equilibrium models, the GSCE concept provides a conceptual framework for describing coexisting different industries having independent investment opportunities and their simultaneously determined industrial organizations.

Interest Equilibrium and Path Choice in the Development of Construction Land Decrement: A Theoretical Analysis Based on the Multi-Agent Game Model

High-quality development is a new-era requirement for modern urban construction. The implementation of construction land decrement has become an inevitable choice to solve the urban land use dilemma and achieve high-quality social and economic development. It is a game process for stakeholders. Based on the multi-agent game model, this research analyzes the game relationship and strategy selection between governments, government and farmers, government and developers, and developers and farmers and examines the balance of interests among multiple subjects. From the perspective of space dimension, index dimension, use dimension and time dimension, a game path is constructed for construction land decrement. The research shows the following: There is a clear relationship between the supervision cost of the higher-level government and the intensity of rewards and punishments for the lower-level government and the implementation of the decrement. The district (county) government’s compensation plan and farmers’ perceptions of the success of the boycott will affect the strategic choices of both parties. Governments at all levels play a direct role in restraining development behavior and supervising rent-seeking behavior after developers intervene in volume reduction. It also proposes optimizing the ratio of game factors such as costs, benefits, rewards, verification and punishment to achieve the game equilibrium of the expression of the interests of village residents, developers and governments at all levels. Based on the path planning and coupling of response, the multi-scheme dynamic path selection for the development of construction land decrement is realized.

Edge Resource Pricing and Scheduling for Blockchain: A Stackelberg Game Approach

Blockchain came to prominence as the distributed ledger underneath Bitcoin, which protects the transaction histories in a fully-connected, peer-to-peer network. The blockchain mining process requires high computing power to solve a Proof-of-Work (PoW) puzzle, which is hard to implement on users’ mobile devices. So these miners may leverage the edge/cloud service providers (ESPs/CSP) to calculate the PoW puzzle. The existing edge-assisted blockchain networks assumed that all ESPs have a uniform propagation delay, which is unrealistic. In this article, we consider a more practical scene where ESPs locate in diverse positions of the blockchain network, which causes different propagation delays when supporting the computation of the PoW puzzle. Additionally, these ESPs connect to a remote CSP for resource scheduling when the computing tasks exceed their maximum capacity. The blockchain mining process generally involves complicated competition and games among CSP, ESPs, and miners. Each service provider focuses on how to determine his resource price so that he can maximize his utility. According to the set resource price, each miner concentrates on scheduling his resource requests for each ESP to maximize individual personal utility, which depends on ESPs’ resource price and propagation delays. We first model such a resource pricing and scheduling problem as a three-stage multi-leader multi-follower Stackelberg game and aim at finding the Stackelberg equilibrium. Then, we analyze the subgame optimization problem in each stage and propose an iterative algorithm based on backward induction to achieve the Nash equilibrium of the Stackelberg game. Finally, extensive simulations are conducted to verify the significant performance of the proposed solution.

Nash Equilibrium Seeking for High-Order Multiagent Systems With Unknown Dynamics

In this article, we consider a Nash equilibrium seeking problem for a class of high-order multiagent systems with unknown dynamics. Different from existing results for single integrators, we aim to steer the outputs of this class of uncertain high-order agents to the Nash equilibrium of some noncooperative game in a distributed manner. To overcome the difficulties brought by the high-order structure, unknown nonlinearities, and the regulation requirement, we first introduce a virtual player for each agent and solve an auxiliary noncooperative game for them. Then, we develop a distributed adaptive protocol by embedding this auxiliary game dynamics into some proper tracking controller for the original agent to resolve this problem. We also discuss the parameter convergence issue under certain persistence of excitation conditions. The efficacy of our algorithms is verified by numerical examples.

Differential Game-Based Optimal Control of Autonomous Vehicle Convoy

Group control of connected and autonomous vehicles on automated highways is challenging for the advanced driver assistance systems (ADAS) and the automated driving systems (ADS). This paper investigates the differential game-based approach to autonomous convoy control with the aim of deployment on automated highways. Under the noncooperative differential games, the coupled vehicles make their decisions independently while their states are interdependent. The receding horizon Nash equilibrium of the linear-quadratic differential game provides the convoy a distributed state-feedback control strategy. This approach suffers a fundamental issue that neither a Nash equilibrium’s existence nor the uniqueness is guaranteed. We convert the individual dynamics-based differential game to a relative dynamics-based optimal control problem that carries all the features of the differential game. The existence of a unique Nash control under the differential game corresponds to a unique solution to the optimal control problem. The latter is shown, as well as the asymptotic stability of the closed-loop system. Simulations illustrate the effectiveness of the presented convey control scheme and how it well suits automated highway driving scenarios.

The economics of China’s between-city height competition: A regression discontinuity approach

In this article, I use a regression discontinuity design to quantify the race between Chinese cities to build taller skyscrapers. I begin by characterizing this height competition with a game-theoretic model for multi-stage, two-player, all-pay auctions with carryover. The dominant mixed strategy equilibrium of this dynamic game implies that a city would be more inclined to construct a taller skyscraper if its current tallest building is merely shorter than the tallest in the rival city, and this inclination is discontinuous at which the heights of these two buildings are equal. Utilizing a large data set of China’s skyscrapers constructed between 2004 and 2019, I confirm the presence of this between-city contest by empirically identifying the discontinuity in a city’s probability of constructing a taller building. I also find that this height competition has been more prevalent among the cities with fewer historic amenities or with leaders that have lower promotion likelihoods prior to the start of office.

Modeling Competition over Multiple Variables under Limited Consumer Awareness*

When analyzing firm competition over two strategic variables (e.g., quality and price), it is important to decide whether to model it as a one‐stage or a two‐stage game. Our analysis focuses on markets in which consumers are not aware of all alternatives. We find that, if consumers are sufficiently unaware, both the one‐stage and the two‐stage equilibria of the game that explicitly models limited awareness are close to the one‐stage equilibrium of the standard game, which assumes full awareness. Therefore, markets in which consumers have limited awareness can be studied with standard models, provided that the one‐stage game is analyzed.