Game-theoretic Framework Research Articles

Reliable Distributed Computing for Metaverse: A Hierarchical Game-Theoretic Approach

The metaverse is regarded as a new wave of technological transformation that provides a virtual space for people to interact through digital avatars. To achieve immersive user experiences in the metaverse, real-time rendering is the key technology. However, computing intensive tasks of real-time rendering from metaverse service providers cannot be processed efficiently on a single resource-limited mobile device. Alternatively, such mobile devices can offload the metaverse rendering tasks to other mobile devices by adopting the collaborative computing paradigm based on Coded Distributed Computing (CDC). Therefore, this paper introduces a hierarchical game-theoretic CDC framework for the metaverse services, especially for vehicular metaverse. In the framework, idle resources from vehicles, acting as CDC workers, are aggregated to handle intensive computation tasks in the vehicular metaverse. Specifically, in the upper layer, a miner coalition formation game is formulated based on a reputation metric to select reliable workers. To guarantee the reliable management of reputation values, the reputation values calculated based on the subjective logical model are maintained in a blockchain database. In the lower layer, a Stackelberg game based incentive mechanism is considered to attract reliable workers selected in the upper layer to participate in rendering tasks. The simulation results illustrate that the proposed framework is resistant to malicious workers. Compared with the baseline schemes, the proposed scheme can improve the utility of metaverse service provider and average profit of CDC workers.

A game theoretic framework for controlling the behavior of a content seeking to be popular on social networking sites

Over the years, people are becoming more dependent on Online Social Networks, through whom they constitute various sorts of relationships. Furthermore, such areas present spaces of interaction among users; they send more messages and posts showing domains they are interested in to guarantee the level of their popularity. This popularity depends on its own rate, the number of comments the posted topic gets but; also on the cost a user has to pay to accomplish his task on this network. However, the selfish behavior of those subscribers is the root cause of competition over popularity among those users. In this paper, we aim to control the behavior of a social networks users who try their best to increase their popularity in a competitive manner. We formulate this competition as a non-cooperative game. We porpose an efficient game theoretical model to solve this competition and find a situation of equilibrium for the said game.

Stackelberg Meta-Learning Based Control for Guided Cooperative LQG Systems

Guided cooperation allows intelligent agents with heterogeneous capabilities to work together by following a leader-follower type of interaction. However, the associated control problem becomes challenging when the leader agent does not have complete information about follower agents. There is a need for learning and adaptation of cooperation plans. To this end, we develop a meta-learning-based Stackelberg game-theoretic framework to address the challenges in the guided cooperative control for linear systems. We first formulate the guided cooperation between agents as a dynamic Stackelberg game and use the feedback Stackelberg equilibrium as the agent-wise cooperation strategy. We further leverage meta-learning to address the incomplete information of follower agents, where the leader agent learns a meta-response model from a prescribed set of followers offline and adapts to a new coming cooperation task with a small amount of learning data. We use a case study in robot teaming to corroborate the effectiveness of our framework. Comparison with other learning approaches also shows that our learned cooperation strategy provides better transferability for different cooperation tasks.

Dynamic Hypergames for Synthesis of Deceptive Strategies With Temporal Logic Objectives

In this paper, we study the use of deception for strategic planning in adversarial environments. We model the interaction between the agent (player 1) and the adversary (player 2) as a two-player concurrent stochastic game in which the adversary has incomplete information about the agent’s task specification given as a temporal logic formula. During the interaction, the adversary can infer the agent’s intention from observations and adapt its strategy so as to prevent the agent from satisfying the objective. To plan against such an adaptive opponent, the agent must leverage its knowledge about the adversary’s incomplete information to influence the behavior of the opponent, and thereby be deceptive. To synthesize a deceptive strategy, we introduce a class of hypergame models that capture the interaction between the agent and its adversary given asymmetric, incomplete information. We develop a solution concept for this class of hypergames and show that the subjectively rationalizable strategy for the agent is deceptive and maximizes the probability of satisfying the task in temporal logic. Such a deceptive strategy is obtained by modeling the opponent’s evolving perception of the agent’s objective and integrating it into planning. This allows the agent to manipulate the opponent’s perception so as to induce the opponent into taking actions that benefit the agent. We demonstrate the effectiveness of our deceptive planning algorithm using robot motion planning examples with temporal logic objectives and design a detection mechanism to notify the agent of potential errors in modeling the adversary’s behavior. Note to Practitioners—Many security and defense applications employ deception mechanisms for strategic advantages. This work presents a game-theoretic framework for planning deceptive strategies in stochastic environments and shows that the opponent modeling plays a key role in the design of effective deception mechanisms. For applications to cyber-physical security, the practitioners can employ temporal logic for specifying security properties in the system and analyze defense with deception using the proposed methods.

MB-CIM: a multi-round budgeted competitive influence maximisation

Influence maximisation is trying to select a small set of seed users in the social network to maximise the spread of influence. An individual's decision to adopt a product or innovation will be highly dependent on the choices made by the individual's neighbours in the social network. In CIM, competitors need to decide which nodes would be an influential one and how many resources should be allocated to this member. Identifying the best algorithm for the influence maximisation under budget constraint has become a demanding task. Predicting, and controlling social influence is an exciting topic in social network analysis. We are interested in multi-round CIM where each competitor needs to decide the location and the amount of budget to invest in the most influential members simultaneously and repeatedly under a given total budget. This paper proposes a tree-approximate game-theoretical framework and introduces the new measurement as a dynamic node weight.

A Game Theoretic Framework for Distributed Mission Slice Allocation and Management for Tactical Networks

A Game Theoretic Framework for Distributed Mission Slice Allocation and Management for Tactical Networks

Public versus private information: The impact of quality information sharing on competition under different channel structures

While prior research studied the impact of information sharing on competition in the supply chain assumes suppliers adopt same selling channels, we contribute to this research by analyzing public and private information sharing under three types of supply chain structures. This paper considers two scenarios including public–public information sharing and public–private information sharing. In each scenario, competing suppliers can sell products in one of three types of supply chain structures including indirect–direct channel structure, indirect–indirect channel structure, and direct–direct channel structure. Using a game-theoretic framework, we get the profits of suppliers under two scenarios and compare the expected profits under different scenarios to analyze the impact of public information sharing and private information sharing on the competition. By comparing the profits of suppliers under different channel structures, we get the existence conditions of each channel structure. We show our key findings as follows. Interestingly, we find that public information sharing enhances supply chain competition and conversely, private information sharing mitigates supply chain competition. This finding suggests that suppliers can use private information sharing as a tool to increase competitive capability in channel competition. We also find that the supplier with low-quality products is willing to share private quality information when the products’ quality difference is low. A surprising finding is that private information sharing achieves a win–lose outcome, where one supplier earns a higher profit compared to public information sharing whereas another supplier earns a lower profit. In addition, only under the public–private information sharing scenario can suppliers adopt the indirect–direct channel structure.

Voluntary vaccination may not stop monkeypox outbreak: A game-theoretic model.

Monkeypox (MPX) is a viral zoonotic disease that was endemic to Central and West Africa. However, during the first half of 2022, MPX spread to almost 60 countries all over the world. Smallpox vaccines are about 85% effective in preventing MPX infections. Our objective is to determine whether the vaccines should be mandated or whether voluntary use of the vaccine could be enough to stop the MPX outbreak. We incorporate a standard SVEIR compartmental model of MPX transmission into a game-theoretical framework. We study a vaccination game in which individuals decide whether or not to vaccinate by assessing their benefits and costs. We solve the game for Nash equilibria, i.e., the vaccination rates the individuals would likely adopt without any outside intervention. We show that, without vaccination, MPX can become endemic in previously non-endemic regions, including the United States. We also show that to "not vaccinate" is often an optimal solution from the individual's perspective. Moreover, we demonstrate that, for some parameter values, there are multiple equilibria of the vaccination game, and they exhibit a backward bifurcation. Thus, without centrally mandated minimal vaccination rates, the population could easily revert to no vaccination scenario.

Optimal channel strategy of luxury brands in the presence of online marketplace and copycats

The strategic interaction between authentic luxury brands and their copycats has evolved since the proliferation of online marketplaces. Using a game-theoretic framework, we examine how an authentic luxury brand, observing the strategic behavior of its competing copycats, should make its optimal entry decision to a third-party online marketplace. Our findings reveal that the authentic luxury brand does not sell on the online marketplace when either the quality or the physical resemblance of the copycat to the authentic luxury brand is high. This contributes to the related literature by offering an explanation for the increasing quality of copycats amid the e-commerce boom —improving the quality of the copycat can deter the authentic luxury brand from selling on the online marketplace. Furthermore, by comparing our equilibrium outcome with the benchmark case where the authentic luxury brand does not consider selling on the online marketplace at all, we show that the authentic luxury brand’s potential entry to the online marketplace is sufficient to induce the copycat to improve its quality and lower its price, thereby improving the aggregate consumer surplus. In addition, the online marketplace can always be better off allowing the entry of the copycat if there is no external enforcement against copycats. We show that our key results are valid in various extensions and they offer multiple managerial implications.

A regulatory arbitrage game: Off-balance-sheet leverage and financial fragility

This study examines a simple banking system in a game-theoretic framework wherein banks act as self-interested agents to maximize leverage at the expense of overall financial stability. The resultant strategic inefficiency raises concerns about how banks manage the "financial stability" good, which is appropriated into a "tragedy of the commons." We conceptualize the inefficiency using the price of anarchy introduced by Koutsoupias & Papadimitriou (2009). We seek the optimal regulatory framework that minimizes the price of anarchy or the degree of financial fragility.

Mean Field Game-Theoretic Framework for Distributed Power Control in Hybrid NOMA

The steady expansion of the number of wireless devices and the ubiquity of the networks give rise to various interesting challenges for the future sixth generation (6G) of wireless communication systems. Particularly, the operators have to handle massive connectivity among Machine Type Devices (MTDs) and increasing demand for eMMB through limited spectrum resources. Non-Orthogonal Multiple Access (NOMA) has been spotlighted as an emerging technology to meet the above-mentioned challenges. In this paper, we consider a densely deployed network in which users are divided into NOMA coalitions. Firstly, we model the power allocation problem as a differential game. Then, we extend the formulated game using a Mean Field Game (MFG) theoretic framework by considering the effect of the collective behavior of devices. Furthermore, we derive a distributed power control algorithm that enables the users to appropriately regulate their transmit power according to brief information received from the BS. Indeed, the analysis of the proposed approach is governed by the two fundamental Hamilton- Jacobi-Bellman (HJB) and Fokker-Planck-Kolmogorov (FPK) equations. Numerical results are presented to analyze the equilibrium behaviors of the proposed power control algorithm and to demonstrate the effectiveness of the formulated MFG compared to existing works in the literature.

Triple Generative Adversarial Networks.

We propose a unified game-theoretical framework to perform classification and conditional image generation given limited supervision. It is formulated as a three-player minimax game consisting of a generator, a classifier and a discriminator, and therefore is referred to as Triple Generative Adversarial Network (Triple-GAN). The generator and the classifier characterize the conditional distributions between images and labels to perform conditional generation and classification, respectively. The discriminator solely focuses on identifying fake image-label pairs. Theoretically, the three-player formulation guarantees consistency. Namely, under a nonparametric assumption, the unique equilibrium of the game is that the distributions characterized by the generator and the classifier converge to the data distribution. As a byproduct of the three-player formulation, Triple-GAN is flexible to incorporate different semi-supervised classifiers and GAN architectures. We evaluate Triple-GAN in two challenging settings, namely, semi-supervised learning and the extremely low data regime. In both settings, Triple-GAN can achieve excellent classification results and generate meaningful samples in a specific class simultaneously. In particular, using a commonly adopted 13-layer CNN classifier, Triple-GAN outperforms extensive semi-supervised learning methods substantially on several benchmarks no matter data augmentation is applied or not.

Values of coordinated residential space heating in demand response provision

Demand side response from space heating in residential buildings can potentially provide huge amount of flexibility for the power system, particularly with deep electrification of the heat sector. In this context, this paper presents a novel distributed control strategy to coordinate space heating across numerous residential households with diversified thermal parameters. By employing an iterative algorithm under the game-theoretical framework, each household adjusts its own heating schedule through demand shift and thermal comfort compensation with the purpose of achieving individual cost savings, whereas the aggregate peak demand is effectively shaved on the system level. Additionally, an innovative thermal comfort model which considers both the temporal and spatial differences in customized thermal comfort requirement is proposed. Through a series of case studies, it is demonstrated that the proposed space heating coordination strategy can facilitate effective energy arbitrage for individual buildings, driving 13.96% reduction in system operational cost and 28.22% peak shaving. Moreover, the superiority of the proposed approach in thermal comfort maintenance is numerically analysed based on the proposed thermal comfort quantification model.

A Stochastic Queueing Model for the Pricing of Time-Sensitive Services in the Demand-Sharing Alliance

The medical alliance has developed rapidly in recent years. This kind of alliance established by multiple hospitals can alleviate the imbalance of medical resources. We investigate the benefit of demand sharing between a hospital with large demand (HD) and another hospital with large supply (HS). Two hospitals are modeled as queueing systems with finite service rates. Both hospitals set prices to maximize the revenues by serving their time-sensitive patients. We adopt a cooperative game theoretic framework to determine when demand sharing is beneficial. We also propose an optimal allocation of this benefit through a commission fee, which makes the alliance stable. We find that demand sharing may not be beneficial even if HS has a low capacity utilization. Demand sharing becomes beneficial for both hospitals only when the idle service capacity of HS exceeds a threshold, which depends on the potential demand rate of the HS and the unit waiting cost of hospitals. Furthermore, if the idle service capacity of HS is smaller than another threshold, which depends on the potential demand of the two hospitals and the service capacity of HD, then the benefit of demand sharing will be independent of the service capacity and potential demand of HD. We also examine the effect of system parameters on revenue gains due to demand sharing.

A bilevel game-theoretic decision-making framework for strategic retailers in both local and wholesale electricity markets

This paper proposes a bilevel game-theoretic model for multiple strategic retailers participating in both wholesale and local electricity markets while considering customers’ switching behaviors. At the upper level, each retailer maximizes its own profit by making optimal pricing decisions in the retail market and bidding decisions in the day-ahead wholesale (DAW) and local power exchange (LPE) markets. The interaction among multiple strategic retailers is formulated using the Bertrand competition model. For the lower level, there are three optimization problems. First, the welfare maximization problem is formulated for customers to model their switching behaviors among different retailers. Second, a market-clearing problem is formulated for the independent system operator (ISO) in the DAW market. Third, a novel LPE market is developed for retailers to facilitate their power balancing. In addition, the bilevel multi-leader multi-follower Stackelberg game forms an equilibrium problem with equilibrium constraints (EPEC) problem, which is solved by the diagonalization algorithm. Numerical results demonstrate the feasibility and effectiveness of the EPEC model and the importance of modeling customers’ switching behaviors. We corroborate that incentivizing customers’ switching behaviors and increasing the number of retailers facilitates retail competition, which results in reducing strategic retailers’ retail prices and profits. Moreover, the relationship between customers’ switching behaviors and welfare is reflected by a balance between the electricity purchasing cost (i.e., electricity price) and the electricity consumption level.

A marketplace model for drone-assisted edge computing in 5G scenarios

The recent evolution of the traditional cloud computing vision towards the so-called edge computing has stimulated the emergence of new network paradigms, such as drone-assisted mobile networks. Here, drones acting as mobile edge servers provide storage and processing services so as to offload data and support ubiquitous connectivity. In such a scenario, inter-user interference represents a critical feature, as it can heavily hinder the network performance, due to the massive user densification of modern 5G-and-beyond networks. This work deals with the interference problem and the resulting network dynamics under a theoretical perspective by presenting a fully-distributed game-theoretical framework. More in detail, the interactions between users and servers are modeled as a marketplace scenario, where servers (i.e., drones), behaving as sellers, offer network functions, while users buy the offered services and, accordingly, interact with servers. The mathematical characterization of the marketplace interactions is achieved by employing a two-stage Stackelberg game in which a unique equilibrium and convergence point can be identified. Moreover, we show that the use of a reinforcement learning algorithm allows to achieve this equilibrium in a practical setting. Our numerical evaluation investigates the dynamics of multiple 5G use cases (namely eMBB, URLLC and a hybrid tradeoff case), each characterized by heterogeneous requirements and diverse KPIs which lead to very dissimilar behavior in terms of requested bandwidth and user distribution at the equilibrium. The results show how our game theoretical framework achieves a reduction of up to 60% in the network interference in a fully-distributed fashion, where each actor in the network can act in an autonomous and independent way to reach the convergence point.

Mean Field Games on Prosumers

In the realm of dynamic demand, prosumers are agents that can produce and consume goods. In this paper, the problem we address involves a large population of prosumers and each prosumer has to decide if (s)he wants to produce or consume a certain amount of goods. The strategy of each agent depends on the average behavior of the population. We set the problem in a game-theoretic framework by modeling every prosumer as a player. For every player, a cost functional is designed to incentivize cooperation among the players. By taking the population size very large, a mean field game arises. The contributions of this paper are as follows. Firstly, we formulate the problem as first-order and second-order mean field games, the latter arises when we take stochastic disturbances into account. Secondly, mean field equilibria are derived by studying the corresponding linear-quadratic optimal control problem. Thirdly, results on stability of the first-order and second-order equilibria are established. A numerical study covering our findings concludes the paper.

Evolutionary Kuramoto dynamics

Biological systems have a variety of time-keeping mechanisms ranging from molecular clocks within cells to a complex interconnected unit across an entire organism. The suprachiasmatic nucleus, comprising interconnected oscillatory neurons, serves as a master-clock in mammals. The ubiquity of such systems indicates an evolutionary benefit that outweighs the cost of establishing and maintaining them, but little is known about the process of evolutionary development. To begin to address this shortfall, we introduce and analyse a new evolutionary game theoretic framework modelling the behaviour and evolution of systems of coupled oscillators. Each oscillator is characterized by a pair of dynamic behavioural dimensions, a phase and a communication strategy, along which evolution occurs. We measure success of mutations by comparing the benefit of synchronization balanced against the cost of connections between the oscillators. Despite the simple set-up, this model exhibits non-trivial behaviours mimicking several different classical games-the Prisoner's Dilemma, snowdrift games, coordination games-as the landscape of the oscillators changes over time. Across many situations, we find a surprisingly simple characterization of synchronization through connectivity and communication: if the benefit of synchronization is greater than twice the cost, the system will evolve towards complete communication and phase synchronization.

Social distancing as a public-good dilemma for socio-economic cost: An evolutionary game approach

Partaking in social distancing can contribute to a public good affected by the perceived risk of infection and socioeconomic cost. Although social distancing can save lives by slowing down the disease transmission before introducing any effective medical intervention, the economic fallout of social distancing can be brutal for the poorest, vulnerable, and marginalized members of society. We combined the epidemiological and evolutionary game theoretical (EGT) framework through the consolidations of the SEIR (Susceptible-Exposed-Infected-Removed) disease model to analyze behavior enticements in a social distancing dilemma situation with the complex behavioral decision-making aspect. Extensive theoretical and numerical analyses reveal that socioeconomic cost and infected individuals' compliance behavior are critical factors in reining disease spread in the community. Lower cost for maintaining relative safety distance encourages maximum avoidance of public interactions by a detected infected individual. The benefitted fraction due to compliance is parted from the naturally immunized population. People get insignificant benefits from social distancing when the disease transmission rate is too low or crosses critical higher values. Average Social Payoff (ASP) analysis suggests the correspondence of significant safety distance with lowest cost setting as the best strategy to derive the maximum goods. But mounting inherent cost converts social distancing obedience to a public good dilemma.

Decision Making for Connected Automated Vehicles at Urban Intersections Considering Social and Individual Benefits

To address the coordination issue of connected automated vehicles (CAVs) at urban scenarios, a game-theoretic decision-making framework is proposed that can advance social benefits, including the traffic system efficiency and safety, as well as the benefits of individual users. Under the proposed decision-making framework, in this work, a representative urban driving scenario, i.e. the unsignalized intersection, is investigated. Once the vehicle enters the focused zone, it will interact with other CAVs and make collaborative decisions. To evaluate the safety risk of surrounding vehicles and reduce the complexity of the decision-making algorithm, the driving risk assessment algorithm is designed with a Gaussian potential field approach. The decision-making cost function is constructed by considering the driving safety and passing efficiency of CAVs. Additionally, decision-making constraints are designed and include safety, comfort, efficiency, control and stability. Based on the cost function and constraints, the fuzzy coalitional game approach is applied to the decision-making issue of CAVs at unsignalized intersections. Two types of fuzzy coalitions are constructed that reflect both individual and social benefits. The benefit allocation in the two types of fuzzy coalitions is associated with the driving aggressiveness of CAVs. Finally, the effectiveness and feasibility of the proposed decision-making framework are verified with three test cases.