Game-theoretic Formulation Research Articles

A game-theoretic approach to managing the composition and structure of a bearing-only measurement system in conditions of a priori uncertainty

The problem of managing the composition and structure of a bearing-only measurements system (BOMS) in a game-theoretic formulation is considered. An approach of cooperative search for the placement of BOMS points and a method for estimating the work-time indicator of the system are proposed. The search for the placement of BOMS points uses the toolkit of multi-agent potential games. The criteria for selecting the placement of points and the type of potential function are determined. The management of the composition and structure of the BOMS is based on the results of the cluster-variation method. A structural and functional description of the simulation model is presented. The above results of simulation modeling confirm the practical effectiveness of the proposed approaches.

Distributed service function chaining in NFV-enabled networks: A game-theoretic learning approach

In network function virtualization (NFV), Service Function Chaining (SFC) provides an ordered sequence of virtual network functions (VNFs) and subsequent steering of traffic flows through them to cater to end-to-end services. This paper addresses the NP-hard problem of minimum cost SFC deployment to support customer services that access the carrier network’s NFV infrastructure (NFVI) through some edge routers. To determine the mappings of VNFs to physical servers, a challenging aspect would be the inter-server latencies that may fluctuate over time because of the sharing nature of cloud data centers. To construct the SFC, we come up with three different formulations, each corresponding to a different informational assumption about the link latencies: First, a centralized integer linear programming (ILP) formulation is given under the assumption of the non-causal availability of exact and instantaneous inter-server latencies. The solution to this ILP can serve as a lower bound to benchmark more scalable and realistic schemes. Next, we give a distributed game-theoretic formulation (with service broker agents as players) which only requires the statistical knowledge of link latency fluctuations. The game provably admits a pure Nash equilibrium (NE) and can be solved iteratively through the well-known best response dynamics (BRD) algorithm. Our main novelty lies in the third formulation in which each service broker has neither instantaneous nor statistical knowledge of the latencies. Instead, it relies on a game-theoretic learning algorithm to compose its VNF chain only based on its own history of adopted decisions and experienced delays on each logical link. We prove that the proposed learning algorithm asymptotically converges to NE and evaluate its performance through simulations in terms of convergence and the impact of network parameters.

Deep Reinforcement Learning for Communication Networks

This research explores optimizing communication tasks with (Multi-Agent) Reinforcement Learning (RL/MARL) in Point-to-Point and Group Communication (GC) networks. The study initially applied RL for Congestion Control in networks with dynamic link properties, yielding competitive results. Then, it focused on the challenge of effective message dissemination in GC networks, by framing a novel game-theoretic formulation and designing methods to solve the task based on MARL and Graph Convolution. Future research will deepen the exploration of MARL in GC. This will contribute to both academic knowledge and practical advancements in the next generation of communication protocols.

Equilibria in schelling games: computational hardness and robustness

In the simplest game-theoretic formulation of Schelling’s model of segregation on graphs, agents of two different types each select their own vertex in a given graph so as to maximize the fraction of agents of their type in their occupied neighborhood. Two ways of modeling agent movement here are either to allow two agents to swap their vertices or to allow an agent to jump to a free vertex. The contributions of this paper are twofold. First, we prove that deciding the existence of a swap-equilibrium and a jump-equilibrium in this simplest model of Schelling games is NP-hard, thereby answering questions left open by Agarwal et al. [AAAI ’20] and Elkind et al. [IJCAI ’19]. Second, we introduce two measures for the robustness of equilibria in Schelling games in terms of the minimum number of edges or the minimum number of vertices that need to be deleted to make an equilibrium unstable. We prove tight lower and upper bounds on the edge- and vertex-robustness of swap-equilibria in Schelling games on different graph classes.

Game Theoretical Formulation for Residential Community Microgrid via Mean Field Theory: Proof of Concept

Game Theoretical Formulation for Residential Community Microgrid via Mean Field Theory: Proof of Concept

UAV SECaaS: Game-Theoretic Formulation for Security as a Service in UAV Swarms

Unmanned aerial vehicles, popularly known as UAVs, have been used in many applications in the recent past. UAVs have also been recently used to provide security as a service (SECaaS). SECaaS involves technical solutions, like antivirus and antispam software, firewalls, using secure operating systems, etc. UAVs are resource-constrained entities, and thus, they avail the computational facilities of the base station (BS) to serve the users in their range. At times, several UAVs cooperatively come together to serve a given region, and such a group of UAVs is called a swarm of UAVs. Generally, a group/swarm of UAVs connect themselves to the BS through cluster head (CH) UAVs, which are intermediary nodes. In real-world scenarios, many stakeholders come together to form a UAV swarm configuration providing services to users. Each stakeholder wants to maximize gains. This work proposes a pricing Stackelberg game among the UAVs, CHs, and the BS by formulating their behavioral utilities. Using particle swarm optimization on each entity’s utility functions, we create an optimal price strategy to maximize profit.

Control frameworks for transactive energy storage services in energy communities

Recently, the decreasing cost of storage technologies and the emergence of economy-driven mechanisms for energy exchange are contributing to the spread of energy communities. In this context, this paper aims at defining innovative transactive control frameworks for energy communities equipped with independent service-oriented energy storage systems. The addressed control problem consists in optimally scheduling the energy activities of a group of prosumers, characterized by their own demand and renewable generation, and a group of energy storage service providers, able to store the prosumers’ energy surplus and, subsequently, release it upon a fee payment. We propose two novel resolution algorithms based on a game theoretical control formulation, a coordinated and an uncoordinated one, which can be alternatively used depending on the underlying communication architecture of the grid. The two proposed approaches are validated through numerical simulations on realistic scenarios. Results show that the use of a particular framework does not alter fairness, at least at the community level, i.e., no participant in the groups of prosumers or providers can strongly benefit from changing its strategy while compromising others’ welfare. Lastly, the approaches are compared with a centralized control method showing better computational results.

Equilibrium Seeking and Optimal Selection Algorithms in Peer-to-Peer Energy Markets

We consider a clearing problem in peer-to-peer energy markets, where prosumers can trade energy among each other and with the main grid to meet their energy demands. By using a game-theoretic formulation and exploiting operator-theoretic methods for generalized Nash equilibrium seeking, we propose two variants of the state-of-the-art distributed market clearing mechanism with improved convergence speeds. Furthermore, we design a third variant that allows for equilibrium selection, i.e., computing a specific market solution based on a convex preference function of the network operator, e.g., a congestion cost. We provide convergence guarantees and numerically show the advantages of our proposed algorithms in terms of convergence speed up and obtaining reduced grid congestion.

Policy Learning for Robust Markov Decision Process with a Mismatched Generative Model

In high-stake scenarios like medical treatment and auto-piloting, it's risky or even infeasible to collect online experimental data to train the agent. Simulation-based training can alleviate this issue, but may suffer from its inherent mismatches from the simulator and real environment. It is therefore imperative to utilize the simulator to learn a robust policy for the real-world deployment. In this work, we consider policy learning for Robust Markov Decision Processes (RMDP), where the agent tries to seek a robust policy with respect to unexpected perturbations on the environments. Specifically, we focus on the setting where the training environment can be characterized as a generative model and a constrained perturbation can be added to the model during testing. Our goal is to identify a near-optimal robust policy for the perturbed testing environment, which introduces additional technical difficulties as we need to simultaneously estimate the training environment uncertainty from samples and find the worst-case perturbation for testing. To solve this issue, we propose a generic method which formalizes the perturbation as an opponent to obtain a two-player zero-sum game, and further show that the Nash Equilibrium corresponds to the robust policy. We prove that, with a polynomial number of samples from the generative model, our algorithm can find a near-optimal robust policy with a high probability. Our method is able to deal with general perturbations under some mild assumptions and can also be extended to more complex problems like robust partial observable Markov decision process, thanks to the game-theoretical formulation.

Game Semantics, Quantifiers and Logical Omniscience

Logical omniscience states that the knowledge set of ordinary rational agents is closed for its logical consequences. Although epistemic logicians in general judge this principle unrealistic, there is no consensus on how it should be restrained. The challenge is conceptual: we must find adequate criteria for separating obvious logical consequences (consequences for which epistemic closure certainly holds) from non-obvious ones. Non-classical game-theoretic semantics has been employed in this discussion with relative success. On the one hand, with urn semantics [15], an expressive fragment of classical game semantics that weakens the dependence relations between quantifiers occurring in a formula, we can formalize, for a broad array of examples, epistemic scenarios in which an individual ignores the validity of some first-order sentence. On the other hand, urn semantics offers a disproportionate restriction of logical omniscience. Therefore, an improvement of this system is needed to obtain a better solution of the problem. In this paper, I argue that our linguistic competence in using quantifiers requires a sort of basic hypothetical logical knowledge that can be formulated as follows: when inquiring after the truth-value of ∀xφ, an individual might be unaware of all substitutional instances this sentence accepts, but at least she must know that, if an element a is given, then ∀xφ holds only if φ(x/a) is true. This thesis accepts game-theoretic formalization in terms of a refinement of urn semantics. I maintain that the system so obtained (US+) affords an improved solution of the logical omniscience problem. To do this, I characterize first-order theoremhood in US+. As a consequence of this result, we will see that the ideal reasoner depicted by US+ only knows the validity of first-order formulas whose Herbrand witnesses can be trivially found, a fact that provides strong evidence that our refinement of urn semantics captures a relevant sense of logical obviousness.

Mean-Variance Portfolio Selection with Partial Information: A Game-theoretic Formulation

Mean-Variance Portfolio Selection with Partial Information: A Game-theoretic Formulation

Tax Authority and Taxpayers: How Does Mutual Collecting of Information Affect the Effectiveness of Tax Control

Lots of works have been devoted to the modelling of tax control. In the classic game-theoretic formulation, the subject of study is the interaction between tax authority and taxpayers. However, along with such attitude to the problem, some works allow us to study auxiliary problems related to tax collection and tax control. Two of these issues are worth mentioning. The first is the dissemination of information about future tax audits among the taxable population. The second is the gathering and analysis of information on the tendency of taxpayers to evasion. It was shown that both processes can be used to adjust the tax authority's strategy and optimize audits in order to improve tax collection. However, the mutual collecting of information on tax audits by the taxpayers and the tax authority decreases the total tax revenue. The study of formulated problem is accompanied by the modelling of both processes, their simulation, and comparative analysis of the results.

A Game Theoretic Approach to Channel Switching in the Presence of Jamming

In this letter, a channel switching problem is investigated in the presence of jamming based on a game theoretic approach. First, a convex formulation of the optimal channel switching problem is proposed for a given jamming strategy. Then, considering a fixed channel switching strategy, an explicit solution of the optimal jammer power allocation problem is obtained. Consequently, a game theoretic formulation is proposed and the existence of a pure-strategy Nash equilibrium is shown for the proposed channel switching game between the transmitter and the jammer.

A differential game view of antagonistic dynamics for cybersecurity

A fundamental understanding of the dynamics of the antagonism between the attacker and the defender can strengthen forward-looking and strategic planning for the cybersecurity. Most of the existing works have one or more of the following limitations: static modeling, non co-evolved strategy and synchronized setting, not accounting for the dynamic nature of the cyber arms race between the defensive and offensive sides. In this paper, we apply differential game theory to analyze the antagonistic dynamics between the attacker and the defender and study two complementary game theoretic formulations, namely the black-box game the and the white-box game: The black-box game can cogently model the opaque-information confrontation and the white-box one is capable to depict the partially transparent-information confrontation. To gain insight into the evolution rule of the antagonistic dynamics between the defensive and the offensive sides, we establish the existence of the Nash equilibrium and the corresponding conditions in the black-box game. Moreover, an iteration algorithm is designed to find the numerical solutions of the Nash equilibrium in the general case and further its analytical solutions in a special case for the white-box game. Extensive numerical simulations have been carried out to evaluate the performance of the proposed games.

Distributed Task Offloading Optimization With Queueing Dynamics in Multiagent Mobile-Edge Computing Networks

Task offloading decision making plays a key role in enabling mobile-edge computing (MEC) technologies in Internet of Things (IoT). However, it meets the significant challenges arising from the stochastic dynamics of task queueing in the application layer and coupled wireless interference in the physical layer in a distributed multiagent network without any centralized communication and computing coordination. In this article, we investigate the distributed task offloading optimization problem with consideration of the upper layer queueing dynamics and the lower-layer coupled wireless interference. We first propose a new optimization model that aims at maximizing the expected offloading rate of multiple agents by optimizing their offloading thresholds. Then, we transform the problem into a game-theoretic formulation, which further leads to the design of a distributed best-response (DBR) iterative optimization framework. The existence of Nash equilibrium strategies in the game-theoretic model has been analyzed. For the individual optimization of each agent's threshold policy, we further propose a programming scheme by transforming a constrained threshold optimization into an unconstrained Lagrangian optimization (ULO). The individual ULO is integrated into the DBR framework to enable agents to cooperate and converge to a global optimum in a distributed manner. Finally, simulation results are provided to validate the proposed method and demonstrate its significant advantage over other existing distributed methods. The numerical results also show that the proposed method can achieve comparable performance to a centralized optimization method.

Tree Search Techniques for Adversarial Target Tracking With Distance-Dependent Measurement Noise

We study the problem of devising a closed-loop strategy to control the position of a robot that is tracking a possibly moving target. The robot obtains noisy measurements of the target's position. The measurement noise depends on the relative states of the robot and the target. We consider scenarios where the measurement values are chosen by an adversary, so as to maximize the estimation error. Furthermore, the target may be actively evading the robot. Our main contribution is to devise a closed-loop control policy for distance-dependent target tracking that plans for a sequence of control actions, instead of acting greedily. We consider a game-theoretic formulation of the problem and seek to minimize the maximum uncertainty (trace of the posterior covariance matrix) over all possible measurement values. We exploit the structural properties of a Kalman Filter to build a policy tree that is orders of magnitude smaller than naive enumeration while still preserving optimality guarantees. We show how to obtain even more computational savings by relaxing the optimality guarantees. The resulting algorithms are evaluated through simulations and experiments with real robots.

Game Theory based Cyber-Insurance to Cover Potential Loss from Mobile Malware Exploitation

Potential for huge loss from malicious exploitation of software calls for development of principles of cyber-insurance. Estimating what to insure and for how much and what might be the premiums poses challenges because of the uncertainties, such as the timings of emergence and lethality of malicious apps, human propensity to favor ease by giving more privilege to downloaded apps over inconvenience of delay or functionality, the chance of infection determined by the lifestyle of the mobile device user, and the monetary value of the compromise of software, and so on. We provide a theoretical framework for cyber-insurance backed by game-theoretic formulation to calculate monetary value of risk and the insurance premiums associated with software compromise. By establishing the conditions for Nash equilibrium between strategies of an adversary and software we derive probabilities for risk, potential loss, gain to adversary from app categories, such as lifestyles, entertainment, education, and so on, and their prevalence ratios. Using simulations over a range of possibilities, and using publicly available malware statistics, we provide insights about the strategies that can be taken by the software and the adversary. We show the application of our framework on the most recent mobile malware data (2018 ISTR report—data for the year 2017) that consists of the top five Android malware apps: Malapp, Fakeinst, Premiumtext, Maldownloader , and Simplelocker and the resulting leaked phone number, location information, and installed app information. Uniqueness of our work stems from developing mathematical framework and providing insights of estimating cyber-insurance parameters through game-theoretic choice of strategies and by showing its efficacy on a recent real malicious app data . These insights will be of tremendous help to researchers and practitioners in the security community.

Some Game-Theoretic Remarks on Two-Player Generalized Cops and Robbers Games

In this paper, we study the two-player generalized cops and robbers (GCR) games introduced by Bonato and MacGillivray. Our main goals are to provide: (a) a game-theoretic formulation of GCR and (b) a self-contained game-theoretic proof that GCR has a value and an optimal strategy profile. To achieve our goals, we first formulate GCR (and CR as a special case) as a zero-sum stochastic game. Then we study a Vertex Labeling (VL) algorithm and prove it computes the value of the GCR game (for every starting “condition”) and that the vertex labels can be used to specify a positional deterministic optimal strategy for each player. We also compare our game-theoretic analysis to some of the usual graph theoretic/combinatorial approaches to CR/GCR.

Dynamic SPICE-model of the regional development: a comparative analysis of the administrative and economic control mechanisms (on the example of South Federal District)

A game theoretic formalization of the mechanisms of control over the regions as parts of a macroregion with consideration of the requirements of sustainable development is proposed. A modified Solow model is used for the description of the regional state dynamics. The model is identified on real data for the South Russian Federal District. A qualitative comparative analysis of efficiency of the administrative and economic control mechanisms is made.

A Framework for Contractual Graphs.

This paper studies contractual graphs, where the formation of edges between nodes result in dyadic exchanges. Each dyadic exchange is analyzed as a contractual agreement that is implemented upon fulfilment of underlying conditions. As these dyadic exchanges proliferate, the resulting population of these exchanges creates a contractual graph. A contractual framework for graphs is especially useful in applications where AI-enabled software is employed to create or automate smart contracts between nodes. While some smart contracts may be easily created and executed, others may contain a higher level of ambiguity which may prevent their efficient implementation. Ambiguity in contractual elements is especially difficult to implement, since nodes have to efficiently sense the ambiguity and allocate appropriate amounts of computational resources to the ambiguous contractual task. This paper develops a two-node contractual model of graphs, with varying levels of ambiguity in the contracts and examines its consequences for a market where tasks of differing ambiguity are available to be completed by nodes. The central theme of this paper is that as ambiguity increases, it is difficult for nodes to efficiently commit to the contract since there is an uncertainty in the amount of resources that they have to allocate for completion of the tasks specified in the contract. Thus, while linguistic ambiguity or situational ambiguity might not be cognitively burdensome for humans, it might become expensive for nodes involved in the smart contract. The paper also shows that timing matters—the order in which nodes enter the contract is important as they proceed to sense the ambiguity in a task and then allocate appropriate resources. We propose a game-theoretic formulation to scrutinize how nodes that move first to complete a task are differently impacted than those that move second. We discuss the applications of such a contractual framework for graphs and obtain conditions under which two-node contracts can achieve a successful coalition.