Strategic Non-cooperative Game Research Articles

Edge computing offloading strategy for space-air-ground integrated network based on game theory

The limited coverage of terrestrial networks makes it difficult to provide low-latency and high-reliable computing services for users and Internet of Thing (IoT) devices in remote areas such as mountainous regions and oceans. Space-Air-Ground Integrated Network (SAGIN) combined with Mobile Edge Computing (MEC) can provide seamless three-dimensional services for users by deploying edge servers on satellites, Unmanned Aerial Vehicles (UAVs) and ground infrastructures. However, due to the limited heterogeneous computing resources in satellites-UAV clusters network and the energy resources of IoT devices, it brings a significant challenge in determining how to offload the computing tasks generated by ground user devices to satellite edge nodes, UAV edge nodes or locally for processing. In this paper, we first propose a satellites-UAV clusters-ground three-layer edge computing network architecture consisting of a global controller, inter-domain controllers and MEC servers. We then model the task offloading problem as a Binary Integer Linear Programming (BILP) aiming at minimizing the offloading cost composed of delay and energy consumption and prove it is NP-hard. Next, the original offloading problem is transformed to a noncooperative strategic game and the existence of Nash equilibrium is proven using potential games. Finally, we propose a Nash Equilibrium Iteration Offloading algorithm based on Game theory (NEIO-G) to find the optimal offloading strategy. Compared with other baseline algorithms, simulation results demonstrate that the NEIO-G can significantly reduce the system offloading overhead in terms of delay and energy consumption.

Examining B2B channel decision-making within differential quality-level zone: a supply chain design using a non-cooperative strategic game theoretic approach (“Stackelberg Supply Chain for B2B”)

Purpose The consumers want to purchase the target products in the right place, whereas the manufacturers want to allocate their possible products to optimal distribution channels. The manufacturer must know how to handle itself in this business. The study aims to examine the B2B channel decision-making with different product qualities in a non-cooperative supply chain. Design/methodology/approach The authors develop a B2B Manufacturer-Stackelberg game as an analytical framework, combining asymmetric preference of purchase channels choice by the consumers, a continuous quality setting of the manufacturer and differential channel structure to study the manufacturer’s product strategy and channel optimisation. By horizontal comparisons across four channel structures, product variety can be classified into the differential quality-level zone through exogenous quality intervention, and the preference of manufacturers in each quality-level zone within the structures can be ranked. Findings Theoretically and practically, the hybrid-channel structure should be completely neglected when the direct channel dominates the retail channel. In contrast, dual-channel structures dominate single channels irrespective of the channel power, and channel preferences between high-quality and low-quality zones are stable, whereas the preference in medium-quality zone is unstable. In addition, the supply chain system cannot achieve global Pareto improvement without any additional coordination mechanism between the manufacturer and the retailer. Originality/value The extended results by numerical examples suggest that the bigger the area of the medium-quality zone, the more significant the product variety of the manufacturer.

Joint beamforming and power allocation between a multistatic MIMO radar network and multiple targets using game theoretic analysis

This paper investigates a countermeasure model between a multistatic multiple-input multiple-output (MIMO) radar network and multiple targets in the presence of continuous surface clutter. As a member of the multistatic MIMO radar network, the main purpose of each radar is to minimize its transmit power under a certain target detection criterion. Based on the selfishness of each radar, a strategic non-cooperative game (SNG) framework between MIMO radars is constructed. For the SNG between MIMO radars, the existence and uniqueness of the Nash equilibrium (NE) solution are proved strictly. And then, an iterative power allocation strategy for each MIMO radar is developed using optimization theory. The receive beamformer weight vectors of the multistatic MIMO radars are obtained by minimum variance distortionless response (MVDR) and linearly constrained minimum variance (LCMV) to suppress cross-channel interferences, respectively. Furthermore, two joint beamforming and power allocation game algorithms are proposed, which converge to the NE of the game. Finally, in order to illustrate the superiority of the proposed algorithms, we compare them with the relevant game algorithm. Numerical results are provided to show the advantages of the proposed algorithms in terms of power allocation and interference suppression.

Competition of Duopoly MVNOs for IoT Applications through Wireless Network Virtualization

Network performance is of great importance for processing Internet of Things (IoT) applications in the fifth-generation (5G) communication system. With the increasing number of the devices, how network services should be provided with better performances is becoming a pressing issue. The static resource allocation of wireless networks is becoming a bottleneck for the emerging IoT applications. As a potential solution, network virtualization is considered a promising approach to enhancing the network performance and solving the bottleneck issue. In this paper, the problem of wireless network virtualization is investigated where one wireless infrastructure provider (WIP), mobile virtual network operators (MVNOs), and IoT devices coexist. In the system model under consideration, with the help of a software-defined network (SDN) controller, the WIP can divide and reconfigure its radio frequency bands to radio frequency slices. Then, two MVNOs, MVNO1 and MVNO2, can lease these frequency slices from the WIP and then provide IoT network services to IoT users under competition. We apply a two-stage Stackelberg game to investigate and analyze the relationship between the two MVNOs and IoT users, where MVNO1 and MVNO2 firstly try to maximize their profits by setting the optimal network service prices. Then, IoT users make decisions on which network service they should select according to the performances and prices of network services. Two competition cases between MVNO1 and MVNO2 are considered, namely, Stackelberg game (SG) where MVNO1 is the leader whose price of network service is set firstly and MVNO2 is the follower whose network service price is set later and noncooperative strategic game (NSG) under which the service prices of MVNO1 and MVNO2 are simultaneously set. Each IoT user decides whether and which MVNO to select on the basis of the network service prices and qualities. The numerical results are provided to show the effectiveness of our game model and the proposed solution method.

Noncooperative Social Welfare Optimization With Resiliency Against Network Anomaly

This article presents a noncooperative game-theoretic framework to model the social welfare optimization (SWO) problem with load aggregators participating in integrated economic dispatch and demand response. In the proposed framework, distribution system operators interact with generation units and load aggregators to maximize the overall social welfare. The proposed SWO problem addresses practical system constraints and falls into the scope of mixed integer nonlinear programs, which cannot be well handled by existing distributed algorithms. The proposed SWO problem is formulated by a special noncooperative strategic game, known as the potential game, and solved by a revised version of the spatial adaptive play under network anomaly. It is shown that the proposed framework has guaranteed convergence to a Nash equilibrium that is also a global optimizer. Simulations on a 15-generator benchmark distribution network have been conducted to validate the proposed framework.

Duopoly Price Competition in Wireless Sensor Network-Based Service Provision.

The Internet of Things (IoT) is emerging as a new communication paradigm and has attracted a significant amount of attention from both academic and engineering communities. In this paper, we consider an IoT market where three roles exist: Wireless Sensor Networks (WSNs), two service providers (SPs) and end users. The WSNs are responsible for sensing and providing data to the two SPs. Based on the sensed data from WSNs, the two SPs compete to provide services to the end users. We model the relationship between the two SPs and end users as a two-stage Stackelberg game, where the two SPs set the prices for their services firstly, and then the end users decide which SP to choose. Specifically, we consider two price-competition scenarios of the two SPs, which are engaged in two games, one is a noncooperative strategic game (NSG) where the two SPs set the prices for services simultaneously, the other is a Stackelberg game (SG) where SP1 who sets the price first is the leader and SP2 who sets the price after is the follower. Each user decides whether and which SP to purchase services from based on prices and service rates. An equilibrium is achieved in each of the two scenarios. Numerical results are conducted to verify our theoretical analysis.

Game‐theoretic beamforming techniques for multiuser multi‐cell networks under mixed quality of service constraints

We propose a game-theoretic approach for the downlink beamformer design for a multiuser multi-cell wireless network under a mixed quality of services criterion. The network has real time users that must attain a specific set of signal-to-interference-plus-noise ratios, and non-real time users whose signal-to-interference-plus-noise ratios should be balanced and maximized. We propose a mixed QoS strategic noncooperative game wherein base stations determine their downlink beamformers in a fully distributed manner. In the case of infeasibility, we have proposed a fall back mechanism which converts the problem to a pure max-min optimization. We further propose the mixed QoS bargain game to improve the Nash equilibrium operating point through Egalitarian and Kalai-Smorodinsky bargaining solutions. We have shown that the results of bargaining games are comparable to that of the optimal solutions.

Game theoretic analysis for MIMO radars with multiple targets

This paper considers a distributed beamforming and resource allocation technique for a radar system in the presence of multiple targets. The primary objective of each radar is to minimize its transmission power while attaining an optimal beamforming strategy and satisfying a certain detection criterion for each of the targets. Therefore, we use convex optimization methods together with noncooperative and partially cooperative game theoretic approaches. Initially, we consider a strategic noncooperative game (SNG), where there is no communication between the various radars of the system. Hence each radar selfishly determines its optimal beamforming and power allocation. Subsequently, we assume a more coordinated game theoretic approach incorporating a pricing mechanism. Introducing a price in the utility function of each radar/player enforces beamformers to minimize the interference induced to other radars and to increase the social fairness of the system. Furthermore, we formulate a Stackelberg game by adding a surveillance radar to the system model, which will play the role of the leader, and hence the remaining radars will be the followers. The leader applies a pricing policy of interference charged to the followers aiming at maximizing his profit while keeping the incoming interference under a certain threshold.We also present a proof of the existence and uniqueness of the Nash equilibrium (NE) in both the partially cooperative and non cooperative games. Finally, the simulation results confirm the convergence of the algorithm in all three cases.

A Game Theoretic Framework for E-Mail Detection and Forgery Analysis

In email forensic, the email detection and forgery conflict is an interdependent strategy selection process, and there exists complex dynamics between the detector and the forger, who have conflicting objectives and influence each other’s performance and decisions. This paper aims to study their dynamics from the perspective of game theory .We firstly analyze the email basic structure and header information, then discuss the email detection and forgery technologies. In this paper, we propose a Detection-Forgery Game (DFG) model and make a classification of players’ strategy with the Operation Complexity (OC). In the DFG model, we regard the interactions between the detector and the forger as a two-player, non-cooperative, non-zero-sum and finite strategic game, and formulate the Nash Equilibrium. The optimal detection and forgery strategies with minimizing cost and maximizing reward will be found by using the model. Finally, we perform empirical experiments to verify the effectiveness and feasibility of the model.

Properly efficient Nash equilibrium in multicriteria noncooperative games

The aim of this paper is to study the concept of properly efficient equilibrium for a multicriteria noncooperative strategic game. Using results of multicriteria optimization programming, we give some characterizations and existence results of this concept in the considered game.

Advance Reservation Games and the Price of Conservatism

Advance reservation (AR) services form a pillar of many branches of the economy, e.g., transportation, lodging, dining, and health care. There has also been increased interest in applying AR in cloud computing systems [1]. For instance, Moab Workload Manager [2] and IBM Platform Computing Solutions [3] support AR. In both of these packages, an administrator can decide whether or not to enable AR and define an AR pricing scheme. In most systems supporting AR, customers can choose whether making AR or not. Since the payoff of each customer is affected by decisions of other customers, it is natural to analyze the behavior of such systems as strategic games. In this work, we study a strategic non-cooperative game, referred to as an advance reservation game. In this game, players (customers) can reserve future resources in advance for a fixed reservation fee C. We consider a slotted loss system with N servers where customers are not flexible, i.e., they leave the system if they cannot be served at their desired time slots. Customers are not informed of the state of the system (i.e., the number of unreserved servers) prior to attempting a reservation. Thus, a customer opting not to make a reservation lowers its chance of finding a server available at the desired time. The number of customers in each slot is an i.i.d. Poisson random variable with parameter λ [4]. Customers have different lead times, where the lead time of a customer is defined as the time elapsing between its arrival and the slot starting time. Each customer only knows its own lead time. However, all lead times are derived from the same continuous distribution known by both the provider and the customers. In [5], we derive the equilibria structure of AR games. We show that for any C > 0, only two types of equilibria are possible. In the first type, none of the customers, regardless of their lead times, makes AR (non-make-AR equilibrium). In the second type, only customers with lead time greater than some threshold make AR (threshold equilibrium). Furthermore, we establish the existence of three different ranges of fees, such that if C falls in the first range only threshold equilibria exist, in the second range both threshold equilibria and a none-make-AR equilibrium exist, and in the third range only a none-make-AR equilibrium exists. In many cases, the fee C that maximizes the provider's profit lies in the second range. However, setting up a fee in that range carries also the risk of zero profit for the provider. Therefore, in order to properly set the AR fee, the provider should consider both the fee yielding the maximum possible profit and the fee yielding the maximum guaranteed profit. A guaranteed profit can be only achieved using fees falling within the first range. In this work, we introduce the concept of price of conservatism ( PoC ), which corresponds to the ratio of the maximum possible profit to the maximum guaranteed profit, and analyze it in different regimes. A greater PoC indicates greater potential profit loss if the provider opts to be conservative. First, we analyze a single-server regime, where we prove that for any fee the equilibrium is unique (the second range collapses in that case). Hence, PoC = 1 and the provider experiences no loss. Next, we analyze a many-server regime where λ = α N and N → ∞. We distinguish between the cases of overloaded and underloaded systems (i.e., α > 1 and α < 1 respectively). For the overloaded case, we show that PoC = α/(α--1). Hence, the price of conservatism increases in an unbounded fashion as α approaches one from above. Finally, for the underloaded case, we show that both the maximum and guaranteed profits converge to zero.

Block-Diagonalization Precoding in a Multiuser Multicell MIMO System: Competition and Coordination

This paper studies a multiuser multicell system where block-diagonalization (BD) precoding is utilized on a per-cell basis. We examine and compare the multicell system under two operating modes: competition and coordination. In the competition mode, the paper considers a strategic non-cooperative game (SNG), where each base-station (BS) greedily determines its BD precoding strategy in a distributed manner, based on the knowledge of the inter-cell interference at its connected mobile-stations (MS). Via the game-theory framework, the existence and uniqueness of a Nash equilibrium in this SNG are subsequently studied. In the coordination mode, the BD precoders are jointly designed across the multiple BSs to maximize the network weighted sum-rate (WSR). Since this WSR maximization problem is nonconvex, we consider a distributed algorithm to obtain at least a locally optimal solution. Finally, we extend our analysis of the multicell BD precoding to the case of BD-Dirty Paper Coding (BD-DPC) precoding. We characterize BD-DPC precoding game for the multicell system in the competition mode and propose an algorithm to jointly optimize BD-DPC precoders for the multicell system in the coordination mode. Simulation results show significant network sum-rate improvements by jointly designing the BD or BD-DPC precoders across the multicell system in the coordination mode over the competition mode.

Optimal resource allocation in fetmocell networks based on Markov modeling of interferers’ activity

Femtocell networks offer a series of advantages with respect to conventional cellular networks. However, a potential massive deployment of femto-access points (FAPs) poses a big challenge in terms of interference management, which requires proper radio resource allocation techniques. In this article, we propose alternative optimal power/bit allocation strategies over a time-frequency frame based on a statistical modeling of the interference activity. Given the lack of knowledge of the interference activity, we assume a Bayesian approach that provides the optimal allocation, conditioned to periodic spectrum sensing, and estimation of the interference activity statistical parameters. We consider first a single FAP accessing the radio channel in the presence of a dynamical interference environment. Then, we extend the formulation to a multi-FAP scenario, where nearby FAP’s react to the strategies of the other FAP’s, still within a dynamical interference scenario. The multi-user case is first approached using a strategic non-cooperative game formulation. Then, we propose a coordination game based on the introduction of a pricing mechanism that exploits the backhaul link to enable the exchange of parameters (prices) among FAP’s.

Statistical Transceiver Designs with ICI Reduction for MIMO-OFDM Systems

In this paper, transceiver designs that take into account inter-carrier interferences (ICI) in the framework of game theory for multiple-input multiple-output orthogonal frequency division multiplexing systems are presented. With statistical channel state information at the transmitter, two transceivers: minimal mean-squared-error equalizer and minimal mean-squared-error decision-feedback equalizer are designed. The transceiver designs with the objective of minimizing the expectation of detection mean squared error become a complicated strategic non-cooperative game problem. In the paper, heuristic algorithms based on the best reply dynamic in game theory are proposed, whose convergence to Nash equilibrium can be numerically verified. Compared with traditional transceivers which ignore ICI effect by assuming perfect orthogonality between subcarriers, our designs require a moderate increase in design complexity. Nevertheless, the proposed transceivers have the same implementation complexity as the traditional counterparts. Numerical results verify that the proposed transceivers are more robust to ICI effect from the perspective of bit error rate than the traditional ones.

Stochastic Precoding for MISO Interference Channels with Channel Mean Feedback

This work considers linear precoding strategies for multiple-input single-out (MISO) interference channels with channel mean feedback at transmitters, where the interference at each receiver is treated as additive noise. The challenge here is that previous precoder designs with perfect channel state information (CSI) at transmitters do not apply and new approaches are required. Based on the Laplace transform order, an altruistic non-equilibrium strategy, i.e., the stochastic zero forcing, is first proposed under practical assumptions, generalizing the traditional zero forcing which requires perfect CSI. Interestingly, the precoding matrices here are all rank-one beamformers as in the traditional zero forcing. The competitive use of the common physical media in MISO interference channels is also formulated as a strategic noncooperative game. In contrast to the perfect CSI case with a unique rank-one Nash equilibrium, with channel mean feedback, the Nash equilibria here are not necessarily rank-one in general. Nevertheless, when achieved by the rank-one beamforming, the equilibrium is unique and convenient for implementation. Accordingly, the condition for beamforming to achieve the equilibrium is derived. Comparisons of the above two strategies reveal no overall dominance of one over the other, thereby establishing stochastic zero forcing as an alternative to the Nash equilibrium designs.

Multiuser Downlink Beamforming in Multicell Wireless Systems: A Game Theoretical Approach

This paper is concerned with the game theoretical approach in designing the multiuser downlink beamformers in multicell systems. Sharing the same physical resource, the base-station of each cell wishes to minimize its transmit power subject to a set of target signal-to-interference-plus-noise ratios (SINRs) at the multiple users in the cell. In this context, at first, the paper considers a strategic noncooperative game (SNG) where each base-station greedily determines its optimal downlink beamformer strategy in a distributed manner, without any coordination between the cells. Via the game theory framework, it is shown that this game belongs to the framework of standard functions. The conditions guaranteeing the existence and uniqueness of a Nash Equilibrium (NE) in this competitive design are subsequently examined. The paper then makes a revisit to the fully coordinated design in multicell downlink beamforming, where the optimal beamformers are jointly designed between the base-stations. A comparison between the competitive and coordinated designs shows the benefits of applying the former over the latter in terms of each design's distributed implementation. Finally, in order to improve the efficiency of the NE in the competitive design, the paper considers a more cooperative game through a pricing mechanism. The pricing consideration enables a base-station to steer its beamformers in a more cooperative manner, which ultimately limits the interference induced to other cells. The study on the existence and uniqueness of the new game's NE is then given. The paper also presents a condition on the pricing factors that allow the new NE point to approach the performance established by the coordinated design, while retaining the distributed nature of the multicell game.

Strategic Analysis of Risk-Shifting Incentives with Convertible Debt

Convertible debt eliminates asset substitution in a one-period setting (Green, 1984). But convertible debt terms are usually set before the asset substitution opportunity. This allows shareholders and convertible debtholders to play a strategic noncooperative game. Two risk-shifting Nash equilibria are attainable: pure asset substitution when, despite no conversion, shareholders benefit from shifting risk, and strategic conversion when, despite early conversion, convertible debtholders expropriate wealth from straight debtholders. Even when initial convertible debt is designed to minimize the risk-shifting likelihood, the risk of asset substitution remains economically substantial — contrasting with the agency theoretic rationale for issuing convertible debt.

Hospital stockpiling for disaster planning

In response to the increasing threat of terrorist attacks and natural disasters, governmental and private organizations worldwide have invested significant resources in disaster planning activities. This article addresses joint inventory stockpiling of medical supplies for groups of hospitals prior to a disaster. Specifically, the problem of determining the stockpile quantity of a medical item at several hospitals is considered. It is assumed that demand is uncertain and driven by the characteristics of a variety of disaster scenarios. Furthermore, it is assumed that hospitals have mutual aid agreements for inventory sharing in the event of a disaster. Each hospital's desire to minimize its stockpiling cost together with the potential to borrow from other stockpiles creates individual incentives well represented in a game-theoretic framework. This problem is modeled as a non-cooperative strategic game, the existence of a Nash equilibrium is proved, and the equilibrium solutions are analyzed. A centralized model of stockpile decision making where a central decision maker optimizes the entire system is also examined and the solutions obtained using this model are compared to those of the decentralized (game) model. The comparison provides some managerial insights and public health policy implications valuable for disaster planning.

Inter-Operator Spectrum Sharing from a Game Theoretical Perspective

We address the problem of spectrum sharing where competitive operators coexist in the same frequency band. First, we model this problem as a strategic non-cooperative game where operators simultaneously share the spectrum according to the Nash Equilibrium (NE). Given a set of channel realizations, several Nash equilibria exist which renders the outcome of the game unpredictable. Then, in a cognitive context with the presence of primary and secondary operators, the inter-operator spectrum sharing problem is reformulated as a Stackelberg game using hierarchy where the primary operator is the leader. The Stackelberg Equilibrium (SE) is reached where the best response of the secondary operator is taken into account upon maximizing the primary operator's utility function. Moreover, an extension to the multiple operators spectrum sharing problem is given. It is shown that the Stackelberg approach yields better payoffs for operators compared to the classical water-filling approach. Finally, we assess the goodness of the proposed distributed approach by comparing its performance to the centralized approach.

A Note on the Interaction between Identity Based Fear and Hate

I model the interaction between the fear experienced by the indigenous population and the hatred felt by certain visible minorities such as Muslims within the context of a strategic non-cooperative game where identity plays a crucial role. The indigenous population is represented by the state or government reflecting the views of the median voter; the formation of dissident behaviour by minorities involves co-opting individuals to act in group interests. An increase in government militancy results from an increase in the vote bank of confrontative populist politicians relying on the supply of repetitive hate-creating stories. A rise in the intrinsic motivation to fight the state by dissidents arises because of the loss in domestic social standing, or the relationship to events in the Muslim world. Space needs to be created so that most Muslim migrants are able to position their personal identities within their adopted European homelands. Economic and social discrimination against Muslims also needs to be addressed.