Achieve Nash Equilibrium Research Articles

Statistical Multiplexing and Traffic Shaping Games for Network Slicing

Next generation wireless architectures are expected to enable slices of shared wireless infrastructure which are customized to specific mobile operators/services. Given infrastructure costs and the stochastic nature of mobile services' spatial loads, it is highly desirable to achieve efficient statistical multiplexing amongst such slices. We study a simple dynamic resource sharing policy which allocates a 'share' of a pool of (distributed) resources to each slice-Share Constrained Proportionally Fair (SCPF). We give a characterization of SCPF's performance gains over static slicing and general processor sharing. We show that higher gains are obtained when a slice's spatial load is more 'imbalanced' than, and/or 'orthogonal' to, the aggregate network load, and that the overall gain across slices is positive. We then address the associated dimensioning problem. Under SCPF, traditional network dimensioning translates to a coupled share dimensioning problem, which characterizes the existence of a feasible share allocation given slices' expected loads and performance requirements. We provide a solution to robust share dimensioning for SCPF-based network slicing. Slices may wish to unilaterally manage their users' performance via admission control which maximizes their carried loads subject to performance requirements. We show this can be modeled as a 'traffic shaping' game with an achievable Nash equilibrium. Under high loads, the equilibrium is explicitly characterized, as are the gains in the carried load under SCPF vs. static slicing. Detailed simulations of a wireless infrastructure supporting multiple slices with heterogeneous mobile loads show the fidelity of our models and range of validity of our high load equilibrium analysis.

An efficient revenue distribution method in a cyber-enabled manufacturing system

Considering a group of suppliers fulfilling the orders in an e-commerce platform, it is desirable for the platform operator to distribute the revenue in a way that the total net utilities of the platform and of each supplier are optimized. Based on the game theory, this paper presents a nonlinear revenue distribution rule to achieve Nash Equilibrium. Simulation studies show that, compared to the proportional and equal distribution rules, the proposed method yields the highest net utility for all. The present work demonstrates an approach to promoting broader participation of manufacturing activities in an internet-based platform enabled by cyber infrastructure.

Response time optimization for cloudlets in Mobile Edge Computing

Mobile Edge computing (MEC) and caching are new forms of computing architecture which brings network functions to the network edge or physical proximity of the users. In MEC, the mobile cloudlets are smart phones which offer computational services to other smart phones available in the physical proximity. Selection of the device for offloading computationally intensive tasks is a very important criterion for end-users Quality of Service. This work focuses on optimal selection of devices which receives offloaded computational tasks. This paper presents a non-cooperative extensive game model where players maximize their pay-offs which leads to minimization of response time. Further, we make our proposed model to implicitly depend upon the battery life of the computational task receivers. The game model achieves Nash Equilibrium by using backward induction technique. This work also takes care of the device availability by clustering the previous availability data. Finally, we evaluate the performance of the proposed model upon response time, end-users utility and memory utilizations. We also see that the proposed work out performs the different schemes which we used for comparisons.

Learning algorithms for joint resource block and power allocation in underlay D2D networks

We investigate the problem of resource block (RB) and power allocation jointly and in a distributed manner using game theoretic learning solutions, in an underlay device-to-device network where device pairs communicate directly with each other by reusing the spectrum allocated to the cellular users. We formulate the joint RB and power allocation as multi-agent learning problems with discrete strategy sets; and suggest partially distributed and fully distributed learning algorithms to determine the RB and power level to be used by each device pair. The partially distributed algorithms, viz., Fictitious Play and its variant Fading Memory Joint Strategy Fictitious Play with Inertia, achieve Nash Equilibrium (NE) of the sum-rate maximization game in a static wireless environment. The completely distributed and uncoupled Stochastic Learning Algorithm converges to pure strategy NE of the interference mitigation game in a time-varying radio environment. We provide proofs for the existence of NE and convergence of the learning algorithms to the NE. Performance of the proposed schemes are evaluated in log-normal, Rayleigh and Nakagami fading environments and compared with an existing hybrid scheme and a centralized scheme. The simulation results show that the partially distributed schemes give the same performance as the centralized scheme, and the fully distributed scheme gives similar performance as the hybrid scheme but with much reduced signaling and computation overhead.

Energy-Efficient Two-Layer Cooperative Defense Scheme to Secure Sensor-Clouds

Sensor-cloud computing is envisioned as a promising technology that can integrate various services by extending the computational capabilities of physical sensor nodes. It is prone to attack because of special characteristics of physical sensor nodes and virtual sensor-service nodes. Considering the intrusion detection threshold, false alarm probability of the intrusion detection system (IDS), and three different attacked scenarios, we devise a physical IDS (PIDS)-to-gateway and virtual IDS (VIDS)-to-gateway detection model for Sensor-Cloud. We formulate a two-layer gateway-assisted detection and defense decision problem involving multiple IDSs using an evolutionary game in order to optimize the intrusion detection strategy for lowering energy consumption and reducing alarm messages. We derive an evolutionary stable strategy and prove that the proposed mechanism achieves Nash equilibrium, such that each IDS completes cooperatively defense tasks. We propose a game-theoretic approach to achieve an energy-efficient cooperative defense scheme for sensor-cloud computing environments. The simulation results demonstrate that the proposed mechanism achieves energy-efficient defense and increases security of data in the Sensor-Cloud.

Single Sample Fictitious Play

This paper is concerned with distributed learning and optimization in large-scale settings. The well-known fictitious play (FP) algorithm has been shown to achieve Nash equilibrium learning in certain classes of multiagent games. However, FP can be computationally difficult to implement when the number of players is large. Sampled FP (SFP) is a variant of FP that mitigates the computational difficulties arising in FP by using a Monte Carlo (i.e., sampling based) approach. Despite its computational advantages, a shortcoming of SFP is that the number of samples that must be drawn at each iteration grows without bound as the algorithm progresses. In this paper, we propose single sample FP (SSFP)—A variant of SFP in which only one sample needs to be drawn in each round of the algorithm. Convergence of SSFP to the set of Nash equilibria is proven. Simulation results show the performance of SSFP is comparable to that of SFP, despite drawing far fewer samples.

A Stochastic Multiple-Leader-Follower Incentive Stackelberg Strategy for Markov Jump Linear Systems

An incentive Stackelberg game for a class of Markov jump linear stochastic systems with multiple leaders and followers is investigated in this letter. An incentive structure is developed that allows the leader’s Nash equilibrium to be achieved. In the game, the followers are assumed to behave in two ways under the leader’s incentive strategy set. One involves achieving a Pareto-optimal solution, and the other involves achieving Nash equilibrium. Consequently, it can be verified that irrespective of how the followers behave, they can be induced to achieve the leader’s Nash equilibrium by using a corresponding incentive strategy set. It is shown that the incentive strategy set can be obtained by solving the cross-coupled stochastic algebraic Riccati-type equations. As another important contribution, a novel concept of incentive possibility is proposed for a special case. In order to demonstrate the effectiveness of the proposed scheme, a numerical example is solved.

Game-Theoretic Approaches for Energy Cooperation in Energy Harvesting Small Cell Networks

Deploying small cells in cellular networks, as a technique for capacity and coverage enhancement, is an indispensable characteristic of future cellular networks. In this paper, two novel online approaches for enabling energy trading in multitier cellular networks with noncooperative energy-harvesting base stations (BSs) are proposed. The goal is to minimize the nonrenewable energy consumption in a multitier cellular network with an arbitrary number of tiers. In the first approach, a decentralized energy trading framework is established in which BSs are stimulated to compensate their energy shortage with the extra harvested energy from other BSs rather than using the nonrenewable energy. Matching theory is used to assign BSs with energy deficit to the BSs with extra harvested energy. In the second approach, which is centralized, BSs with extra harvested energy and BSs with energy deficit enter a double auction for energy trading. The centralized approach also motivates the BSs with deficient energy to use other BSs extra harvested energy and satisfies a number of properties including truthfulness, individual rationalities, and budget balance. Both approaches achieve Nash equilibrium and motivate noncooperative BSs to share their extra harvested energy. The extra harvested energy is exchanged by the smart grid. We show that the amount of information exchanged in the network to enable BSs to trade energy is reduced in the centralized algorithm compared to the decentralized algorithm at the expense of using a control center. Simulation results verify that the proposed approaches reduce the nonrenewable energy consumption conspicuously. Furthermore, by applying the proposed approaches, BSs gain more profit, and consequently, their utility functions enhance.

A new approach to cooperative competition in facility location problems: Mathematical formulations and an approximation algorithm

This paper deals with cooperative competition in facility location problems in which potential players (investors) are in competition (or conflict) over acquiring suitable sites and clients. In order to formulate the problem, a game-theoretical multi-objective model with the objective of maximizing investor utility is presented. In the proposed method, an acceptance threshold constraint is applied to facility allocation that is based on a combination of distance between a facility and clients, and investors’ product prices. Since the common solution methods for multi-objective optimization, such as weighted sums, ε-constraints, multi-objective meta-heuristic algorithms, etc. are not efficient enough, and cannot guarantee achieving Nash equilibrium points, a new approach is developed to solve the presented problem. Moreover, according to the computational complexity of the problem, an approximation algorithm is introduced for large-sized problems. Finally, the computational results demonstrate that the proposed algorithm performs efficiently in obtaining Nash equilibrium points.

A Game Theoretic Analysis of Public Goods Allocation in P2P Networks

This paper presents a game theoretic approach to analyze the public goods (PGs) allocation in peer-to-peer (p2p) networks. In order to reduce the free-riders and promote the cooperation among peers, we propose an incentive mechanism with cooperation-based game theory. In this paper, we regarded the contributed resources by cooperators as public goods (PGs). We also build the PGs allocation in P2P networks to be the optimization problem, and the optimal solution of PGs allocation satisfies the Bowen- Lindahl-Samuelson equilibrium. Firstly, based on the subscriber mechanism, we analyze the feasibility and prove the validity, which can achieve Nash equilibrium. However, this strategy cannot meet to Bowen-Lindahl-Samuelson equilibrium as the free-riders do not pay with their private goods for consuming the PGs. Secondly, based on the Walker mechanism, we analyze the feasibility and prove the validity for the same allocation problem, which meets to Bowen-Lindahl-Samuelson equilibrium and achieves Pareto efficiency within cooperative game. Simulations show that the proposed walker mechanism can significantly improve the network performance of throughout, and effectively alleviate free-riding problem in P2P networks.

Incentive mechanisms for device-to-device communications

D2D communication has recently been proposed as a promising technique to improve resource utilization of cellular networks by offloading the traffic through base stations to local direct links between devices. While various optimization frameworks have been intensively studied, little attention has been given to how to attract users to adopt D2D communication. In this article we fill the gap by designing incentive mechanisms to encourage users to work under D2D mode. We consider two basic market types, open markets and sealed markets, where users have information of all users or only their own, respectively. For open markets, we design a Stackelberg game based incentive mechanism that can achieve Nash equilibrium. For sealed markets, we design an auction based incentive mechanism that guarantees truthfulness.

Cost-Based Stackelberg Potential Game for Cognitive Radio Ad Hoc Network

In cognitive radio ad hoc networks, the opportunistic access of vacant wireless channel opens a new frontier for efficient spectrum utilization as in many situations, a wide range of spectrum is not even partially utilized by the license owners (primary users, PUs). While the idea seems to be lucrative for spectrum hungry users without licenses, a natural competition between potential stake holders arises, which needs to be regulated in order to efficiently utilize available resources and avoid chaos. With the introduction of unlicensed users in licensed bands, the operations and interests of PUs need to be protected, hence the spectrum owners are given an advantage and control over the multiple access policy (a leader-follower scenario). In this work, we address the problems in spectrum access and channel selection equilibrium in a leader (PU)-follower (secondary user, SU) setup. In contrast to previous game formulations that lack efficient power and pricing schemes, we present a cooperative Stackelberg potential game for cognitive players. A dynamic cost function is articulated to induce awareness in players to mitigate the effects of selfish choices in spectrum access while at the same time steer the distributed network towards achieving Nash equilibrium. The proposed scheme is mutually beneficial for all players and focuses on improving the network performance and power efficiency. We design the network potential function such that the nodes have performance based incentives to cooperate and achieve a Nash equilibrium solution for efficient channel acquisition and capacity. Simulation results show fast convergence in channel selection strategies and increase in capacity for the entire network.

Dynamic Spectrum Access in Multi-Channel Cognitive Radio Networks

In this paper, dynamic spectrum access (DSA) in multi-channel cognitive radio networks (CRNs) is studied. The two fundamental issues in DSA, spectrum sensing and spectrum sharing, for a general scenario are revisited, where the channels present different usage characteristics and the detection performance of individual secondary users (SUs) varies. First, spectrum sensing is investigated, where multiple SUs are coordinated to cooperatively sense the channels owned by the primary users (PUs) for different interests. When the PUs' interests are concerned, cooperative spectrum sensing is performed to better protect the PUs while satisfying the SUs' requirement on the expected access time. For the SUs' interests, the objective is to maximize the expected available time while keeping the interference to PUs under a predefined level. With the dynamics in the channel usage characteristics and the detection capacities, the coordination problems for the above two cases are formulated as nonlinear integer programming problems accordingly, which are proved to be NP-complete. To find the solution efficiently, for the former case, the original problem is transformed into a variant of convex bipartite matching problem by constructing a complete bipartite graph and defining proper weight vectors. Based on the problem transformation, a channel selection algorithm is proposed to compute the solution. For the latter case, the deterministic optimization problem is first transformed to an associated stochastic optimization problem, which is then solved by cross-entropy (CE) method of stochastic optimization. Then, the sharing of the available channels by SUs after sensing is modeled by a channel access game, based on the framework of weighted congestion game. An algorithm for SUs to select access channels to achieve Nash equilibrium (NE) is proposed. Simulation results are presented to validate the performance of the proposed algorithms.

A Hybrid Pricing Framework for TV White Space Database

According to the recent rulings of the Federal Communications Commission (FCC), TV white spaces (TVWS) can now be accessed by secondary users (SUs) after a list of vacant TV channels is obtained via a geo-location database. Proper business models are therefore essential for database operators to manage geo-location databases. Database access can be simultaneously priced under two different schemes: the registration scheme and the service plan scheme. In the registration scheme, the database reserves part of the TV bandwidth for registered White Space Devices (WSDs). In the service plan scheme, the WSDs are charged according to their queries. In this paper, we investigate the business model for the TVWS database under a hybrid pricing scheme. We consider the scenario where a database operator employs both the registration scheme and the service plan scheme to serve the SUs. The SUs' choices of different pricing schemes are modeled as a non-cooperative game and we derive distributed algorithms to achieve Nash Equilibrium (NE). Considering the NE of the SUs, the database operator optimally determines pricing parameters for both pricing schemes in terms of bandwidth reservation, registration fee and query plans.

Novel Pre-pushing & Downloading Model in Mobile Peer-assisted Streaming Network

The popularization of streaming networks and mobile devices brings a new kind of network called mobile peer-assisted streaming network. In this network, service provider not only offers downloading services, but also pre-pushes resources to users for caching. Users can download their demanded resources while working as servers for uploading the cached data. Also the mobile characteristic makes high package losing probability in this network. So we study how the service provider pre-pushes or the user downloads resources efficiently and effectively while considering the package losing in this paper. We build utility models for service provider and user, and solve the models using Bellman’s theory to achieve Nash Equilibrium which shows the service provider’s optimal pre-pushing speed and user’s optimal downloading speed. The numerical simulation demonstrates the efficiency and effectiveness of our proposed pre-pushing and downloading scheme by comparing to the traditional scheme.

IMPACT OF RETAILER COMPETITION ON MANUFACTURER'S DECISIONS AND PROFITS AT EQUILIBRIUM

As most of the supply chains in practice are decentralized, a key issue in supply chain management is to study the coordination of supply chain. The interactions among players are typically of two types, viz. vertical competition and horizontal competition. We use a game theoretic framework to analyze a two-stage supply chain. The supply chain is modeled as a Stackelberg game with a manufacturer as leader and multiple retailers as followers. We consider multiple retailers competing on quantities (Cournot competition) and study its impact on manufacturer's equilibrium decisions and profits. We show that the wholesale price contract does not achieve Nash equilibrium when retailers offer uniform pricing. On the other hand, in case of perfect price discrimination we prove the existence of unique Nash equilibrium in both deterministic and stochastic demand set-up. Under stochastic demand set-up, we consider information asymmetry between the manufacturer and retailers with respect to demand signal. Furthermore, we show the retailers' selling effort boost up the sales. As variance of sales can hurt the manufacturer's production decisions badly, we conjecture that the manufacturer can offer a retailer incentive contract which can manipulate retailers' equilibrium decision.

Game-Based Broadcast over Reliable and Unreliable Wireless Links in Wireless Multihop Networks

This paper addresses the minimum transmission broadcast problem in wireless networks and presents efficient solutions, including an optimal broadcast scheme and a distributed game-based algorithm. Distinct from related work in the literature which typically assumes wireless links are reliable, we address the issue of broadcasting over both reliable wireless links and unreliable wireless links. Our main contributions are as follows: We first formulate the minimum transmission broadcast problems over reliable links and over unreliable links as two mixed integer linear programming (MILP) problems, respectively. This way, optimal broadcast schemes can be easily obtained using any existing MILP solver, for small-scale networks. For large-scale networks, we propose a distributed game-based algorithm and prove that the game-based algorithm achieves Nash Equilibrium. Using simulation, we confirm that compared with existing algorithms in the literature and optimal solutions obtained by our MILP techniques, the proposed game-based algorithm performs very well in terms of delivery ratio, the number of transmissions, and convergence speed.

Spectrum sharing in cognitive radio networks: an adaptive game approach

Throughout this study, an adaptive competitive second-price pay-to-bid sealed auction game is presented as a solution to the fairness problem of spectrum sharing among a number of users in a cognitive radio environment. First, a comparison among three main spectrum-sharing game models; optimal, cooperative and competitive game models is discussed to highlight the advantages and disadvantages of each model. The results prove that cooperative games aim to achieve Nash equilibrium between primary and secondary players and provide better revenue to them. Also, it proves that cooperative games are best when the number of secondary users changes dynamically, but only when the number is low. As in practical situations, the number of secondary users might increase dramatically and cooperative games will lose their powerful advantage once that happens. As a result, the proposed mechanism creates a competition between the bidders and offers better revenue to all players in terms of fairness. The proposed model ensures that users with better channel quality, higher traffic priority and fairer bids will get a better chance to share the offered spectrum. It is shown by numerical results that the proposed mechanism could reach the maximum total profit for all users with better fairness.

Predictable Energy Aware Routing based on Dynamic Game Theory in Wireless Sensor Networks

A routing algorithm named Sub-Game Energy Aware Routing (SGEAR) modeled by Dynamic Game Theory is proposed in this paper to make better routing choices. SGEAR takes the residual energy of the nodes and the energy consumption of the path into consideration and achieves Nash Equilibrium using Backward Induction. Compared with Energy Aware Routing, SGEAR can provide stable routing choices for relaying nodes and the energy of the network can still burn evenly. Moreover, this algorithm is more suitable for being combined with sleeping scheduling scheme and thus prolongs the lifetime of Wireless Sensor Networks. Simulation results show that, combined with sleeping scheduling scheme, SGEAR has an increase of 20% in energy saving compared with Energy Aware Routing.

Opportunistic Spectrum Access in Unknown Dynamic Environment: A Game-Theoretic Stochastic Learning Solution

We investigate the problem of distributed channel selection using a game-theoretic stochastic learning solution in an opportunistic spectrum access (OSA) system where the channel availability statistics and the number of the secondary users are apriori unknown. We formulate the channel selection problem as a game which is proved to be an exact potential game. However, due to the lack of information about other users and the restriction that the spectrum is time-varying with unknown availability statistics, the task of achieving Nash equilibrium (NE) points of the game is challenging. Firstly, we propose a genie-aided algorithm to achieve the NE points under the assumption of perfect environment knowledge. Based on this, we investigate the achievable performance of the game in terms of system throughput and fairness. Then, we propose a stochastic learning automata (SLA) based channel selection algorithm, with which the secondary users learn from their individual action-reward history and adjust their behaviors towards a NE point. The proposed learning algorithm neither requires information exchange, nor needs prior information about the channel availability statistics and the number of secondary users. Simulation results show that the SLA based learning algorithm achieves high system throughput with good fairness.