Showing papers on "Stackelberg competition published in 2015"

Distributed Energy Trading in Microgrids: A Game-Theoretic Model and Its Equilibrium Analysis

Abstract: This paper proposes a distributed mechanism for energy trading among microgrids in a competitive market. We consider multiple interconnected microgrids in a region where, at a given time, some microgrids have superfluous energy for sale or to keep in storage facilities, whereas some other microgrids wish to buy additional energy to meet local demands and/or storage requirements. Under our approach, sellers lead the competition by independently deciding the amount of energy for sale subject to a tradeoff between the attained satisfaction from the received revenue and that from the stored energy. Buyers follow the sellers' actions by independently submitting a unit price bid to the sellers. Correspondingly, the energy is allocated to the buyers in proportion to their bids, whereas the revenue is allocated to the sellers in proportion to their sales. We study the economic benefits of such an energy trading mechanism by analyzing its hierarchical decision-making scheme as a multileader–multifollower Stackelberg game. We show that distributing the energy based on a well-defined utility function converges to a unique equilibrium solution for maximizing the payoff of all participating microgrids. This game-theoretic study provides an incentive for energy trading among microgrids in future power grids.

Energy Pricing and Dispatch for Smart Grid Retailers Under Demand Response and Market Price Uncertainty

Abstract: This paper proposes a two-stage two-level model for the energy pricing and dispatch problem faced by a smart grid retailer who plays the role of an intermediary agent between a wholesale energy market and end consumers. Demand response of consumers with respect to the retail price is characterized by a Stackelberg game in the first stage, thus the first stage has two levels. A risk-aversive energy dispatch accounting for market price uncertainty is modeled by a linear robust optimization with objective uncertainty in the second stage. The proposed model is transformed to a mixed integer linear program (MILP) by jointly using the Karush-Kuhn-Tucker (KKT) condition, the disjunctive constraints, and the duality theory. We propose a heuristic method to select the parameter in disjunctive constraints based on the interpretation of Lagrange multipliers. Moreover, we suggest solving an additional linear program (LP) to acquire a possible enhanced bidding strategy that guarantees a Pareto improvement on the retailer's profit over the entire uncertainty set. Case studies demonstrate the proposed model and method is valid.

Three-Party Energy Management With Distributed Energy Resources in Smart Grid

Abstract: In this paper, the benefits of distributed energy resources are considered in an energy management scheme for a smart community consisting of a large number of residential units (RUs) and a shared facility controller (SFC). A noncooperative Stackelberg game between the RUs and the SFC is proposed in order to explore how both entities can benefit, in terms of achieved utility and minimizing total cost respectively, from their energy trading with each other and the grid. From the properties of the game, it is shown that the maximum benefit to the SFC, in terms of reduction in total cost, is obtained at the unique and strategy-proof Stackelberg equilibrium (SE). It is further shown that the SE is guaranteed to be reached by the SFC and RUs by executing the proposed algorithm in a distributed fashion, where participating RUs comply with their best strategies in response to the action chosen by the SFC. In addition, a charging–discharging scheme is introduced for the SFC's storage device that can further lower the SFC's total cost if the proposed game is implemented. Numerical experiments confirm the effectiveness of the proposed scheme.

Secrecy Rate Optimizations for a MIMO Secrecy Channel With a Cooperative Jammer

Abstract: In this paper, we study different secrecy rate optimization techniques for a multiple-input–multiple-output (MIMO) secrecy channel, where a multiantenna cooperative jammer is employed to improve secret communication in the presence of a multiantenna eavesdropper. Specifically, we consider two optimization problems, namely, power minimization and secrecy rate maximization. These problems are not jointly convex in terms of the transmit covariance matrices of the legitimate transmitter and the cooperative jammer. To circumvent these nonconvexity issues, we alternatively design the transmit covariance matrix of the legitimate transmitter and the cooperative jammer. For a given transmit covariance matrix at the cooperative jammer, we solve the power minimization and secrecy rate maximization problems based on a Taylor series expansion. Then, we propose two iterative algorithms to solve these approximated problems. In addition, we develop a robust scheme by incorporating channel uncertainties associated with the eavesdropper. By exploiting S-Procedure , we show that these robust optimization problems can be formulated into semidefinite programming. Moreover, we consider the secrecy rate maximization problem based on game theory, where the jammer introduces charges for its jamming service based on the amount of the interference caused to the eavesdropper. This secrecy rate maximization problem is formulated into a Stackelberg game where the jammer and the transmitter are the leader and the follower of the game, respectively. For the proposed game, Stackelberg equilibrium is analytically derived. Simulation results have been provided to validate the convergence and performance of the proposed algorithms. In addition, it is shown that the proposed robust scheme outperforms the nonrobust scheme in terms of the achieved secrecy rate and the worst-case secrecy rate. Finally, the Stackelberg equilibrium solution has been validated through numerical results.

Energy Storage Sharing in Smart Grid: A Modified Auction Based Approach

Abstract: This paper studies the solution of joint energy storage (ES) ownership sharing between multiple shared facility controllers (SFCs) and those dwelling in a residential community. The main objective is to enable the residential units (RUs) to decide on the fraction of their ES capacity that they want to share with the SFCs of the community in order to assist them storing electricity, e.g., for fulfilling the demand of various shared facilities. To this end, a modified auction-based mechanism is designed that captures the interaction between the SFCs and the RUs so as to determine the auction price and the allocation of ES shared by the RUs that governs the proposed joint ES ownership. The fraction of the capacity of the storage that each RU decides to put into the market to share with the SFCs and the auction price are determined by a noncooperative Stackelberg game formulated between the RUs and the auctioneer. It is shown that the proposed auction possesses the incentive compatibility and the individual rationality properties, which are leveraged via the unique Stackelberg equilibrium (SE) solution of the game. Numerical experiments are provided to confirm the effectiveness of the proposed scheme.

When security games go green: designing defender strategies to prevent poaching and illegal fishing

Abstract: Building on the successful applications of Stackelberg Security Games (SSGs) to protect infrastructure, researchers have begun focusing on applying game theory to green security domains such as protection of endangered animals and fish stocks. Previous efforts in these domains optimize defender strategies based on the standard Stackelberg assumption that the adversaries become fully aware of the defender's strategy before taking action. Unfortunately, this assumption is inappropriate since adversaries in green security domains often lack the resources to fully track the defender strategy. This paper (i) introduces Green Security Games (GSGs), a novel game model for green security domains with a generalized Stackelberg assumption; (ii) provides algorithms to plan effective sequential defender strategies -- such planning was absent in previous work; (iii) proposes a novel approach to learn adversary models that further improves defender performance; and (iv) provides detailed experimental analysis of proposed approaches.

Anti-Jamming Transmission Stackelberg Game With Observation Errors

Abstract: As smart jammers that can analyze the ongoing radio transmission with flexible and powerful control on jamming signals throw serious threats on cognitive radio networks, game theory provides a powerful approach to study the interactions between smart jammers and secondary users (SUs). In this work, the power control strategy of an SU against a smart jammer under power constraints is formulated as a Stackelberg game. The jammer as the follower of the game chooses the jamming power according to the observed ongoing transmission, while the SU as the leader determines its transmit power based on the estimated jamming power. The impact of the observation accuracy of the jammer regarding the transmit power of the SU is investigated. The Stackelberg equilibrium of the anti-jamming game is derived and compared with the Nash equilibrium of the game. Simulation results show that the transmission of an SU benefits from the observation error of the jammer with a higher signal-to-interference-plus-noise ratio and utility.

Game-Theoretic Frameworks for Demand Response in Electricity Markets

Abstract: This paper presents game-theoretic frameworks for demand response at both electricity market and consumer levels. First, the interaction between a demand response aggregator (DRA) and electricity generators is modeled as a Stackelberg game in which the DRA, as the leader of the game, makes demand reduction bids, and generators, as followers, compete for maximizing their profits based on the reduced demand. Next, the interaction between the DRA and consumers is modeled as a mechanism design problem wherein the DRA seeks to minimize the aggregate inconvenience of consumers while achieving the targeted load curtailment. The inconvenience function of each consumer is captured by a type value, which is used by the DRA to solve the load curtailment problem. A Vickrey-Clarke-Groves-based mechanism is proposed, which guarantees that each consumer reveals its true type value to the DRA. A case study of the Stackelberg game shows that, in the South Australian electricity market where there is significant renewable penetration, peak period demand response provides the maximum potential profit, but off-peak demand response even in a concentrated market is not financially attractive.

Commitment Without Regrets: Online Learning in Stackelberg Security Games

Abstract: In a Stackelberg Security Game, a defender commits to a randomized deployment of security resources, and an attacker best-responds by attacking a target that maximizes his utility. While algorithms for computing an optimal strategy for the defender to commit to have had a striking real-world impact, deployed applications require significant information about potential attackers, leading to inefficiencies. We address this problem via an online learning approach. We are interested in algorithms that prescribe a randomized strategy for the defender at each step against an adversarially chosen sequence of attackers, and obtain feedback on their choices (observing either the current attacker type or merely which target was attacked). We design no-regret algorithms whose regret (when compared to the best fixed strategy in hindsight) is polynomial in the parameters of the game, and sublinear in the number of times steps.

Interference-Aware Energy-Efficient Resource Allocation for OFDMA-Based Heterogeneous Networks With Incomplete Channel State Information

Abstract: Heterogeneous wireless networks are considered as promising technologies to improve energy efficiency. In heterogeneous networks, interference management is very important since the interference due to spectrum sharing can significantly degrade overall performance. In the existing work, various resource allocation methods are proposed to either improve energy efficiency or mitigate interference in orthogonal frequency-division multiple access (OFDMA)-based multicell networks. To the best of our knowledge, no research on resource allocation has jointly considered improving energy efficiency and performing interference control, especially using interference power constraint strategies. Furthermore, most existing work assumes that all of the channel state information (CSI) is known completely, which might not be realistic in heterogeneous networks due to the limited capacity of the backhaul links and varied ownership of network devices. In this paper, we propose a game-theoretical scheme using energy-efficient resource allocation and interference pricing for an interference-limited environment in heterogeneous networks. We formulate the problems of resource allocation and interference management as a Stackelberg game with incomplete CSI. A backward induction method is used to analyze the proposed game. A closed-form expression of the Stackelberg equilibrium (SE) is obtained for the proposed game with various interference power constraints. Simulation results are presented to show the effectiveness of the proposed scheme.

The Maximum Principle for Global Solutions of Stochastic Stackelberg Differential Games

Abstract: National Science Foundation (DMS 1303775); Research Grant Council of the HKSAR, (CityU 500113)

Exploring information asymmetry in two-stage security games

Abstract: Stackelberg security games have been widely deployed to protect real-world assets. The main solution concept there is the Strong Stackelberg Equilibrium (SSE), which optimizes the defender's random allocation of limited security resources. However, solely deploying the SSE mixed strategy has limitations. In the extreme case, there are security games in which the defender is able to defend all the assets "almost perfectly" at the SSE, but she still sustains significant loss. In this paper, we propose an approach for improving the defender's utility in such scenarios. Perhaps surprisingly, our approach is to strategically reveal to the attacker information about the sampled pure strategy. Specifically, we propose a two-stage security game model, where in the first stage the defender allocates resources and the attacker selects a target to attack, and in the second stage the defender strategically reveals local information about that target, potentially deterring the attacker's attack plan. We then study how the defender can play optimally in both stages. We show, theoretically and experimentally, that the two-stage security game model allows the defender to achieve strictly better utility than SSE.

Competitive Charging Station Pricing for Plug-in Electric Vehicles

Abstract: This paper considers the problem of charging station pricing and plug-in electric vehicles (PEVs) station selection. When a PEV needs to be charged, it selects a charging station by considering the charging prices, waiting times, and travel distances. Each charging station optimizes its charging price based on the prediction of the PEVs' charging station selection decisions and the other station's pricing decision, in order to maximize its profit. To obtain insights of such a highly coupled system, we consider a one-dimensional system with two competing charging stations and Poisson arriving PEVs. We propose a multi-leader-multi-follower Stackelberg game model, in which the charging stations (leaders) announce their charging prices in Stage I, and the PEVs (followers) make their charging station selections in Stage II. We show that there always exists a unique charging station selection equilibrium in Stage II, and such equilibrium depends on the charging stations' service capacities and the price difference between them. We then characterize the sufficient conditions for the existence and uniqueness of the pricing equilibrium in Stage I. We also develop a low complexity algorithm that efficiently computes the pricing equilibrium and the subgame perfect equilibrium of the two-stage Stackelberg game.

Downlink Power Control in Two-Tier Cellular OFDMA Networks Under Uncertainties: A Robust Stackelberg Game

Abstract: We consider the problem of robust downlink power control in orthogonal frequency-division multiple access (OFDMA)-based heterogeneous wireless networks (HetNets) composed of macrocells and underlaying small cells. A non-cooperative setting is assumed where the macro base stations (MBSs) and small cell base stations (SBSs) compete with each other to maximize their own capacities considering imperfect channel state information. A robust Stackelberg game (RSG) is formulated to model this hierarchical competition where the MBSs and SBSs act as the leaders and the followers, respectively. The formulated RSG can be expressed as an equilibrium program with equilibrium constraints (EPEC). A comprehensive study of this RSG is provided considering various power constraints (e.g., total and spectral mask), various interference constraints (e.g., individual and global), and different uncertainty models (e.g., column-wise and ellipsoidal). We show how the different constraints and uncertainty models change the property of the game (e.g., Nash equilibrium problem (NEP) or generalized Nash equilibrium problem (GNEP)) and accordingly impact the choice of analysis method (e.g., game theory or variational inequality (VI)), solution (e.g., closed-form or numerical), and the design of algorithms and their distributive properties (e.g., totally distributed, semi-distributed, and centralized). A robust Stackelberg equilibrium (RSE) is considered to be the solution and its existence and uniqueness are investigated. Also, algorithms are proposed to arrive at the RSE. Numerical results show the effectiveness of robust solutions in an imperfect information environment.

Quality-Optimized Joint Source Selection and Power Control for Wireless Multimedia D2D Communication Using Stackelberg Game

Abstract: In wireless device-to-device (D2D) networks, devices are reluctant to forward packets because of limited energy and possible delays for their own data. The incentive mechanisms that motivate devices to constitute direct communication for wireless multimedia quality optimality in D2D systems have been overlooked in the past. In this paper, we propose a new low-complexity distributed game-theoretic source selection and power control scheme that enhances the multimedia transmission quality with latency constraints. This approach has two major contributions. First, the proposed approach optimally selects the most beneficial source devices by analyzing the interactions between the base station's (BS's) rewarding strategies (denoted by price) and the devices' contributing behaviors (denoted by transmission power) using a Stackelberg game model. Second, optimal transmission power is adjusted for each selected source device in D2D networks by deriving Stackelberg equilibrium, wherein the BS and the device both achieve maximum utility. Computer simulations demonstrate that significant improvement in D2D multimedia transmission quality can be obtained by deploying the proposed scheme.

Pricing and return policy under various supply contracts in a closed-loop supply chain

Abstract: This study investigates pricing and return policies under various supply contracts in a closed-loop supply chain in which a supplier has more bargaining power than a retailer. We develop integrated supply contract models based on the principal–agent paradigm. Specifically, the supplier with more bargaining power devises a supply contract, acting as a Stackelberg leader. Then, given the contract offer, the retailer decides on pricing and return policies which affect consumers’ demand and return behaviours. We look into three commonly used supply contracts, i.e. wholesale price, buy-back and quantity discount contracts. The main purpose of this study is to explore how each supply contract affects the retailer’s decision on pricing and return policies, which in turn influence the profits of the entire supply chain and of its members. In doing so, we focus on investigating which contract coordinates the supply chain involving the retailer’s moral hazard. Through analytic comparison of contracts and extensive ...

Power control with reinforcement learning in cooperative cognitive radio networks against jamming

Abstract: In this paper, we study the anti-jamming power control problem of secondary users (SUs) in a large-scale cooperative cognitive radio network attacked by a smart jammer with the capability to sense the ongoing transmission power. The interactions between cooperative SUs and a jammer are investigated with game theory. We derive the Stackelberg equilibrium of the anti-jamming power control game consisting of a source node, a relay node and a jammer and compare it with the Nash equilibrium of the game. Power control strategies with reinforcement learning methods such as Q-learning and WoLF-PHC are proposed for SUs without knowing network parameters (i.e., the channel gains and transmission costs of others and so on) to achieve the optimal powers against jamming in this cooperative anti-jamming game. Simulation results indicate that the proposed power control strategies can efficiently improve the anti-jamming performance of SUs.

Information Disclosure as a Means to Security

Abstract: In this paper we present a novel Stackelberg-type model of security domains: Security Assets aSsignment with Information disclosure (SASI). The model combines both the features of the Stackelberg Security Games (SSGs) model and of the Bayesian Persuasion (BP) model. More specifically, SASI includes: a) an uncontrolled, exogenous security state that serves as the Defender's private information; b) multiple security assets with non-accumulating, targetlocal defence capability; c) a pro-active, verifiable and public, unidirectional information disclosure channel from the Defender to the Attacker. We show that SASI with a non-degenerate information disclosure can be arbitrarily more efficient, than a "silent" Stackelberg assets allocation. We also provide a linear program reformulation of SASI that can be solved in polynomial time in SASI parameters. Furthermore, we show that it is possible to remove one of SASI parameters and, rather than require it as an input, recover it by computation. As a result, SASI becomes highly scalable.

Joint Mode Selection and Spectrum Partitioning for Device-to-Device Communication: A Dynamic Stackelberg Game

Abstract: Device-to-device (D2D) communication technology is a promising add-on component for future wireless networks to provide local area services with increased spectrum efficiency and improved user experience. Three modes (i.e., cellular mode, reuse mode, and dedicated mode) can be used for D2D communication. A potential D2D user equipment (UE) can select a communication mode and dynamically adapt the mode selection according to the performance and the cost. This is referred to as the user-controlled mode selection problem. Also, a base station (BS) needs to reserve a spectrum band for the dedicated mode of operation, which we refer to as spectrum partitioning. The optimal spectrum partitioning needs to consider the utility of the BS that depends on the distribution of the users' mode selection, which, in turn, is governed by the spectrum partitioning. To jointly address the problems of spectrum partitioning and user-controlled mode selection (which are cyclically dependent on each other), we propose a dynamic Stackelberg game framework in which the BS and the potential D2D UEs act as the leader and the followers, respectively. Specifically, the adaptive mode selection of potential D2D UEs is formulated as a follower evolutionary game, and an evolutionary stable strategy is considered to be the solution. The dynamic control of spectrum partitioning by the BS is formulated as a leader optimal control problem. We also extend the formulation by considering information delays in control and state. Numerical analysis is performed to evaluate the effectiveness of the proposed framework, which shows that although the mode selection is performed in a distributed and user-controlled manner, the dynamic spectrum partitioning can be viewed as an effective incentive mechanism to drive the user distribution close to the optimal one.

Incentive Mechanism Design for Heterogeneous Peer-to-Peer Networks: A StackelbergGame Approach

Abstract: With high scalability, high video streaming quality, and low bandwidth requirement, peer-to-peer (P2P) systems have become a popular way to exchange files and deliver multimedia content over the internet. However, current P2P systems are suffering from “free-riding” due to the peers’ selfish nature. In this paper, we propose a credit-based incentive mechanism to encourage peers to cooperate with each other in a heterogeneous network consisting of wired and wireless peers. The proposed mechanism can provide differentiated service to peers with different credits through biased resource allocation. A Stackelberg game is formulated to obtain the optimal pricing and purchasing strategies, which can jointly maximize the revenue of the uploader and the utilities of the downloaders. In particular, peers’ heterogeneity and selfish nature are taken into consideration when designing the utility functions for theStackelberg game. It is shown that the proposed resource allocation scheme is effective in providing service differentiation for peers and stimulating them to make contribution to the P2P streaming system.

Optimal quantity discount coordination for supply chain optimization with one manufacturer and multiple suppliers under demand uncertainty

Abstract: In this paper, a coordination strategy is developed to integrate business decisions and manufacturing planning in supply chain management. We consider one manufacturer and multiple suppliers to determine production, prices, and inventory simultaneously with uncertain demands. This paper aims at providing an optimal discount policy derived from Stackelberg equilibrium to coordinate a manufacturer and multiple suppliers. The optimal discount coordination mechanism helps the manufacturer to select suppliers in order to maintain long-term relationship with the contracted suppliers under demand uncertainty. Noncooperative game is applied in order to resolve decision-making in order to determine quantities of components, price, production, and selection of suppliers simultaneously. Computational experiments are conducted to demonstrate the effectiveness and efficiency of the proposed approach.

Dynamic Pricing, Production, and Channel Coordination with Stochastic Learning

Abstract: We consider a decentralized two-period supply chain in which a manufacturer produces a product with benefits of cost learning, and sells it through a retailer facing a price-dependent demand. The manufacturer's second-period production cost declines linearly in the first-period production, but with a random learning rate. The manufacturer may or may not have the inventory carryover option. We formulate the resulting problems as two-period Stackelberg games and obtain their feedback equilibrium solutions explicitly. We then examine the impact of mean learning rate and learning rate variability on the pricing strategies of the channel members, on the manufacturer's production decisions, and on the retailer's procurement decisions. We show that as the mean learning rate or the learning rate variability increases, the traditional double marginalization problem becomes more severe, leading to greater efficiency loss in the channel. We obtain revenue sharing contracts that can coordinate the dynamic supply chain. In particular, when the manufacturer may hold inventory, we identify two major drivers for inventory carryover: market growth and learning rate variability. Finally, we demonstrate the robustness of our results by examining a model in which cost learning takes place continuously