Showing papers on "Stackelberg competition published in 2013"

Dependable Demand Response Management in the Smart Grid: A Stackelberg Game Approach

Abstract: Demand Response Management (DRM) is a key component in the smart grid to effectively reduce power generation costs and user bills. However, it has been an open issue to address the DRM problem in a network of multiple utility companies and consumers where every entity is concerned about maximizing its own benefit. In this paper, we propose a Stackelberg game between utility companies and end-users to maximize the revenue of each utility company and the payoff of each user. We derive analytical results for the Stackelberg equilibrium of the game and prove that a unique solution exists. We develop a distributed algorithm which converges to the equilibrium with only local information available for both utility companies and end-users. Though DRM helps to facilitate the reliability of power supply, the smart grid can be succeptible to privacy and security issues because of communication links between the utility companies and the consumers. We study the impact of an attacker who can manipulate the price information from the utility companies. We also propose a scheme based on the concept of shared reserve power to improve the grid reliability and ensure its dependability.

Supply chain coordination through cooperative advertising with reference price effect

Abstract: Cooperative advertising, which usually occurs in a vertical supply chain, is typically a cost sharing and promotion mechanism for the manufacturer to affect retail performance. Research in the literature, however, rarely considers the important phenomenon that advertising has a positive effect on the consumer's reference price. In fact, when a consumer makes a decision to buy a product or not, a reference price is usually in his mind and plays a determinant role. Taking into account the impact of advertising on the reference price, this paper proposes a dynamic cooperative advertising model for a manufacturer-retailer supply chain and analyzes how the reference price effect would influence the decisions of all the channel members. In our model, both the consumer's goodwill and reference price for the product are assumed to be influenced by the advertising and are modeled in differential dynamic equations. In addition, the advertising level, the consumer's goodwill and the reference price are all assumed to have positive effect on sales. Utilizing differential game theory, this paper formulates the optimal decisions of the manufacturer and the retailer in two different game scenarios: Stackelberg game and cooperative game. Also, this paper proposes a new mechanism to coordinate the supply chain in which both the manufacturer and the retailer share each other's advertising costs.

Joint scheduling and resource allocation for device-to-device underlay communication

Abstract: Device-to-device (D2D) communication as an underlay to cellular networks can bring significant benefits to users' throughput. However, as D2D user equipments (TIEs) can cause interference to cellular TIEs, the scheduling and allocation of channel resources and power to D2D communication need elaborate coordination. In this paper, we propose a joint scheduling and resource allocation scheme to improve the performance of D2D communication. We take network throughput and TIEs' fairness into account by performing interference management. Specifically, we develop a Stackelberg game framework in which we group a cellular TIE and a D2D TIE to form a leader-follower pair. The cellular user is the leader, and the D2D TIE is the follower who buys channel resources from the leader. We analyze the equilibrium of the game, and propose an algorithm for joint scheduling and resource allocation. Finally, we perform computer simulations to study the performance of the proposed algorithm.

Coping with a Smart Jammer in Wireless Networks: A Stackelberg Game Approach

Abstract: Jamming defense is an important yet challenging problem. In this paper, we study the jamming defense problem in the presence of a smart jammer, who can quickly learn the transmission power of the user and adaptively adjust its transmission power to maximize the damaging effect. We consider both the single-channel model and the multi-channel model. By modeling the problem as a Stackelberg game, we compute the optimal transmission power for the user to maximize its utility, in the presence of a smart jammer. For the single-channel model, we prove the existence and uniqueness of the Stackelberg Equilibrium (SE) by giving closed-form expressions for the SE strategies of both the user and the player. For the multi-channel model, we prove the existence of the SE. We design algorithms for computing the jammer's best response strategy and approximating the user's optimal strategy. Finally, we validate our theoretical analysis through extensive simulations.

On the advantage of quantity leadership when outsourcing production to a competitive contract manufacturer

Abstract: This study investigates a supply chain comprising an original equipment manufacturer (OEM) and a contract manufacturer (CM), in which the CM acts as both upstream partner and downstream competitor to the OEM. The two parties can engage in one of three Cournot competition games: a simultaneous game, a sequential game with the OEM as the Stackelberg leader, and a sequential game with the CM as the Stackelberg leader. On the basis of these three basic games, this study investigates the two parties' Stackelberg leadership/followership decisions. When the outsourcing quantity and wholesale price are exogenously given, either party may prefer Stackelberg leadership or followership. For example, when the wholesale price or the proportion of production outsourced to the CM is lower than a threshold value, both parties prefer Stackelberg leadership and, consequently, play a simultaneous game in the consumer market. When the outsourcing quantity and wholesale price are decision variables, the competitive CM sets a wholesale price sufficiently low to allow both parties to coexist in the market, and the OEM outsources its entire production to this CM. This study also examines the impact of the supply chain parties' bargaining power on contract outcomes by considering a wholesale price that is determined via the generalized Nash bargaining scheme, finding a Stackelberg equilibrium to be sustained when the CM's degree of bargaining power is great and the non-competitive CM's wholesale price is high.

Advance Selling in a Supply Chain Under Uncertain Supply and Demand

Abstract: We examine three selling strategies of a manufacturer who produces and sells a seasonal product to a retailer under uncertain supply and demand: 1 advance selling---presells the product before observing uncertain supply and demand; 2 regular selling---sells the product after supply and demand are realized; and 3 dynamic selling---combines both advance and regular selling strategies. We model the first two strategies as single-period Stackelberg games, and we model the last strategy as a two-period dynamic Stackelberg game. By comparing the equilibria of these games, we formalize our understanding of several intuitive results. For example, from the manufacturer's perspective, dynamic selling dominates advance selling and regular selling: having more selling opportunities is beneficial to the manufacturer. However, from the retailer's perspective, we find two counterintuitive results: a postponing the ordering decision can be detrimental---the retailer can be worse off under regular selling than under advance selling; and b more ordering opportunities can be detrimental---the retailer can be worse off under dynamic selling than under advance selling. In addition, we analyze the impact of supply and demand uncertainties under these strategies and find that both types of uncertainties can be beneficial to the retailer.

Supply Chain Contracting Under Competition: Bilateral Bargaining vs. Stackelberg

Abstract: We analyze contracting behaviors in a two-tier supply chain system consisting of competing manufacturers and competing retailers. We contrast the contracting outcome of a Stackelberg game, in which the manufacturers offer take-it-or-leave-it contracts to the retailers, with that of a bargaining game, in which the firms bilaterally negotiate contract terms via a process of alternating offers. The manufacturers in the Stackelberg game possess a Stackelberg-leader advantage in that the retailers are not entitled to make counteroffers. Our analysis suggests that whether this advantage would benefit the manufacturers depends on the contractual form. With simple contracts such as wholesale-price contracts, which generally do not allow one party to fully extract the trade surplus, the Stackelberg game replicates the boundary case of the bargaining game with the manufacturers possessing all the bargaining power. In contrast, with sophisticated contracts such as two-part tariffs, which enable full surplus extraction, the two games lead to distinct outcomes. We further show that the game structure being Stackelberg or bargaining critically affects firms' preferences over contract types and thus their equilibrium contract choices. These observations suggest that the Stackelberg game may not be a sufficient device to predict contracting behaviors in reality where bargaining is commonly observed.

A Game-Theoretical Scheme in the Smart Grid With Demand-Side Management: Towards a Smart Cyber-Physical Power Infrastructure

Abstract: The smart grid is becoming one of the fundamental cyber-physical systems due to the employment of information and communication technology. In the smart grid, demand-side management (DSM) based on real-time pricing is an important mechanism for improving the reliability of the grid. Electricity retailers in the smart grid can procure electricity from various supply sources, and then sell it to the customers. Therefore, it is critical for retailers to make effective procurement and price decisions. In this paper, we propose a novel game-theoretical decision-making scheme for electricity retailers in the smart grid using real-time pricing DSM. We model and analyze the interactions between the retailer and electricity customers as a four-stage Stackelberg game. In the first three stages, the electricity retailer, as the Stackelberg leader, makes decisions on which electricity sources to procure electricity from, how much electricity to procure, and the optimal retail price to offer to the customers, to maximize its profit. In the fourth stage, the customers, who are the followers in the Stackelberg game, adjust their individual electricity demand to maximize their individual utility. Simulation results show that the retailer and customers can achieve a higher profit and higher utility using our proposed decision-making scheme. We also analyze how the system parameters affect the procurement and price decisions in the proposed decision-making scheme.

Supply Chain Contracting under Competition: Bilateral Bargaining vs. Stackelberg

Abstract: We analyze contracting behaviors in a two-tier supply chain system consisting of competing manufacturers and competing retailers. We contrast the contracting outcome of a Stackelberg game, in which the manufacturers offer take-it-or-leave-it contracts to the retailers, with that of a bargaining game, in which the firms bilaterally negotiate contract terms via a process of alternating offers. The manufacturers in the Stackelberg game possess a Stackelberg-leader advantage in that the retailers are not entitled to make counteroffers. Our analysis suggests that whether this advantage would benefit the manufacturers depends on the contractual form. With simple contracts such as wholesale-price contracts, which generally do not allow one party to fully extract the trade surplus, the Stackelberg game replicates the boundary case of the bargaining game with the manufacturers possessing all bargaining power. In contrast, with sophisticated contracts such as two-part tariffs, which enable full surplus extraction, the two games lead to distinct outcomes. We further show that the game structure being Stackelberg or bargaining critically affects firms’ preferences over contract types and thus their equilibrium contract choices. These observations suggest that the Stackelberg game may not be a sufficient device to predict contracting behaviors in reality where bargaining is commonly observed.

Hierarchical Competition for Downlink Power Allocation in OFDMA Femtocell Networks

Abstract: This paper considers the problem of downlink power allocation in an orthogonal frequency-division multiple access (OFDMA) cellular network with macrocells underlaid with femtocells. The femto-access points (FAPs) and the macro-base stations (MBSs) in the network are assumed to compete with each other to maximize their capacity under power constraints. This competition is captured in the framework of a Stackelberg game with the MBSs as the leaders and the FAPs as the followers. The leaders are assumed to have foresight enough to consider the responses of the followers while formulating their own strategies. The Stackelberg equilibrium is introduced as the solution of the Stackelberg game, and it is shown to exist under some mild assumptions. The game is expressed as a mathematical program with equilibrium constraints (MPEC), and the best response for a one leader-multiple follower game is derived. The best response is also obtained when a quality-of-service constraint is placed on the leader. Orthogonal power allocation between leader and followers is obtained as a special case of this solution under high interference. These results are used to build algorithms to iteratively calculate the Stackelberg equilibrium, and a sufficient condition is given for its convergence. The performance of the system at a Stackelberg equilibrium is found to be much better than that at a Nash equilibrium.

Markov Game Analysis for Attack-Defense of Power Networks Under Possible Misinformation

Abstract: Electricity grids are critical infrastructures They are credible targets of active (eg, terrorist) attacks since their disruption may lead to sizable losses economically and in human lives It is thus crucial to develop decision support that can guide administrators in deploying defense resources for system security and reliability Prior work on the defense of critical infrastructures has typically used static or Stackelberg games These approaches view network interdictions as one-time events However, infrastructure protection is also a continual process in which the defender and attacker interact to produce dynamic states affecting their best actions, as witnessed in the continual attack and defense of transmission networks in Colombia and Yemen In this paper, we use zero-sum Markov games to model these interactions subject to underlying uncertainties of real-world events and actions We solve equilibrium mixed strategies of the players that maximize their respective minimum payoffs with a time-decayed metric We also show how the defender can use deception as a defense mechanism Using results for a 5-bus system, a WECC 9-bus system, and an IEEE standard 14-bus system, we illustrate that our game model can provide useful insights We also contrast our results with those of static games, and quantify the gain in defender payoff due to misinformation of the attacker

Game-theoretic randomization for security patrolling with dynamic execution uncertainty

Abstract: In recent years there has been extensive research on game-theoretic models for infrastructure security. In time-critical domains where the security agency needs to execute complex patrols, execution uncertainty(interruptions) affect the patroller's ability to carry out their planned schedules later. Indeed, experiments in this paper show that in some real-world domains, small fractions of execution uncertainty can have a dramatic impact. The contributions of this paper are threefold. First, we present a general Bayesian Stackelberg game model for security patrolling in dynamic uncertain domains, in which the uncertainty in the execution of patrols is represented using Markov Decision Processes. Second, we study the problem of computing Stackelberg equilibrium for this game. We show that when the utility functions have a certain separable structure, the defender's strategy space can be compactly represented, and we can reduce the problem to a polynomial-sized optimization problem. Finally, we apply our approach to fare inspection in the Los Angeles Metro Rail system. Numerical experiments show that patrol schedules generated using our approach outperform schedules generated using a previous algorithm that does not consider execution uncertainty.

A Stackelberg game-theoretic approach to optimal real-time pricing for the smart grid

Abstract: This paper proposes a Stackelberg game approach to maximize the profit of the electricity retailer (utility company) and minimize the payment bills of its customers. The electricity retailer determines the retail price through the proposed smart energy pricing scheme to optimally adjust the real-time pricing with the aim to maximize its profit. The price information is sent to the customers through a smart meter. According to the announced price, the customers can automatically manage the energy use of appliances in the households by the proposed optimal electricity consumption scheduling system with the aim to minimize their electricity bills. We model the interactions between the retailer and its electricity customers as a 1-leader, N-follower Stackelberg game. At the leader's side, i.e., for the retailer, we adopt genetic algorithms to maximize its profit while at the followers' side, i.e., for customers, we develop an analytical solution to the linear programming problem to minimize their bills. Simulation results show that the proposed approach is beneficial for both the customers and the retailer.

A continuum approximation approach to competitive facility location design under facility disruption risks

Abstract: This paper presents game-theoretical models based on a continuous approximation (CA) scheme to optimize service facility location design under spatial competition and facility disruption risks. The share of customer demand in a market depends on the functionality of service facilities and the presence of nearby competitors, as customers normally seek the nearest functioning facility for service. Our game-theoretical models incorporate these complicating factors into an integrated framework, and use continuous and differentiable density functions to represent discrete location decisions. We first analyze the existence of Nash equilibria in a symmetric two-company competition case. Then we build a leader–follower Stackelberg competition model to derive the optimal facility location design when one of the companies has the first mover advantage over its competitor. Both models are solved effectively, and closed-form analytical solutions can be obtained for special cases. Numerical experiments (with hypothetical and empirical data) are conducted to show the impacts of competition, facility disruption risks and transportation cost metrics on the optimal design. Properties of the models are analyzed to cast interesting managerial insights.

Multi-objective Stackelberg game between a regulating authority and a mining company: A case study in environmental economics

Abstract: Bilevel programming problems are often found in practice. In this paper, we handle one such bilevel application problem from the domain of environmental economics. The problem is a Stakelberg game with multiple objectives at the upper level, and a single objective at the lower level. The leader in this case is the regulating authority, and it tries to maximize its total tax revenue over multiple periods while trying to minimize the environmental damages caused by a mining company. The follower is the mining company whose sole objective is to maximize its total profit over multiple periods under the limitations set by the leader. The solution to the model contains the optimal taxation and extraction decisions to be made by the players in each of the time periods. We construct a simplistic model for the Stackelberg game and provide an analytical solution to the problem. Thereafter, the model is extended to incorporate realism and is solved using a bilevel evolutionary algorithm capable of handling multiple objectives.

Optimal patrol strategy for protecting moving targets with multiple mobile resources

Abstract: Previous work on Stackelberg Security Games for scheduling security resources has mostly assumed that the targets are stationary relative to the defender and the attacker, leading to discrete game models with finite numbers of pure strategies. This paper in contrast focuses on protecting mobile targets that lead to a continuous set of strategies for the players. The problem is motivated by several real-world domains including protecting ferries with escorts and protecting refugee supply lines. Our contributions include: (i) a new game model for multiple mobile defender resources and moving targets with a discretized strategy space for the defender and a continuous strategy space for the attacker; (ii) an efficient linear-program-based solution that uses a compact representation for the defender's mixed strategy, while accurately modeling the attacker's continuous strategy using a novel sub-interval analysis method; (iii) a heuristic method of equilibrium refinement for improved robustness and (iv) detailed experimental analysis in the ferry protection domain.

Output commitment through product bundling: Experimental evidence

Abstract: We analyze the impact of product bundling in experimental markets. One firm has monopoly power in a first market but competes with another firm a la Cournot in a second market. We compare treatments where the multi-product firm (i) always bundles, (ii) never bundles, and (iii) chooses whether to bundle. We also contrast the simultaneous and the sequential order of moves in the duopoly market. Our data indicate support for the theory of product bundling: with bundling and simultaneous moves, the multi-product firm offers the predicted number of units. When the multi-product firm is the Stackelberg leader, the predicted equilibrium is better attained with bundling, especially when it chooses to bundle, even though in theory bundling should not make a difference here. In sum, bundling works as a commitment device that enables the transfer of market power from one market to another.

Distributed resource allocation for D2D communication underlaying cellular networks

Abstract: In the paper, the distributed joint spectrum sharing and power allocation scheme is proposed to improve the local services in the Device-to-Device (D2D) communication underlaying cellular networks (CNs) with limited signaling overhead. The scheme aims to optimize the throughput of D2D communications over the shared uplink frequency spectrum meanwhile the base station (BS) protects the cellular users (CUs) from the interference of D2D users. Stackelberg game (SG) is formulated to model the problem for deriving the distributed scheme. In the game, the BS, as a leader, coordinates the interference from the D2D users to the cellular uplinks and maximizes its own profit by pricing the interference. On the other hand, D2D pairs, as followers, compete for the spectrum as a Nash non-cooperative game to maximize their own data rates individually. The pricing mechanism at the BS converging to the Stackelberg Equilibrium is studied. Finally, numerical examples are presented to verify the proposed scheme. It is shown that the scheme is effective on the resource allocation and the CU protection with limited signaling overhead.

Pricing-based decentralized spectrum access control in cognitive radio networks

Abstract: This paper investigates pricing-based spectrum access control in cognitive radio networks, where primary users (PUs) sell the temporarily unused spectrum and secondary users (SUs) compete via random access for such spectrum opportunities. Compared to existing market-based approaches with centralized scheduling, pricing-based spectrum management with random access provides a platform for SUs contending for spectrum access and is amenable to decentralized implementation due to its low complexity. We focus on two market models, one with a monopoly PU market and the other with a multiple-PU market. For the monopoly PU market model, we devise decentralized pricing-based spectrum access mechanisms that enable SUs to contend for channel usage. Specifically, we first consider SUs contending via slotted Aloha. Since the revenue maximization problem therein is nonconvex, we characterize the corresponding Pareto-optimal region and obtain a Pareto-optimal solution that maximizes the SUs' throughput subject to their budget constraints. To mitigate the spectrum underutilization due to the "price of contention," we revisit the problem where SUs contend via CSMA, which results in more efficient spectrum utilization and higher revenue. We then study the tradeoff between the PU's utility and its revenue when the PU's salable spectrum is controllable. Next, for the multiple-PU market model, we cast the competition among PUs as a three-stage Stackelberg game, where each SU selects a PU's channel to maximize its throughput. We explore the existence and the uniqueness of Nash equilibrium, in terms of access prices and the spectrum offered to SUs, and develop an iterative algorithm for strategy adaptation to achieve the Nash equilibrium. Our findings reveal that there exists a unique Nash equilibrium when the number of PUs is less than a threshold determined by the budgets and elasticity of SUs.