Showing papers on "Stackelberg competition published in 2014"

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

Abstract: In this paper, the benefits of distributed energy resources (DERs) 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 non-cooperative Stackelberg game between 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 (SD) that can further lower the SFC's total cost if the proposed game is implemented. Numerical experiments confirm the effectiveness of the proposed scheme.

Game-Theoretic Demand-Side Management With Storage Devices for the Future Smart Grid

Abstract: We study the demand side management (DSM) problem when customers are equipped with energy storage devices. Two games are discussed: the first is a non-cooperative one played between the residential energy consumers, while the second is a Stackelberg game played between the utility provider and the energy consumers. We introduce a new cost function applicable to the case of users selling back stored energy. The non-cooperative energy consumption game is played between users who schedule their energy use to minimize energy cost. The game is shown to have a unique Nash equilibrium, that is also the global system optimal point. In the Stackelberg game, the utility provider sets the prices to maximize its profit knowing that users will respond by minimizing their cost. We provide existence and uniqueness results for the Stackelberg equilibrium. The Stackelberg game is shown to be the general case of the minimum Peak-to-Average power ratio (PAR) problem. Two algorithms, centralized and distributed, are presented to solve the Stackelberg game. We present results that elucidate the interplay between storage capacity, energy requirements, number of users and system performance measured in total cost and peak-to-average power ratio (PAR).

Prioritizing Consumers in Smart Grid: A Game Theoretic Approach

Abstract: This paper proposes an energy management technique for a consumer-to-grid system in smart grid. The benefit to consumers is made the primary concern to encourage consumers to participate voluntarily in energy trading with the central power station (CPS) in situations of energy deficiency. A novel system model motivating energy trading under the goal of social optimality is proposed. A single-leader multiple-follower Stackelberg game is then studied to model the interactions between the CPS and a number of energy consumers (ECs), and to find optimal distributed solutions for the optimization problem based on the system model. The CPS is considered as a leader seeking to minimize its total cost of buying energy from the ECs, and the ECs are the followers who decide on how much energy they will sell to the CPS for maximizing their utilities. It is shown that the game, which can be implemented distributedly, possesses a socially optimal solution, in which the sum of the benefits to all consumers is maximized, as the total cost to the CPS is minimized. Numerical analysis confirms the effectiveness of the game.

Pricing, Spectrum Sharing, and Service Selection in Two-Tier Small Cell Networks: A Hierarchical Dynamic Game Approach

Abstract: Small cells overlaid with macrocells can increase the capacity of two-tier cellular wireless networks by offloading traffic from macrocells. To motivate the small cell service providers (SSPs) to open portion of the access opportunities to macro users (i.e., to operate in a hybrid access mode), we design an incentive mechanism in which the macrocell service provider (MSP) could pay to the SSPs. According to the price offered by the MSP, the SSPs decide on the open access ratio , which is the ratio of shared radio resource for macro users and the total amount of radio resource in a small cell. The users in this two-tier network can make service selection decisions dynamically according to the performance satisfaction level and cost, which again depend on the pricing and spectrum sharing between the MSP and SSPs. To model this dynamic interactive decision problem, we propose a hierarchical dynamic game framework. In the lower level, we formulate an evolutionary game to model and analyze the adaptive service selection of users. An evolutionary stable strategy (ESS) is considered to be the solution of this game. In the upper level, the MSP and SSPs sequentially determine the pricing strategy and the open access ratio, respectively, taking into account the distribution of dynamic service selection at the lower-level evolutionary game. A Stackelberg differential game is formulated where the MSP and SSPs act as the leader and followers, respectively. An open-loop Stackelberg equilibrium is considered to be the solution of this game. We also extend the hierarchical dynamic game framework and investigate the impact of information delays on the equilibrium solutions. Numerical results show the effectiveness and advantages of dynamic control of the open access ratio and pricing.

Learning Optimal Commitment to Overcome Insecurity

Abstract: Game-theoretic algorithms for physical security have made an impressive real-world impact. These algorithms compute an optimal strategy for the defender to commit to in a Stackelberg game, where the attacker observes the defender's strategy and best-responds. In order to build the game model, though, the payoffs of potential attackers for various outcomes must be estimated; inaccurate estimates can lead to significant inefficiencies. We design an algorithm that optimizes the defender's strategy with no prior information, by observing the attacker's responses to randomized deployments of resources and learning his priorities. In contrast to previous work, our algorithm requires a number of queries that is polynomial in the representation of the game.

Game-theoretic security patrolling with dynamic execution uncertainty and a case study on a real transit system

Abstract: Attacker-Defender Stackelberg security games (SSGs) have emerged as an important research area in multi-agent systems. However, existing SSGs models yield fixed, static, schedules which fail in dynamic domains where defenders face execution uncertainty, i.e., in domains where defenders may face unanticipated disruptions of their schedules. A concrete example is an application involving checking fares on trains, where a defender's schedule is frequently interrupted by fare evaders, making static schedules useless. To address this shortcoming, this paper provides four main contributions. First, we present a novel general Bayesian Stackelberg game model for security resource allocation in dynamic uncertain domains. In this new model, execution uncertainty is handled by using a Markov decision process (MDP) for generating defender policies. Second, we study the problem of computing a Stackelberg equilibrium for this game and exploit problem structure to reduce it to a polynomial-sized optimization problem. Shifting to evaluation, our third contribution shows, in simulation, that our MDP-based policies overcome the failures of previous SSG algorithms. In so doing, we can now build a complete system, that enables handling of schedule interruptions and, consequently, to conduct some of the first controlled experiments on SSGs in the field. Hence, as our final contribution, we present results from a real-world experiment on Metro trains in Los Angeles validating our MDP-based model, and most importantly, concretely measuring the benefits of SSGs for security resource allocation.

Green Cognitive Mobile Networks With Small Cells for Multimedia Communications in the Smart Grid Environment

Abstract: High-data-rate mobile multimedia applications can greatly increase energy consumption, leading to an emerging trend of addressing the “energy efficiency” aspect of mobile networks. Cognitive mobile networks with small cells are important techniques for meeting the high-data-rate requirements and improving the energy efficiency of mobile multimedia communications. However, most existing works do not consider the power grid, which provides electricity to mobile networks. Currently, the power grid is experiencing a significant shift from the traditional grid to the smart grid. In the smart grid environment, only considering energy efficiency may not be sufficient since the dynamics of the smart grid will have significant impacts on mobile networks. In this paper, we study green cognitive mobile networks with small cells in the smart grid environment. Unlike most existing studies on cognitive networks, where only the radio spectrum is sensed, our cognitive networks sense not only the radio spectrum environment but also the smart grid environment, based on which power allocation and interference management for multimedia communications are performed. We formulate the problems of electricity price decision, energy-efficient power allocation, and interference management as a three-stage Stackelberg game. A homogeneous Bertrand game with asymmetric costs is used to model price decisions made by the electricity retailers. A backward induction method is used to analyze the proposed Stackelberg game. Simulation results show that our proposed scheme can significantly reduce operational expenditure and $\hbox{CO}_{2}$ emissions in cognitive mobile networks with small cells for multimedia communications.

Coordination of dual-channel supply chains under demand disruptions management decisions

Abstract: This paper examines optimal decisions and coordination models for a dual-channel supply chain when the two end competition market demands are simultaneously disrupted Firstly, we developed the pricing and production decisions models without demand disruptions and propose a revenue sharing contract to coordinate the dual-channel supply chain where the manufacturer is a Stackelberg leader and the retailer is a follower We derived the conditions under which the maximum profit can be achieved in detailed We compared the profits under normal case and disrupted case and quantified the information value of knowing demand disruptions We proposed an improved revenue sharing contract to coordinate the dual-channel supply chain with demand disruptions The results indicate that the adjusting prices and production quantity are the optimal decisions whether the demand disruptions case or normal case We also find that the original revenue sharing contract is a special case of improved revenue sharing contract and

Two-Stage Spectrum Sharing With Combinatorial Auction and Stackelberg Game in Recall-Based Cognitive Radio Networks

Abstract: The dynamic spectrum access (DSA) among multiple heterogeneous primary spectrum owners (POs) and secondary users (SUs) in recall-based cognitive radio networks is investigated in this paper. In our framework, SUs demand a different amount of spectrum for their transmissions. Each PO provides a portion of radio resources for leasing and also offers its own primary users (PUs) a certain degree of quality of service (QoS). Furthermore, POs are allowed to have different spectrum trading areas and as well as heterogeneous activities between POs' users. We propose a Two-stage resource allocation scheme with combinatorial Auction and Stackelberg Game in spectrum Sharing (TAGS) to deal with the allocation problem in such a complicated system. In the first stage, a spectrum allocation is decided by running a geographi- cally restricted combinatorial auction without the consideration of spectrum recall. In the second stage, a Stackelberg game is formulated for all users to determine their best strategies with respect to the potential spectrum recall. Both theoretical and simulation results prove that TAGS provides a feasible solution for the problem and ensures the desired economic properties for all individuals.

Game-theoretical models for competition analysis in a new emerging liner container shipping market

Abstract: This paper develops three game-theoretical models to analyze shipping competition between two carriers in a new emerging liner container shipping market. The behavior of each carrier is characterized by an optimization model with the objective to maximize his payoff by setting optimal freight rate and shipping deployment (a combination of service frequency and ship capacity setting). The market share for each carrier is determined by the Logit-based discrete choice model. Three competitive game strategic interactions are further investigated, namely, Nash game, Stackelberg game and deterrence by taking account of the economies of scale of the ship capacity settings. Three corresponding competition models with discrete pure strategy are formulated as the variables in shipment deployment are indivisible and the pricing adjustment is step-wise in practice. A ɛ -approximate equilibrium and related numerical solution algorithm are proposed to analyze the effect of Nash equilibrium. Finally, the developed models are numerically evaluated by a case study. The case study shows that, with increasing container demand in the market, expanding ship capacity setting is preferable due to its low marginal cost. Furthermore, Stackelberg equilibrium is a prevailing strategy in most market situations since it makes players attain more benefits from the accommodating market. Moreover, the deterrence effects largely depend on the deterrence objective. An aggressive deterrence strategy may make potential monopolist suffer large benefit loss and an easing strategy has little deterrence effect.

Stackelberg Game for Bandwidth Allocation in Cloud-Based Wireless Live-Streaming Social Networks

Abstract: Multimedia social networks have been introduced as a new technology to enrich people's lives through enhanced multimedia distribution. On the other hand, a media cloud system can perform multimedia processing and storage, and provide heterogeneous multimedia services. However, the challenges still remain for end users (e.g., mobile devices and PCs) to receive multimedia streaming from the cloud system with satisfied quality-of-service (QoS). To address these challenges, an efficient multimedia distribution approach taking advantage of live-streaming social networks is innovated in this paper to deliver the media services from the cloud to both desktop and wireless end users. Our approach allows bandwidth limited mobile users to acquire live multimedia streaming from desktop users, directly based on their social relationships rather than from the cloud. When a number of mobile users compete for limited bandwidth access with the desktop users, a bandwidth allocation problem must be solved to meet all users' QoS requirements in the live-streaming social network. We formulate the problem as a two-stage Stackelberg game, in which both desktop users and mobile users target at maximizing their utilities. In our study, a noncooperative game is used to model the competition among the desktop users in terms of shared bandwidth and price in the first stage of the game. The second stage of the game models the behavior of a mobile user selecting the desktop users by an evolutionary game. In addition, a case study is conducted following the general Stackelberg game formulation, where the existence of a unique Nash equilibrium is proved. Based on our game modeling, we design protocols for both desktop and mobile users and evaluate them with numerical examples.

Integrated Scheduling and Dynamic Optimization by Stackelberg Game: Bilevel Model Formulation and Efficient Solution Algorithm

Abstract: We propose a novel method to solve the integrated scheduling and dynamic optimization problem for sequential batch processes. The scheduling problem and the dynamic optimization problems are collaborated by a Stackelberg game (leader–followers game). Mathematically, the integrated problem is formulated into a bilevel program. The scheduling problem in the upper level acts as the leader, while the dynamic optimization problems in the lower level are the followers. The follower problems have their own objectives, but the leader problem can coordinate the follower problems to pursue its objective. To efficiently solve the bilevel program, we develop a decomposition algorithm. It first solves the lower-level problems to determine the response functions. The response functions are then represented by piecewise linear functions to solve the upper-level problem. The integrated method is consistent with the ISA 95 standard and can be easily implemented in an IT infrastructure following the standard. The performan...

Computing solutions in infinite-horizon discounted adversarial patrolling games

Abstract: Stackelberg games form the core of a number of tools deployed for computing optimal patrolling strategies in adversarial domains, such as the US Federal Air Marshall Service and the US Coast Guard. In traditional Stackelberg security game models the attacker knows only the probability that each target is covered by the defender, but is oblivious to the detailed timing of the coverage schedule. In many real-world situations, however, the attacker can observe the current location of the defender and can exploit this knowledge to reason about the defender's future moves. We show that this general modeling framework can be captured using adversarial patrolling games (APGs) in which the defender sequentially moves between targets, with moves constrained by a graph, while the attacker can observe the defender's current location and his (stochastic) policy concerning future moves. We offer a very general model of infinite-horizon discounted adversarial patrolling games. Our first contribution is to show that defender policies that condition only on the previous defense move (i.e., Markov stationary policies) can be arbitrarily sub-optimal for general APGs. We then offer a mixed-integer nonlinear programming (MINLP) formulation for computing optimal randomized policies for the defender that can condition on history of bounded, but arbitrary, length, as well as a mixed-integer linear programming (MILP) formulation to approximate these, with provable quality guarantees. Additionally, we present a non-linear programming (NLP) formulation for solving zero-sum APGs. We show experimentally that MILP significantly outperforms the MINLP formulation, and is, in turn, significantly outperformed by the NLP specialized to zero-sum games.

An optimal real-time pricing for demand-side management: A Stackelberg game and genetic algorithm approach

Abstract: This paper proposes a real-time pricing scheme for demand response management in the context of smart grids. The electricity retailer determines the retail price first and announces the price information to the customers through the smart meter systems. According to the announced price, the customers automatically manage the energy use of appliances in the households by the proposed energy management system with the aim to maximize their own benefits. We model the interactions between the electricity retailer and its customers as a 1-leader, N-follower Stackelberg game. By taking advantage of the two-way communication infrastructure, the sequential equilibrium can be obtained through backward induction. At the followers' side, given the electricity price information, we develop efficient algorithms to maximize customers' satisfaction. At the leader's side, we develop a genetic algorithms based real-time pricing scheme by considering the expected customers' reactions to maximize retailer's profit. Experimental results indicate that the proposed scheme can not only benefit the retailers but also the customers.

Power structure and profitability in assembly supply chains

Abstract: This paper studies the impact of supply chain power structure on firms' profitability in an assembly system with one assembler and two suppliers. Two power regimes are investigated�in a Single Power Regime, a more powerful firm acts as the Stackelberg leader to decide the wholesale price but not the quantity whereas in a Dual Power Regime, both the price and quantity decisions are granted to the more powerful firm. Tallying the power positions of the three firms, for each power regime we study three power structures and investigate the system's as well as the firms' preference of power. We find that when the assembler is the most powerful firm among the three, the system-wide profit is the highest and so is the assembler's profit. The more interesting finding is that, if the assembler is not the most powerful player in the system, more power does not necessarily guarantee her a higher profit. Similarly, a supplier's profit can also decrease with the power he has. These results contrast with the conclusion for serial systems, where a firm always prefers more power. We also find that when both suppliers are more (less) powerful than the assembler, it can be beneficial (indifferent) for everyone if the two suppliers merge into a mega supplier to make decisions jointly. When the assembler is more powerful than one supplier and less so than the other, it is always better for the system to have the two suppliers merge, and for each individual firm, merging is preferred if the firm becomes the more powerful party after merging.

Incentive Mechanism Design for Heterogeneous Peer-to-Peer Networks: A Stackelberg Game 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 the Stackelberg 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.

Solving the Bilevel Facility Location Problem under Preferences by a Stackelberg-Evolutionary Algorithm

Abstract: This research highlights the use of game theory to solve the classical problem of the uncapacitated facility location optimization model with customer order preferences through a bilevel approach. The bilevel model provided herein consists of the classical facility location problem and an optimization of the customer preferences, which are the upper and lower level problems, respectively. Also, two reformulations of the bilevel model are presented, reducing it into a mixed-integer single-level problem. An evolutionary algorithm based on the equilibrium in a Stackelberg’s game is proposed to solve the bilevel model. Numerical experimentation is performed in this study and the results are compared to benchmarks from the existing literature on the subject in order to emphasize the benefits of the proposed approach in terms of solution quality and estimation time.

Explaining Strategic Coordination: Cognitive Hierarchy Theory, Strong Stackelberg Reasoning, and Team Reasoning

Abstract: In common interest games, players generally manage to coordinate their actions on mutually optimal outcomes, but orthodox game theory provides no reason for them to play their individual parts in these seemingly obvious solutions and no justification for choosing the corresponding strategies. A number of theories have been suggested to explain coordination, among the most prominent being versions of cognitive hierarchy theory, theories of team reasoning, and social projection theory (in symmetric games). Each of these theories provides a plausible explanation but is theoretically problematic. An improved theory of strong Stackelberg reasoning avoids these problems and explains coordination among players who care about their co-players’ payoffs and who act as though their co-players can anticipate their choices. Two experiments designed to test cognitive hierarchy, team reasoning, and strong Stackelberg theories against one another in games without obvious, payoff-dominant solutions suggest that each of the theories provides part of the explanation. Cognitive hierarchy Level-1 reasoning, facilitated by a heuristic of avoiding the worst payoff, tended to predominate, especially in more complicated games, but strong Stackelberg reasoning occurred quite frequently in the simpler games and team reasoning in both the simpler and the more complicated games. Most players considered two or more of these reasoning processes before choosing their strategies.

Regret-based optimization and preference elicitation for stackelberg security games with uncertainty

Abstract: Stackelberg security games (SSGs) have been deployed in a number of real-world domains. One key challenge in these applications is the assessment of attacker payoffs, which may not be perfectly known. Previous work has studied SSGs with uncertain payoffs modeled by interval uncertainty and provided maximin-based robust solutions. In contrast, in this work we propose the use of the less conservative minimax regret decision criterion for such payoff-uncertain SSGs and present the first algorithms for computing minimax regret for SSGs. We also address the challenge of preference elicitation, using minimax regret to develop the first elicitation strategies for SSGs. Experimental results validate the effectiveness of our approaches.

Revenue Sharing Based Resource Allocation for Dynamic Spectrum Access Networks

Abstract: We propose a revenue sharing based resource allocation scheme for dynamic spectrum access (DSA) networks. In our scheme, based on a mutually agreed revenue sharing scheme, a primary network operator (PNO) actively shares its radio resource with a secondary network operator (SNO), which provides access service to secondary users (SUs) for its revenue maximization. To investigate the coupling effect between the revenue sharing and resource allocation, we formulate the interaction between PNO and SNO as a two-layered game, which includes a top layer game to model their revenue sharing and a bottom layer game to model their joint resource allocations. Specifically, in the top layer, based on their joint resource allocation decisions, the PNO and SNO form a Nash bargaining game to determine the revenue sharing scheme such that both of them can benefit from cooperation satisfactorily. Then, in the bottom layer, under the given revenue sharing scheme, the PNO and SNO form a Stackelberg game to determine their joint resource allocation decisions, which also influence their respective revenues. The two games work iteratively such that the PNO and SNO reach a final equilibrium state at which neither PNO nor SNO will change its decisions unilaterally in both layers. We propose efficient algorithms to solve both the top layer and bottom layer games and compute the final equilibrium of the two-layered game. Specifically, despite the non-convexity of joint resource allocation optimization problem in the bottom layer, we identify its hidden monotonic structure and propose an efficient algorithm, which is based on the polyblock approximation, to achieve the optimal solutions. Moreover, in the top layer, to tackle with the difficulty due to the lack of an analytical objective function for the revenue sharing problem, we explore its hidden unimodal property and propose a Brent's method based algorithm to achieve the optimal solution. Numerical results are presented to verify the performance of our algorithms and show that our revenue sharing based resource allocation scheme yields a win-win situation for the PNO and SNO.

A Shared-Constraint Approach to Multi-Leader Multi-Follower Games

Abstract: Multi-leader multi-follower games are a class of hierarchical games in which a collection of leaders compete in a Nash game constrained by the equilibrium conditions of another Nash game amongst the followers. The resulting equilibrium problem with equilibrium constraints is complicated by nonconvex agent problems and therefore providing tractable conditions for existence of global or even local equilibria has proved challenging. Consequently, much of the extant research on this topic is either model specific or relies on weaker notions of equilibria. We consider a modified formulation in which every leader is cognizant of the equilibrium constraints of all leaders. Equilibria of this modified game contain the equilibria, if any, of the original game. The new formulation has a constraint structure called shared constraints, and our main result shows that if the leader objectives admit a potential function, the global minimizers of the potential function over this shared constraint are equilibria of the modified formulation. We provide another existence result using fixed point theory that does not require potentiality. Additionally, local minima, B-stationary, and strong-stationary points of this minimization problem are shown to be local Nash equilibria, Nash B-stationary, and Nash strong-stationary points of the corresponding multi-leader multi-follower game. We demonstrate the relationship between variational equilibria associated with this modified shared-constraint game and equilibria of the original game from the standpoint of the multiplier sets and show how equilibria of the original formulation may be recovered. We note through several examples that such potential multi-leader multi-follower games capture a breadth of application problems of interest and demonstrate our findings on a multi-leader multi-follower Cournot game.