Stackelberg competition

About: Stackelberg competition is a research topic. Over the lifetime, 6611 publications have been published within this topic receiving 109213 citations.

Component Procurement Strategies in Decentralized Assemble-to-Order Systems with Time-Dependent Pricing

Abstract: We consider a contract manufacturer who procures multiple components from independent suppliers to produce an assemble-to-order customized product for a client. The unit price of the product depends on the manufacturer's delivery lead time. We explore how the manufacturer can use a vendor-managed consignment inventory (VMCI) scheme to manage the underlying risk and coordinate independent suppliers' decisions on the production quantities of their components under demand uncertainty. We formulate the problem as a Stackelberg game played by the manufacturer against her component suppliers to determine her pricing policy for suppliers' consignment inventories. We further develop an efficient algorithm for finding the manufacturer's optimal pricing scheme. Our results provide useful insights for managing components in these types of assemble-to-order environments and for understanding how component production cost and procurement lead times affect individual firms' performance in decentralized assembly channels.

Probabilistic Analysis on QoS Provisioning for Internet of Things in LTE-A Heterogeneous Networks With Partial Spectrum Usage

Abstract: This paper investigates quality of service (QoS) provisioning for Internet of Things (IoT) in long-term evolution advanced (LTE-A) heterogeneous networks (HetNets) with partial spectrum usage (PSU). In HetNets, the IoT users with ubiquitous mobility support or low-rate services requirement can connect with macrocells (MCells), while femtocells (FCells) with PSU mechanism can be deployed to serve the IoT users requiring high-data-rate transmissions within small coverage. Despite the great potentials of HetNets in supporting various IoT applications, the following challenges exist: 1) how to depict the unplanned random behaviors of the IoT-oriented FCells and cope with the randomness in user QoS provisioning and 2) how to model the interplay of resource allocation (RA) between MCells and FCells under PSU mechanism. In this work, the stochastic geometry (SG) theory is first exploited to statistically analyze how the unplanned random behaviors of the IoT-oriented FCells impact the user performance, considering the user QoS requirements and FCell PSU policy. Particularly, to satisfy the QoS requirements of different IoT user types, the concept of effective bandwidth (EB) is leveraged to provide the users with probabilistic QoS guarantee, and a heuristic algorithm named QA-EB algorithm is proposed to make the EB determination tractable. Then, the interplay of RA between the MCells and FCells is formulated into a two-level Stackelberg game, where the two parties try to maximize their own utilities through optimizing the macro-controlled interference price and the femto-controlled PSU policy. A backward induction method is proposed to achieve the Stackelberg equilibrium. Finally, extensive simulations are conducted to corroborate the derived SINR and ergodic throughput performance of different user types and demonstrate the Stackelberg equilibrium under varying user QoS requirements and spectrum aggregation capabilities.

A Hierarchical Game Theoretic Framework for Cognitive Radio Networks

Abstract: We consider OFDMA-based cognitive radio (CR) networks where multiple secondary users (SUs) compete for the available sub-bands in the spectrum of multiple primary users (PUs). We focus on maximizing the payoff of both SUs and PUs by jointly optimizing transmit powers of SUs, sub-band allocations of SUs, and the prices charged by PUs. To further improve the performance of SUs, we allow SUs who share the same sub-band to cooperate with each other to send and receive signals. To help us understand the interaction among SUs and PUs, we study the proposed network model from a game theoretic perspective. More specifically, we first formulate a coalition formation game to study the sub-band allocation problem of SUs and then integrate the coalition formation game into a Stackelberg game-based hierarchical framework. We propose a simple distributed algorithm for SUs to search for the optimal sub-bands. We prove that the transmit power and sub-band allocation of SUs and the price charged by PUs are interrelated by the pricing function of PUs. This makes the joint optimization possible. More importantly, we prove that if the pricing coefficients of PUs have a fixed linear relationship, the sub-band allocation of SUs will be stable and the Stackelberg equilibrium of the hierarchical game framework will be unique and optimal. We propose a simple distributed algorithm to achieve the Stackelberg equilibrium of the hierarchical game. Our proposed algorithm does not require SUs to know the interference temperature limit of each PU, and has low communication overheads between SUs and PUs.

Stackelberg Strategies for Selfish Routing in General Multicommodity Networks

Abstract: A natural generalization of the selfish routing setting arises when some of the users obey a central coordinating authority, while the rest act selfishly. Such behavior can be modeled by dividing the users into an α fraction that are routed according to the central coordinator’s routing strategy (Stackelberg strategy), and the remaining 1−α that determine their strategy selfishly, given the routing of the coordinated users. One seeks to quantify the resulting price of anarchy, i.e., the ratio of the cost of the worst traffic equilibrium to the system optimum, as a function of α. It is well-known that for α=0 and linear latency functions the price of anarchy is at most 4/3 (J. ACM 49, 236–259, 2002). If α tends to 1, the price of anarchy should also tend to 1 for any reasonable algorithm used by the coordinator. We analyze two such algorithms for Stackelberg routing, LLF and SCALE. For general topology networks, multicommodity users, and linear latency functions, we show a price of anarchy bound for SCALE which decreases from 4/3 to 1 as α increases from 0 to 1, and depends only on α. Up to this work, such a tradeoff was known only for the case of two nodes connected with parallel links (SIAM J. Comput. 33, 332–350, 2004), while for general networks it was not clear whether such a result could be achieved, even in the single-commodity case. We show a weaker bound for LLF and also some extensions to general latency functions. The existence of a central coordinator is a rather strong requirement for a network. We show that we can do away with such a coordinator, as long as we are allowed to impose taxes (tolls) on the edges in order to steer the selfish users towards an improved system cost. As long as there is at least a fraction α of users that pay their taxes, we show the existence of taxes that lead to the simulation of SCALE by the tax-payers. The extension of the results mentioned above quantifies the improvement on the system cost as the number of tax-evaders decreases.