Stackelberg competition

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

Event-Driven Energy Trading System in Microgrids: Aperiodic Market Model Analysis With a Game Theoretic Approach

Abstract: This paper presents the design of an event-driven energy trading system among microgrids. Each microgrid can be either a provider or a consumer depending on the status of its energy generation and local demands. Under this approach, an aperiodic market model is newly proposed such that trading occurs when one of the consumers requests energy from the trading market. To promote the trading system, a consumer-side reward concept is introduced. The consumer makes a decision on the size of the posted reward to procure energy depending on its required energy level. Providers then react to this posted reward by submitting their energy bid. Accordingly, the posted reward is allocated to the providers in proportion to their energy bids. Moreover, for practical concerns, a transmission and distribution loss factor is considered as a heterogeneous energy trading system. The problem is then formulated as a non-cooperative Stackelberg game model. The existence and uniqueness of Stackelberg equilibrium (SE) are shown and the closed form of the SE is derived. Using the SE, an optimal trading algorithm for microgrids is provided. The stability of the energy trading system is verified due to the unique SE. In this approach, no expected waiting time for trading is required for sustaining an energy trading market.

Stackelberg Network Pricing Games

Abstract: We study a multi-player one-round game termed Stackelberg Network Pricing Game, in which a leader can set prices for a subset of m priceable edges in a graph. The other edges have a fixed cost. Based on the leader’s decision one or more followers optimize a polynomial-time solvable combinatorial minimization problem and choose a minimum cost solution satisfying their requirements based on the fixed costs and the leader’s prices. The leader receives as revenue the total amount of prices paid by the followers for priceable edges in their solutions. Our model extends several known pricing problems, including single-minded and unit-demand pricing, as well as Stackelberg pricing for certain follower problems like shortest path or minimum spanning tree. Our first main result is a tight analysis of a single-price algorithm for the single follower game, which provides a (1+e)log m-approximation. This can be extended to provide a (1+e)(log k+log m)-approximation for the general problem and k followers. The problem is also shown to be hard to approximate within $\mathcal{O}(\log^{\varepsilon}k + \log^{\varepsilon}m)$ for some e>0. If followers have demands, the single-price algorithm provides an $\mathcal{O}(m^{2})$ -approximation, and the problem is hard to approximate within $\mathcal{O}(m^{\epsilon})$ for some e>0. Our second main result is a polynomial time algorithm for revenue maximization in the special case of Stackelberg bipartite vertex-cover, which is based on non-trivial max-flow and LP-duality techniques. This approach can be extended to provide constant-factor approximations for any constant number of followers.

Carrier Aggregation Between Operators in Next Generation Cellular Networks: A Stable Roommate Market

Abstract: This paper studies carrier aggregation between multiple mobile network operators (MNOs), referred to as interoperator carrier aggregation (IO-CA). In IO-CA, each MNO can transmit on its own licensed spectrum and aggregate the spectrum licensed to other MNOs. We focus on the case that MNOs are partitioned and distributed into small groups, called IO-CA pairs, each of which consists of two MNOs that mutually agree to share their spectrum with each other. We model the IO-CA pairing problem between MNOs as a stable roommate market and derive a condition for which a stable matching structure among all MNOs exist. We propose an algorithm that achieves a stable matching if it exists. Otherwise, the algorithm results in a stable partition. For each IO-CA pair, we derive the optimal transmit power for each spectrum aggregator and establish a Stackelberg game model to analyze the interaction between the licensed subscribers and aggregators in the spectrum of each MNO. We derive the Stackelberg equilibrium of our proposed game and then develop a joint optimization algorithm that achieves the stable matching structure among MNOs as well as the optimal transmit powers for the aggregators and prices for the subscribers of each MNO.

On the approximate controllability of Stackelberg-Nash strategies

Abstract: Let us consider a distributed system, i.e. a system whose state is defined by the solution of a Partial Differential Equation (PDE). We assume that we can act on this system by a hierarchy of controls. There is a “global” control v, which is the leader, and there are N “local” controls, denoted by w 1,…, w N , which are the followers. The followers, assuming that the leader has made a choice v of its policy, look for a Nash equilibrium of their cost functions (the criteria they are interested in). Then the leader makes its final choice for the whole system. This is the Stackelberg-Nash strategy.