Stackelberg competition

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

Joint Pricing and Power Allocation for Multibeam Satellite Systems With Dynamic Game Model

Abstract: Multibeam satellite systems (MSS) enable transmission flexibility and spatial diversity while efficiently reusing the scarce spectrum resource. However, as spectrum reuses tend to introduce co-channel interference, MSS need to address power allocation and interference management carefully. In this paper, we tackle the joint interference pricing and power allocation problems of MSS by formulating the underlying resource allocation problem as a dynamic game model—the Stackelberg model. In our proposed scheme, a fresh satellite user will be charged according to its interference on the satellite system. MSS can dynamically adjust the interference price in order to make a tradeoff between intercell interference and operating profit. Meanwhile, for the satellite user, an equilibrium power allocation should be ascertained in response to the MSS's pricing. A novel market-based solution is proposed for interference management in MSS by introducing an elastic price mechanism. The Nash equilibrium for interference pricing and its iterative convergence for power allocation have further been proven. Numerical results are provided to evaluate the impact of different prices on the utility functions of both MSS and satellite users.

On Hierarchical Spatial Competition

Abstract: In this paper we consider a hierarchical model of spatial electoral competition with two dominant players (incumbents) and one entrant. The incumbents engage in a non-cooperative game against each other and act as Stackelberg leaders with respect to a vote-maximizing entrant. We prove that the equilibrium of this game, called a hierarchical equilibrium, exists and is unique for an arbitrary single-peaked distribution of voters' ideal points. Moreover, we fully characterize the set of equilibrium strategies and show its equivalence to the set of strategies generated by a perfect-foresight equilibrium. Most of the recently developed models of entry in oligopolistic markets and the theory of political competition deal with the case of dominant firms or parties which face a threat of potential entry. These models possess a number of features on which they may be compared and contrasted. The most important of these features are the ways in which the existing parties or firms compete against each other for votes or profits, and types of expectations the incumbents have about the responses of potential entrants to changes in their decisions. In most of the cases an electoral or oligopolistic competition is represented by some type of a non-cooperative game played by parties or firms. In this paper we also consider a non-cooperative model of electoral race where the established parties (incumbents) compete against each other by offering positions ("ideologies") to the population of voters. Given the profile of voters' preferences over the space of "ideologies" (or, issue space), each of the established parties attempts to maximize its vote share. In making their choices, the incumbents, however, anticipate that a new party (an entrant) will join the electoral race. Consistent with the other parties' objectives, the entrant is assumed to maximize its share of voters while taking the incumbents' choices as given. The resulting non-cooperative game possesses, therefore, a structural hierarchy: the established parties behave as Nash players with respect to each other, whereas acting as Stackelberg leaders with respect to the entrant and correctly anticipating its vote-maximizing response to their choices in the issue space. The main purpose of this paper is to study the properties of the game we described and, in particular, to characterize its equilibrium, which we will call "hierarchical equilibrium". Naturally, some assumptions are needed in order to guarantee the existence of the equilibrium. We assume that there are two established parties, the issue space I is the uni-dimensional interval, all voters have symmetric single peaked-peaked preferences over I and the distribution of the voters' ideal points is represented by a quasi-concave continuous density function. Under these rather mild assumptions, we are able to prove the existence and uniqueness of the hierarchical equilibrium and to completely

Finding Multiple Nash Equilibria in Pool-Based Markets: A Stochastic EPEC Approach

Abstract: We present a compact formulation to find all pure Nash equilibria in a pool-based electricity market with stochastic demands. The equilibrium model is formulated as a stochastic equilibrium problem subject to equilibrium constraints (EPEC). The problem is based on a Stackelberg game where the generating companies (GENCOs) optimize their strategic bids anticipating the solution of the independent system operator (ISO) market clearing. A finite strategy approach both in prices and quantities is applied to transform the nonlinear and nonconvex set of Nash inequalities into a mixed integer linear problem (MILP). A procedure to find all Nash equilibria is developed by generating “holes” that are added as linear constraints to the feasibility region. The result of the problem is the set of all pure Nash equilibria and the market clearing prices and assigned energies by the ISO. A case study illustrates the methodology and proper conclusions are reached.