Stackelberg competition

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

Competitive Charging Station Pricing for Plug-In Electric Vehicles

Abstract: This paper considers the problem of charging station pricing and plug-in electric vehicles (PEVs) station selection. When a PEV needs to be charged, it selects a charging station by considering the charging prices, waiting times, and travel distances. Each charging station optimizes its charging price based on the prediction of the PEVs’ charging station selection decisions, and the other station’s pricing decision, in order to maximize its profit. To obtain insights of such a highly coupled system, we consider a 1-D system with two competing charging stations and Poisson arriving PEVs. We propose a multileader-multifollower Stackelberg game model, in which the charging stations (leaders) announce their charging prices in stage I and the PEVs (followers) make their charging station selections in stage II. We show that there always exists a unique charging station selection equilibrium in stage II, and such equilibrium depends on the charging stations’ service capacities and the price difference between them. We then characterize the sufficient conditions for the existence and uniqueness of the pricing equilibrium in stage I. We also develop a low complexity algorithm that efficiently computes the pricing equilibrium and the subgame perfect equilibrium of the two-stage Stackelberg game.

Equilibrium problems with equilibrium constraints: stationarities, algorithms, and applications

Abstract: An equilibrium problem with equilibrium constraints (EPEC) is a member of a new class of mathematical programs that often arise in engineering and economics applications. One important application of EPECs is the multi-leader-follower game in economics, where each leader is solving a Stackelberg game formulated as a mathematical program with equilibrium constraints (MPEC). Motivated by applied EPEC models for studying the strategic behavior of generating firms in deregulated electricity markets, the aim of this thesis is to study theory, algorithms, and new applications for EPECs. We begin by defining EPEC stationarity concepts. We then propose a sequential nonlinear complementarity (SNCP) method for solving EPECs and establish its convergence. We present the numerical results of the SNCP method and give a comparison with two best-reply iterations, nonlinear Jacobi and nonlinear Gauss-Seidel, on a set of randomly generated test problems. The computational experience to date shows that both the SNCP algorithm and the nonlinear Gauss-Seidel method outperform the nonlinear Jacobi method. We investigate the issue of existence of an EPEC solution in Chapter 4. In general, an EPEC solution may not exist because of nonconvexity of the associated MPECs. However, we show that the existence result can be established for the spot-forward market model proposed by Allaz and Vila or the two-period Cournot game studied by Saloner. We observe that the mathematical structure of the spot-forward market model is similar to that of the multiple leader Stackelberg model analyzed by Sherali when new variables are introduced for spot market sales. Consequently, we are able to adapt Sherali's analysis to establish the existence of a forward market equilibrium for M asymmetric producers with nonidentical linear cost functions. In Chapter 5, we present a novel MPEC approach for solving the static moral-hazard problem in economics. We consider deterministic contracts as well as contracts with action and/or compensation lotteries and formulate each case as an MPEC. We propose a hybrid procedure that combines the best features of the MPEC approach and the LP lottery approach. Numerical results on an example show that the hybrid procedure outperforms the LP lottery approach in both computational time and solution quality in terms of the optimal objective value.