Asymmetric First-Price Auctions—A Dynamical-Systems Approach
提出一种基于动力系统的新方法，用于分析和数值模拟非对称第一价格拍卖，证明了均衡策略的存在唯一性，并设计了稳定的正向打靶法。
We introduce a new approach for analysis and numerical simulations of asymmetric first-price auctions, which is based on dynamical systems. We apply this approach to asymmetric auctions in which players' valuations are power-law distributed. We utilize a dynamical-systems formulation to provide a proof of the existence and uniqueness of the equilibrium strategies in the cases of two coalitions and of two types of players. In the case of n different players, the singular point of the original system at b = 0 corresponds to a saddle point of the dynamical system with n − 1 admissible directions. This insight enables us to use forward solutions in the analysis and in the numerical simulations, in contrast with previous analytic and numerical studies that used backward solutions. The dynamical-systems approach provides an intuitive explanation for why the standard backward-shooting method for computing the equilibrium strategies is inherently unstable, and enables us to devise a stable forward-shooting method. In particular, in the case of two types of players, this method is extremely simple, as it does not require any shooting.