Globally and universally convergent price adjustment processes
讨论了三种在交换经济中保证收敛到竞争均衡的价格调整过程，并详细解释了其数学工具，适用于研究一般均衡和价格调整的经济学者。
We discuss three processes of price adjustment in an exchange economy, proposed by Smale (1976), Laan and Talman (1987), and Kamiya (1990), respectively. Under a regularity condition on the economy, the first process is guaranteed to converge to a competitive equilibrium for almost every initial price system such that one of the prices is equal to zero. The process of Kamiya (1990) is guaranteed to converge to the set of competitive equilibria for almost every initial price system, under a condition on the boundary behavior of the excess demand function of the economy. The Laan and Talman (1987) process was shown by Herings (1997) to converge to a competitive equilibrium for a generic set of exchange economies for any initial price system. The simplest way to describe these processes is by characterizing the path of prices that they generate. Convergence proofs then rely on results from differential topology and establish that these paths have a manifold structure. The required tools, involving regular constraint sets and manifolds with generalized boundary, are explained in detail and can be fruitfully applied in other domains as well. The paper concludes with an overview of globally and universally convergent processes in other environments like production economies, economies with price rigidities, and game theory.