In a dynamic matching and bargaining game, a large population of traders interacts repeatedly in a decentralized market. Every trading period, traders are matched to form small groups where they bargain over the terms of trade. If they fail to reach an agreement, at some cost they can wait until the next period to be rematched into a new group. These waiting costs are the frictions of trading in the decentralized market. A major question in the literature concerns the trading outcome when frictions become small: Will the outcome become efficient? Ideally, one would like not only to find answers for particular trading institutions but also to gain a general understanding of the conditions under which trading with vanishing frictions has this property and the conditions under which it does not. This is the task of this paper. Its primary goal is to provide a general, "detail free" framework for the analysis of decentralized markets. The paper can be found at http://www-personal.umich.edu/~slauerma/lauermann_general_approach.pdf.