Two Folk Manipulability Theorems in the General One-to-one Two-sided Matching Markets with Money

We prove a “General Manipulability Theorem” for general one-to-one two-sided matching markets with money. This theorem implies two folk theorems, the Manipulability Theorem and the General Impossibility Theorem, and provides a sort of converse of the Non-Manipulability Theorem (Demange, 1982, Leonard, 1983, Demange and Gale, 1985).