  Duality of linear programming is a standard approach to the classical
weighted maximum matching problem. From an economic perspective, the dual
variables can be regarded as prices of products and payoffs of buyers in a
two-sided matching market. Traditional duality-based algorithms, e.g.,
Hungarian, essentially aims at finding a set of prices that clears the market.
Under such market-clearing prices, a maximum matching is formed when buyers buy
their most preferred products respectively. We study the property of
market-clearing prices without the use of duality, showing that: (1) the space
of market-clearing prices is convex and closed under element-wise maximum and
minimum operations; (2) any market-clearing prices induce all maximum
matchings.
