Matching Market Equilibrium Algorithms
Years and Authors of Summarized Original Work
1971; Shapley, Shubik
1982; Kelso, Crawford
1986; Demange, Gale and Sotomayor
The study of matching market equilibrium was initiated by Shapley and Shubik  in an assignment model. A classical instance of the matching market involves a set B of n unit-demand buyers and a set Q of m indivisible items, where each buyer wants to buy at most one item and each item can be sold to at most one buyer. Each buyer i has a valuation vij ≥ 0 for each item j, representing the maximum amount that i is willing to pay for item j. Each item j has a reserve price rj ≥ 0, below which it won’t be sold. Without loss of generality, one can assume there is a null item whose value is zero to all buyers and whose price is always zero.
An output of the matching market is a tuple (p, x), where p = (p1, …, pm) ≥ 0 is a price vector with pj denoting the price charged for item j and x = (x1, …, xn) ≥ 0 is an allocation vector with xidenoting the...
KeywordsCompetitive equilibrium Matching market Maximum competitive equilibrium Minimum competitive equilibrium
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