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Implementation of stable solutions to marriage problems. (English) Zbl 0852.90011
Summary: This note analyzes the possibility of implementing stable outcomes for marriage markets. Our first result shows a contradiction between the use of stable mechanisms and the hypothesis of agents’ behavior considered in the Nash equilibrium concept. We analyze the possibility of implementing two sets of stable allocations, by employing two types of mechanisms. The first mechanism is a “now-or-never” choice process that permits us to implement in undominated Nash equilibria the set of all the stable allocations. The second choice process is the classic algorithm in matching theory, the Gale-Shapley mechanism. A reversal property is observed in such a mechanism when agents act strategically. The use of a mechanism which selects the best solution for one side of the market in the absence of strategic behavior yields the best stable solution for the agents on the other side under dominance solvability.

91B14 Social choice
91B08 Individual preferences
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