Implementation of Stable Solutions to Marriage Problems
This paper analyzes the possibility of irnplementing stable outcomes for marriage markets. Our first result shows a contradiction between the use of stable mechanisins and the hypotesis of agents' behaviour consiclered in the Nash equilibriurn concept . We analyze the possibility of irnplementing two sets of stable allocations, by employing two types of rnechanisms. The first mechanisrn is a "now-or- never" choice process that permits us to irnplement 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 behaviour yields the best stable solution for the agents on the other side under dominance solvability.