Social integration in two-sided matching markets

Abstract

When several two-sided matching markets merge into one, it is inevitable that some agents will become worse off if the matching mechanism used is stable. I formalize this observation by defining the property of integration monotonicity, which requires that every agent becomes better off after any number of matching markets merge. Integration monotonicity is also incompatible with the weaker efficiency property of Pareto optimality.Nevertheless, I obtain two possibility results. First, stable matching mechanisms never hurt more than one half of the society after the integration of several matching markets occurs. Second, in random matching markets there are positive expected gains from integration for both sides of the market, which I quantify.

Gainers and Losers from Market Integration

“…The result has been reported as Proposition 8 in Gersbach and Haller (2015). Proposition 2 of Ortega (2018) asserts that with strict preferences, at most half of the population are losers, which is a corollary of our result. He obtains additional results on the integration of matching markets.…”

The losses from integration in matching markets can be large

“…Proof. From Proposition 2 in Ortega (2018), we know that the number of agents who get hurt by integration is weakly lower than the number of agents who benefit from integration. The smallest gain from integration is (+1) in raw ranking terms.…”

“…In this paper, I show theoretically that, in worst-case scenarios, matching markets may fail to integrate because doing so would inevitable generate welfare losses in a well-defined sense. This worst-case result is somewhat surprising since the integration of two-sided matching markets never harms more people than those it benefits ex-post and generates expected welfare gains for both sides of the market (Ortega, 2018).…”

Coalitional game theory based local power exchange algorithm for networked microgrids

“…The matching problem was first introduced by Gale and Shapley [21] in 1962. After them, different matching models have been proposed and applied in many areas, such as biological computation [22,23], economics [24], computer vision [25], and climate [26,27]. However, to authors' knowledge, none of the famous existing matching models [28][29][30] are suitable for this networked MG coalitional local power exchange situation.…”