Conditions for Stability in Strategic Matching

by   James P. Bailey, et al.

We consider the stability of matchings when individuals strategically submit preference information to a publicly known algorithm. Most pure Nash equilibria of the ensuing game yield a matching that is unstable with respect to the individuals' sincere preferences. We introduce a well-supported minimal dishonesty constraint, and obtain conditions under which every pure Nash equilibrium yields a matching that is stable with respect to the sincere preferences. The conditions on the matching algorithm are to be either fully-randomized, or monotonic and independent of non-spouses (INS), an IIA-like property. These conditions are significant because they support the use of algorithms other than the Gale-Shapley (man-optimal) algorithm for kidney exchange and other applications. We prove that the Gale-Shapley algorithm always yields the woman-optimal matching when individuals are minimally dishonest. However, we give a negative answer to one of Gusfield and Irving's open questions: there is no monotonic INS or fully-randomized stable matching algorithm that is certain to yield the egalitarian-optimal matching when individuals are strategic and minimally dishonest. Finally, we show that these results extend to the student placement problem, where women are polyandrous but must be honest but do not extend to the admissions problem, where women are both polyandrous and strategic.


page 1

page 2

page 3

page 4


EPTAS for stable allocations in matching games

Gale-Shapley introduced a matching problem between two sets of agents wh...

On Finding Pure Nash Equilibria of Discrete Preference Games and Network Coordination Games

This paper deals with the complexity of the problem of computing a pure ...

Allocating Indivisible Goods to Strategic Agents: Pure Nash Equilibria and Fairness

We consider the problem of fairly allocating a set of indivisible goods ...

The Effect of Strategic Noise in Linear Regression

We build on an emerging line of work which studies strategic manipulatio...

The Instability of Stable Matchings: The Influence of One Strategic Agent on The Matching Market

Consider a matching problem with n men and n women, with preferences dra...

Games on Endogenous Networks

We study network games in which players both create spillovers for one a...

The Influence of One Strategic Agent on The Matching Market

Consider a matching problem with n men and n women, with preferences dra...

Please sign up or login with your details

Forgot password? Click here to reset