Two-Sided Random Acceptability graph Matching Markets: m 1 Ex-Ante - - PowerPoint PPT Presentation

Two-Sided Random Matching Markets:

Ex-Ante Equivalence of the Deferred Acceptance Procedures Simon Mauras simon.mauras@irif.fr

Université de Paris, IRIF

Two-Sided Matching Market

Acceptability graph

m1 m2 m3 m4 m5 w1 w2 w3 w4

Agents order their neighbours uniformly at random.

Mauras (Université de Paris, IRIF) EC’20 Poster 1 / 4

You are an evil decision maker You need to chose the procedure:

• MPDA: Men Proposing

Deferred Acceptance

• WPDA: Women Proposing

Deferred Acceptance You really like this matching:

µ

m1 m2 m3 m4 m5 w1 w2 w3 w4

What should you do to maximize the probability of chosing µ?

Mauras (Université de Paris, IRIF) EC’20 Poster 2 / 4

Output distribution of MPDA. P[MPDA outputs µ] = 299/5184 Output distribution of WPDA. P[WPDA outputs µ] = 299/5184

Mauras (Université de Paris, IRIF) EC’20 Poster 3 / 4

• Theorem. “Ex-ante equivalence”

MPDA and WPDA have the same

• utput distribution.

If you don’t know the preferences, you cannot “manipulate”... In the talk/paper:

1 Proof of the Theorem. 2 Non-uniform distributions.

In the proof... Lattice of stable matchings. Probability of stability.

Mauras (Université de Paris, IRIF) EC’20 Poster 4 / 4