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School Choice and Information: An Experimental Study on

Matching Mechanisms

Joana Pais (ISEG) and

Ágnes Pintér (Universidad Carlos III de Madrid)

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Main objectives• Analyze the performance of three well-

known matching mechanisms regarding strategy-proofness, efficiency, and stability;

• Examine the role of information in the decision making in these situations:– Does the amount of information

participants hold affect the performance of the mechanisms? How?

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Motivation• Matching: pervasive phenomenon arising

both in social and economic situations• Examples:

– Assignment of civil servants to positions– Students’ admission to schools– Some entry-level labor markets– Assignment of donated organs to patients

• Rarely exists complete information

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Two-sided matching markets• Agents belong to one of two disjoint sets (e.g.

teachers and schools);• Each agent has preferences over the other side of

the market and the prospect of being unmatched;• Matching problem: to assign teachers to schools.• Highly valued properties of matching

mechanisms:– Stability: no pair of agents who are not matched

together would rather prefer to be so matched.– Strategy-proofness: truth is dominant strategy– Pareto efficiency

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The mechanisms and properties

Mechanism

BostonGale-

ShapleyTop Trading

Cycle

Strategy-proof

NO YES YES

Pareto efficient

NO* NO* YES

Stable NO YES NO

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Experimental design• School choice model:

– 5 teachers to fill 5 vacancies across 3 schools– Teachers: strict preferences over schools; Schools:

strict preferences (exogenous) over teachers and fixed capacity

• 3x3 design: for each mechanism three different info setting (zero-, partial- or full-information);

• Symmetric payoffs (3, 9 or 15 euro), but not necessarily symmetric induced preferences – average payoffs were around 13 euro.

• Schools are NOT strategic agents!

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Strategy-proofness, efficiency, and stability

Mechanism Info Truth Efficiency Stability

Boston

Zero 87% 93% 17%

Partial 47% 74% 11%

Full 47% 81% 44%

Gale &Shapley

Zero 82% 87% 56%

Partial 67% 69% 78%

Full 67% 79% 44%

Top Trading Cycles

Zero 96% 95% 11%

Partial 76% 87% 22%

Full 87% 91% 11%

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Results• Across mechanims:

– Truthtelling: B0 = GS0 < TTC0; B1<GS1=TTC1; B2<GS2<TTC2

– Efficiency: B0=GS0=TTC0; B=GS<TTC– Stability: GS0>TTC0, GS0=B0, B0=TTC0;

GS1>TTC1=B1; B2=GS2=TTC2

• Across informational scenarios:– Truthtelling: B0>B1=B2; GS0>GS1=GS2;

TTC0>TTC1, TTC0=TTC2, TTC1=TTC2– Efficiency: B0>B2=B1; GS0>GS1, GS0=GS2,

GS1=GS2; TTC0=TTC1=TTC2– Stability: Info0=Info1=Info2

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Summarizing

Therefore, we conclude that – information plays an important role in

decision making, and

– the use of the TTC mechanism in practice would be more desirable than of the others.