保育園利用調整の現状と課題：マーケットデザインの観点から

（2016年12月）
・東京23区の利用調整方法
・マッチング理論による定式化
・シリアル・ディクテーターシップの課題

Transcript

1. อҭԂར༻ௐ੔ͷݱঢ়ͱ՝୊ɿ ϚʔέοτσβΠϯͷ؍఺͔Β ࠤʑ໦ɹ߁࿕ ๺཮ઌ୺Պֶٕज़େֶӃେֶɹ஌ࣝՊֶܥ 2016 ೥ 12 ݄ 1 / 30
2. ϚʔέοτσβΠϯͱ͸ ʮࢢ৔ʯͷ੍౓ઃܭΛѻ͏ܦࡁֶɾήʔϜཧ࿦ͷҰ෼໺ Ϛονϯάͷཧ࿦͕ൃలɺݱ࣮ͷԠ༻ྫ΋ଟ͍ ʢྫʣݚमҩϚονϯάɺֶߍબ୒ɺଁثަ׵ͳͲ 2012 ೥ϊʔϕϧܦࡁֶ৆ʢRoth & Shapleyʣ ຊࢿྉͰ͸ɺอҭԂͷར༻ௐ੔ΛϚʔέοτσβΠϯͷ؍఺͔Β ֓؍ɻ ʢཧ࿦తʹ͸ֶߍબ୒ͷಛघέʔεʣ 2 / 30
3. อҭԂͷར༻ௐ੔ ࣏ࣗମʢࢢொଜʣ͝ͱʹࣇಐͱอҭॴΛϚονϯάʢࣇಐ෱ࢱ๏ ୈ 24 ৚ʣ ɻ௨ৗɺࣇಐͷ೥ྸผʹ࣮ࢪɻ ࠃ͕ࣔ͢ௐ੔ํ๏ͷݪଇ*ɿ ʮ֤ࢢொଜʹ͓͍ͯɺར༻ऀ͝ͱʹอҭͷඞཁ౓ʹ͍ͭͯࢦ ਺ʢ༏ઌॱҐʣ͚ͮΛߦ͏ɻͦͷ্Ͱɺ ʢུʣߴ͍ࢦ਺ͷॱ ൪͔Β͋ͬͤΜ্ͨ͠Ͱɺಉ͡ࢦ਺Ͱ͋Ε͹ɺར༻ر๬ॱҐ Λ;·͑ͯར༻Λ͋ͬͤΜ͢Δ͜ͱͱ͢Δɻ ʯ ͨͩ͠ɺ࣮ࡍͷӡ༻ʹ͍ͭͯ͸࣏ࣗମʹࡋྔ͕͋Γɺ࣏ࣗମ ʹΑͬͯҟͳΔϚονϯάํࣜΛ࠾༻ɻ *ʮࣇಐ෱ࢱ๏ʹجͮ͘อҭॴ౳ͷར༻ௐ੔ͷऔѻ͍ʹ͍ͭͯʢ௨஌ʣ ʯ ʢฏ੒ 27 ೥ 2 ݄ 3 ೔෎੓ڞੜୈ 98 ߸ޏࣇൃ 0203 ୈ 3 ߸ʣΑΓൈਮɻ 3 / 30
4. ౦ژ 23 ۠ͷར༻ௐ੔ํ๏ ֤͕۠࡞੒ɾެ։͍ͯ͠Δ 2016 ೥ 4 ݄ೖॴر๬ऀ޲͚Ҋ಺Λ΋ ͱʹௐࠪɻ ʢશ۠ڞ௨ʣ શͯͷࣇಐʹอҭͷඞཁ౓ʹԠͯ͡ࢦ਺ʢ༏ઌॱҐʣ෇͚ Ұൠతʹ͸อޢऀͷब࿑ঢ়گ΍Ոఉঢ়گ౳Ͱ൑அɻ ʢৄࡉ͸ ࣏ࣗମʹΑͬͯҟͳΔʣ ಉҰࢦ਺ͱͳΔࣇಐ͕ෳ਺ଘࡏ͠ಘΔɻ ͔ͦ͜Βઌ͸ɺେ͖͘෼͚ͯ 3 ͭͷํ๏ʢˠ࣍ϖʔδʣ 4 / 30
5. ౦ژ 23 ۠ͷར༻ௐ੔ํ๏ ํ๏ 1 ࢦ਺ͷߴ͍ॱʹར༻͋ͬͤΜɻಉҰࢦ਺ͷ৔߹ɺ௥Ճతج४ʹΑ Γ༏ྼΛ൑அɻ ํ๏ 2 ࢪઃ͝ͱʹୈҰر๬ΛऔΓ·ͱΊɺͦͷத͔Βࢦ਺ͷߴ͍ॱʹར ༻͋ͬͤΜɻ ʢಉҰࢦ਺ͷ৔߹ɺ௥Ճతج४ʹΑΓ൑அɻୈҰر ๬Ͱܾ·Βͳ͍৔߹ɺୈೋɺୈࡾر๬ҎԼͰಉ༷ͷૢ࡞ɻ ʣ ํ๏ 3 ࢦ਺ͷߴ͍ॱʹར༻͋ͬͤΜɻಉҰࢦ਺ͷ৔߹ɺ౰֘ࢪઃͷر๬ ॱҐ͕ߴ͍ํΛ༏ઌɻ ʢر๬ॱҐ΋ಉ͡৔߹ʹ͸ɺ͞Βʹ௥Ճత ج४ʹΑΓ൑அʣ 5 / 30
6. ౦ژ 23 ۠ͷར༻ௐ੔ํ๏ ํ๏ ۠ ํ๏ 1 ઍ୅ాɺதԝɺߓɺ৽॓ɺจژɺ୆౦ɺ๽ాɺߐ ౦ɺ඼઒ɺ໨ࠇɺੈా୩ɺौ୩ɺத໺ɺ๛ౡɺ๺ɺ ߥ઒ɺ൘ڮɺ࿅അɺ׉০ɺߐށ઒ʢެཱʣ ํ๏ 2 ߐށ઒ʢࢲཱʣ ํ๏ 3 େాɺਿฒ ʢෆ໌ʣ ଍ཱ* *ʮࢦ਺ͷॱʹར༻͋ͬͤΜʯͱ͍ͯ͠Δ͕ɺಉҰࢦ਺ͷ৔߹ͷج४͕໌ࣔ͞Ε ͍ͯͳ͔ͬͨͨΊɺ෼ྨͤͣɻ ʢํ๏ 1 ͔ 3 ͔෼͔Βͣʣ 6 / 30
7. Ϛονϯάཧ࿦ʹ͓͚Δ֤ௐ੔ํ๏ͷҐஔ෇͚ ํ๏ 1 ˠγϦΞϧɾσΟΫςʔλʔγοϓʢSDʣ* ཧ࿦తʹ๬·͍͠ੑ࣭Λຬͨ͢ɻ ʢޙड़ʣ ํ๏ 2 ˠϘετϯํࣜ ֶߍબ୒ͳͲͰΑ͘ݟΒΕΔ͕ɺཧ࿦తʹܽ఺͋Γɻ ʢޙड़ʣ ํ๏ 3 ˠʢطଘݚڀʹ͸ແ͠ʣ جຊతʹ͸ SD ͰɺಉҰࢦ਺ͷ৔߹ʹϘετϯํࣜͰϚονϯά ͢Δํ๏ͱղऍՄɻ ʢࠃͷࣔ͢ݪଇʹ࠷΋͍ۙʣ *ࢦ਺ͷߴ͍ॱʹɺఆһʹۭ͖ͷ͋ΔอҭॴͷதͰ࠷΋ر๬ॱҐ͕ߴ͍ͱ͜Ζ΁ ͋ͬͤΜͨ͠৔߹ɻ ʢଟ͘ͷ۠ͷެ։ࢿྉͰ͸ɺ͜͜·Ͱݫີͳهࡌ͸ͳ͘ɺ࣮ ࡍʹ SD ͕༻͍ΒΕ͍ͯΔ͔͸அఆͰ͖ͳ͍ɻͨͩ͠ɺࣇಐͷر๬Λߟྀ͢Δ ͱɺSD ͸࠷΋ૉ௚ͳํ๏ͱݴ͑Δɻ ʣ 7 / 30
8. ར༻ௐ੔ͷఆࣜԽ Sɿอҭॴͷू߹ Cɿอҭॴͷू߹ qsɿอҭॴ s ͷఆһʢqs ∈ Z+ʣ ≻cɿࣇಐ c ͷબ޷ S ∪ {∅} ্ͷઢܗॱংʢݫີͳબ޷ॱংɺಉॱҐ͸ͳ͍ʣ ∅ɿΞϯϚονʢͲͷอҭॴͱ΋Ϛονͤͣʣ s ≻c s′ ⇔ ࣇಐ c ͸อҭॴ s′ ΑΓ s Λر๬ s ≻c ∅ ⇔ ࣇಐ c ʹͱͬͯอҭॴ s ͸ Acceptableʢͦ͏Ͱͳ͚ Ε͹ Unacceptableʣ 8 / 30
9. ར༻ௐ੔ͷఆࣜԽ rcɿࣇಐ c ͷϥϯΫʢrc ∈ Rʣ rc > rc′ ⇔ ࣇಐ c ͸ c′ ΑΓ΋ϥϯΫʢ༏ઌॱҐʣ͕ߴ͍ ݫີͳϥϯΫ෇͚ΛԾఆʢಉॱҐ͸ͳ͍ʣ ఆٛ (S, C, (qs)s∈S , {≻c}c∈C , (rc)c∈C ) ΛอҭॴϚονϯά໰୊ͱ͍͏ɻ ֶߍબ୒໰୊Ͱɺશֶߍͷબ޷͕ಉ͡ಛघέʔε* *બ޷ͷڞ௨ੑ͸ɺݫີʹ͸੒ཱ͠ͳ͍৔߹΋͋Δɻྫ͑͹ɺܑఋͷಉ࣌௨ԂΛ ༏۰͢ΔͨΊɺ౰֘ࢪઃʹ͍ͭͯͷΈ༏ઌॱҐΛ্͛ΔͳͲɻ͜ͷ৔߹ɺอҭ ॴ͝ͱʹҟͳΔબ޷Λ࣋ͪಘΔֶߍબ୒໰୊ͱͯ͠ϞσϧԽ͢Δඞཁ͕͋Δɻ 9 / 30
10. Ϛονϯά ఆٛ ҎԼͷੑ࣭Λຬͨؔ͢਺ µ : C → S ∪ C ΛϚονϯάͱ͍͏ɻ શͯͷ c ∈ C ʹ͍ͭͯɺµ(c) ∈ S ∪ {∅} શͯͷ s ∈ S ʹ͍ͭͯɺ|µ−1(s)| ≤ qs µ(c) ͸ࣇಐ c ͱϚονͨ͠อҭॴɻ ʢµ(c) = ∅ ͷ৔߹͸Ξϯ Ϛονʣ ֤ࣇಐ͸ɺߴʑҰͭͷอҭॴͱϚονͰ͖Δɻ֤อҭॴ͸ɺ ఆһΛ্ݶͱͯ͠ࣇಐͱϚονͰ͖Δɻ ఆٛ อҭॴϚονϯά໰୊ʹରͯ͋͠ΔϚονϯάΛఆΊΔؔ਺Λɺ Ϛονϯάํࣜͱ͍͏ɻ 10 / 30
11. ݸਓ߹ཧੑɺແବ͕ͳ͍ ఆٛ Ϛονϯά µ ͕ݸਓ߹ཧతʢindividually rationalʣͰ͋Δɻ ⇔ શͯͷ c ∈ C ʹ͍ͭͯɺµ(c) ≻c ∅ ·ͨ͸ µ(c) = ∅ ʢҙຯʣUnacceptable ͳอҭॴͱϚον͍ͯ͠Δࣇಐ͕͍ͳ͍ɻ ఆٛ Ϛονϯά µ ʹ͸ແବ͕ͳ͍ʢnon-wastefulʣ ɻ ⇔ શͯͷ c ∈ Cɺٴͼ s ≻c µ(c) Ͱ͋ΔΑ͏ͳશͯͷ s ∈ S ʹͭ ͍ͯɺ|µ−1(s)| = qs ʢҙຯʣ ʮࣗ෼͕ೖॴ͔͕ͨͬͨ͠Ͱ͖ͳ͔ͬͨอҭॴʹɺ·ͩఆ һʹۭ͖͕͋Δʯͱߟ͑Δࣇಐ͕͍ͳ͍ɻ 11 / 30
12. ެฏੑ ఆٛ Ϛονϯά µ ͕ެฏతʢfairʣͰ͋Δɻ ⇔ શͯͷ s ∈ S ٴͼ c ∈ C ʹ͍ͭͯɺs ≻c µ(c) Ͱ͋Δ৔߹ɺͲ ͷΑ͏ͳ c′ ∈ µ−1(s) ʹ͍ͭͯ΋ rc′ > rc ʢҙຯʣ ʮࣗ෼͕ೖॴ͔͕ͨͬͨ͠Ͱ͖ͳ͔ͬͨอҭॴʹɺࣗ෼Α ΓϥϯΫͷ௿͍ࣇಐ͕ೖॴͨ͠ʯͱߟ͑Δࣇಐ͕͍ͳ͍ɻ ্ه 3 ੑ࣭Λຬͨ͢͜ͱ͸ɺҰൠతͳҰରଟϚονϯάʹ͓͚Δ ҆ఆੑʢstabilityʣͱಉ஋ɻ 12 / 30
13. ޮ཰ੑ ఆٛ ೋͭͷϚονϯά µ ͱ µ′ ʹؔͯ͠ɺµ′ ͸ µ ΛύϨʔτࢧ഑͢Δɻ ⇔ શͯͷࣇಐ c ʹ͍ͭͯ µ(c) ≻c µ′(c) Ͱͳ͘ɺ͔ͭগͳ͘ͱ΋ Ұਓͷࣇಐ c′ ʹ͍ͭͯ µ′(c′) ≻c′ µ(c′) ఆٛ Ϛονϯά µ ͕ޮ཰తʢefficientʣͰ͋Δɻ ⇔µ ͕ɺଞͷ͍͔ͳΔϚονϯάʹ΋ύϨʔτࢧ഑͞Εͳ͍ɻ ܦࡁֶʹ͓͚ΔύϨʔτޮ཰ੑͱಉ͡ɻ ʢͨͩ͠ࣇಐͷްੜ ͷΈΛߟྀʣ ޮ཰తͳϚονϯά͸ɺඞͣݸਓ߹ཧత͔ͭແବ͕ͳ͍ɻ 13 / 30
14. Ϛονϯάํࣜͷੑ࣭ ఆٛ ͋ΔϚονϯάํ͕ࣜɺ଱ઓུతʢstrategy-proofʣͰ͋Δɻ ⇔ શͯͷࣇಐ͸ɺਅͷબ޷Λද໌͢Δ͜ͱ͕ৗʹ࠷దɻ ͲͷΑ͏ͳબ޷ʢر๬ॱҐʣΛද໌͢Δ͔͕ઓུͰ͋Δήʔ ϜΛߟ͑ͨ৔߹ɺਅͷબ޷Λද໌͢Δ͜ͱ͕ࢧ഑ઓུɻ ଱ઓུੑ͕ຬͨ͞Εͳ͍ྫʕϓϩ໺ٿυϥϑτձٞ ఆٛ ͋ΔϚονϯάํ͕ࣜɺݸਓ߹ཧతʗແବ͕ͳ͍ʗެฏతʗޮ཰ తͰ͋Δɻ ⇔ ݸਓ߹ཧతʗແବ͕ͳ͍ʗެฏతʗޮ཰తͳϚονϯά͕ৗʹ ੜ੒͞ΕΔɻ 14 / 30
15. γϦΞϧɾσΟΫςʔλʔγοϓʢSDʣ εςοϓ 1ɿ࠷΋ϥϯΫ͕ߴ͍ࣇಐΛɺAcceptable Ͱɺ͔ͭ ఆһʹۭ͖͕͋Δอҭॴͷ͏ͪɺ͜ͷࣇಐ͕࠷΋ر๬͢Δอ ҭॴͱϚονϯάͤ͞ΔɻͦͷΑ͏ͳอҭॴ͕ͳ͍৔߹ɺΞ ϯϚονͱͳΔɻ εςοϓ 2ɿ2 ൪໨ʹϥϯΫ͕ߴ͍ࣇಐΛʜʢҎԼಉ༷ʣ ʢҎԼɺϥϯΫͷߴ͍ॱʹಉ༷ͷૢ࡞ʣ 15 / 30
16. ྫ 3 ࣇಐͱ 2 อҭॴͷϚονϯάɿ ࣇಐ 1 ͷબ޷ɿอҭॴ A ࣇಐ 2 ͷબ޷ɿอҭॴ A, อҭॴ B ࣇಐ 3 ͷબ޷ɿอҭॴ B, อҭॴ A ϥϯΫɿࣇಐ 1, ࣇಐ 2, ࣇಐ 3 อҭॴͷఆһɿA, B ͱ΋ 1 ʢSD ʹΑΔϚονϯάʣ ࣇಐ 1ʕอҭॴ A ࣇಐ 2ʕอҭॴ B ࣇಐ 3 ˠެฏత͔ͭޮ཰తͳϚονϯά 16 / 30
17. γϦΞϧɾσΟΫςʔλʔγοϓͷੑ࣭ ໋୊ʢBalinski & S¨ onmez, 1999ʣ SD ͸ɺެฏత͔ͭޮ཰తͳ།ҰͷϚονϯάํࣜͰ͋Δɻ ໋୊ʢSvensson, 1999ʣ SD ͸ɺ଱ઓུతͰ͋Δɻ ୯७ͳΞϧΰϦζϜͰ͋Γͳ͕Βɺ๬·͍͠ੑ࣭Λຬͨ͢ɻ ௨ৗͷҰରଟϚονϯάͱݟͳͨ͠৔߹ʢࣇಐͷϥϯΫʹ֤ อҭॴڞ௨ͷબ޷ʣ ɺৗʹ҆ఆϚονϯάΛಋ͘डೖอཹํ ࣜʢGale & Shapley, 1962ʣͱಉ஋ɻ 17 / 30
18. Ϙετϯํࣜ εςοϓ 1ɿ֤อҭॴʹɺ౰֘อҭॴΛୈҰر๬ͱ͢Δࣇಐ ΛɺఆһͷൣғͰϥϯΫͷߴ͍ॱʹϚονϯάͤ͞Δɻ εςοϓ k(≥ 2)ɿεςοϓ k − 1 ·Ͱʹఆһ͕ຬͨ͞Ε͍ͯ ͳ͍֤อҭॴʹɺ౰֘อҭॴΛୈ k ر๬ͱ͢Δɺεςοϓ k − 1 ·ͰʹϚονϯά͍ͯ͠ͳ͍ࣇಐΛɺఆһͷൣғͰϥ ϯΫͷߴ͍ॱʹϚονϯάͤ͞Δɻ ऴྃϧʔϧɿ͋Δεςοϓͷऴྃ࣌఺Ͱɺશͯͷࣇಐ͕͍ͣ Ε͔ͷอҭॴͱϚον͢Δ͔ɺ·ͩϚονϯά͍ͯ͠ͳ͍ࣇ ಐʹ͸͍ͣΕ΋ Acceptable ͳอҭॴ͕࢒͍ͬͯͳ͍৔߹ɺΞ ϧΰϦζϜΛऴྃɻ 18 / 30
19. Ϙετϯํࣜͷੑ࣭ p.16 ͱಉ͡ྫͰʜ ʢϘετϯํࣜʹΑΔϚονϯάʣ ࣇಐ 1ʕอҭॴ A ࣇಐ 2 ࣇಐ 3ʕอҭॴ B ެฏతͰͳ͍ɻ ʢ2 ΑΓϥϯΫͷ௿͍ 3 ͕ B ʹೖॴʣ ଱ઓུతͰͳ͍ɻ ʢ2 ͸ B ΛୈҰر๬ʹ͢Ε͹Α͔ͬͨʣ 19 / 30
20. SD ͷ՝୊ SD ͸ཧ࿦తʹ๬·͍͠ੑ࣭Λຬͨ͠ɺ࣮ࡍʹଟ͘ͷ۠Ͱ࠾༻͞ Ε͍ͯΔɻ ˣ SD Λ࠾༻͍ͯ͠Δ৔߹ɺݱঢ়͸Ϛονϯάͷ੍౓ઃܭͷ໘͔Β ͸จ۟ͷ͚ͭΑ͏͕ͳ͍ʢमਖ਼ͷ༨஍͸ͳ͍ʣ ʁ ˣ ͦΜͳ͜ͱ͸ͳ͍ɻ ҎԼɺ͍͔ͭ͘ͷ՝୊ɾ࿦఺Λఏࣔɻ 20 / 30
21. ଱ઓུੑͷ์غʁ ʮઓུతͳཁૉΛؚΊͯ΄͍͠ͱͷࢢຽχʔζ͕Ұఆఔ౓͋Δʯ ʢ๭࣏ࣗମ୲౰ऀʣ ͔͠͠ɺ଱ઓུੑΛຬͨ͞ͳ͍ํࣜ΁มߋͨ͠৔߹ɺҎԼͷΑ͏ ͳ՝୊͕ɻ ʢ࣮຿໘ʣਃ੥ظؒதʹɺଟ͘ͷอޢऀ͕Ԡืঢ়گͷ։ࣔΛ ٻΊΔՄೳੑ͕͋Γɺ૬Ԡͷߦ੓ίετʢࢿྉ੔ཧɺ૭ޱର Ԡͷෛ୲૿౳ʣ͕ൃੜ͠ಘΔɻ ʢཧ࿦໘ʣެฏੑ͔ޮ཰ੑͷগͳ͘ͱ΋ҰํΛ์غ͠ͳ͚Ε ͹ͳΒͳ͍ɻ 21 / 30
22. ਃ੥Մೳ਺ͷ੍໿ SD Ͱ΋ɺਃ੥Մೳ਺ʹ্ݶ͕͋Δ৔߹͸଱ઓུੑΛຬͨ͞ͳ͍ɻ ʢHaeringer & Klijn, 2009ʣ p.16 ͱಉ͡ྫͰɺਃ੥Մೳ਺͕ 1 ͷ৔߹ɿ ʢSD ʹΑΔϚονϯάʣ ࣇಐ 1ʕอҭॴ A ࣇಐ 2 ࣇಐ 3ʕอҭॴ B ˠ 2 ͸ɺB ΛୈҰر๬ʹ͓͚ͯ͠͹Α͔ͬͨɻ 22 / 30
23. ਃ੥Մೳ਺ͷ੍໿ʢ౦ژ 23 ۠ʣ ਃ੥Մೳ਺ ۠ ্ݶͳ͠ தԝɺ৽॓ɺੈా୩ɺौ୩ɺத໺ɺ๺ɺ൘ڮ 20 ߓ 13 ࿅അ 10 ୆౦ɺ໨ࠇ 9 ๛ౡ 8 ඼઒ 7 ๽ాɺਿฒ 6 େా 5 ઍ୅ా*ɺจژɺߥ઒ɺ଍ཱɺߐށ઒ 4 ߐ౦ɺ׉০ ʢ2016 ೥ 3 ݄࣌఺ͷ֤۠ެ։ࢿྉʹج͖ͮ࡞੒ʣ *ઍ୅ా۠Ͱ͸ɺ ʮೖԂͰ͖Ε͹Ͳ͜Ͱ΋Α͍ʯͱ͍͏બ୒ࢶ΋͋Γɻ 23 / 30
24. ແࠩผબ޷ͷߟྀ ࣮ࡍʹ͸ɺࣇಐͷબ޷͸ݫີͱ͸ݶΒͳ͍ʕʮอҭॴ A ͱ B ͸ɺೖॴͰ͖Ε͹ͲͪΒͰ΋Α͍ʯ ͔͠͠ɺ௨ৗɺݫີʹر๬ॱҐΛ͚ͭͯਃ੥͢Δඞཁ͋Γɻ ແࠩผੑΛԿΒ͔ͷํ๏Ͱղফͯ͠ɺSD Λద༻ͨ݁͠ՌಘΒΕ ΔϚονϯά͸ɺਅͷʢʹແࠩผੑΛղফ͢Δલͷʣબ޷ͷ΋ͱ ͰͷެฏతͳϚονϯάʹύϨʔτࢧ഑͞ΕಘΔɻ ʢErdil & Ergin, 2015ʣ ˞ϥϯΫͷແࠩผੑͷղফʹ΋ಉ༷ͷ໰୊͋Γɻ 24 / 30
25. ྫ ࣇಐ 1 ͷબ޷ɿ ʢอҭॴ A, อҭॴ Bʣɹ˞ A ͱ B ͸ແࠩผ ࣇಐ 2 ͷબ޷ɿอҭॴ A ϥϯΫɿࣇಐ 1, ࣇಐ 2 อҭॴͷఆһɿA, B ͱ΋ 1 ࣇಐ 1 ͸ɺA ΛୈҰر๬ɺB Λୈೋر๬ͱͯ͠ϦετΛఏग़ɻ ʢSD ʹΑΔϚονϯάʣ ࣇಐ 1ʕอҭॴ A ࣇಐ 2 25 / 30
26. ྫʢଓ͖ʣ ҎԼͷΑ͏ͳผͷϚονϯάΛߟ͑Δɻ ࣇಐ 1ʕอҭॴ B ࣇಐ 2ʕอҭॴ A ˠਅͷબ޷ͷ΋ͱͰެฏతɻ͔͠΋ SD ʹΑΔϚονϯάΛύ Ϩʔτࢧ഑ɻ Erdil & Ergin (2015) ͸ɺਅͷબ޷ͷ΋ͱͰެฏతͳʢʴݸਓ߹ཧ తˍແବ͕ͳ͍ʣϚονϯάͷதͰޮ཰తͳϚονϯάΛબ୒͢ ΔΞϧΰϦζϜΛఏҊɻ ʢͨͩ͠ɺ଱ઓུੑ͸ຬͨ͞ͳ͍ʁʣ 26 / 30
27. ΞϯϚον࡟ݮͱͷτϨʔυΦϑ SD ͸ɺଞͷํࣜʹൺ΂ͯɺΞϯϚον͕૿͑ΔՄೳੑ͕͋Δɻ ఆһ͕ʮ׬શʹʯຬͨ͞Ε͍ͯΔ࣏ࣗମͰ͸໰୊ͱͳΒͳ͍ ʢSD Ҏ֎ͷํࣜʹͯ͠΋ɺSD ͷ๬·͍͠ੑ࣭Λ٘ਜ਼ʹ͢Δ ͚ͩʣ ɻͦ͏Ͱͳ͍࣏ࣗମʢ଴ػࣇಐ͕ଘࡏ͢ΔҰํͰɺఆ һະॆ଍ͷอҭॴ͋ΓʣͰ͸ɺٞ࿦ͷ༨஍͋Γʁ ʮޮ཰తʯ͔ͭʮSD ͰΞϯϚονͰͳ͍ࣇಐ͸ΞϯϚον ʹͳΒͳ͍ʯൣғͰ΋ɺ ʢSD ʹൺ΂ͯʣແࢹͰ͖ͳ͍΄ͲΞ ϯϚον࡟ݮͰ͖ΔՄೳੑ͋Γɻ ʢSasaki & Ura, 2016ʣ ͨͩ͠ɺ௨ৗɺެฏੑͷ์غ͸ࠔ೉ɻ·ͨɺΞϯϚον࡟ݮ ͱ଱ઓུੑΛཱ྆͢ΔϚονϯάํ͕ࣜ͏·͘ઃܭͰ͖Δ͔ ΋ෆ໌ɻ 27 / 30
28. ྫ ࣇಐ 1 ͷબ޷ɿอҭॴ A, อҭॴ B ࣇಐ 2 ͷબ޷ɿอҭॴ A ϥϯΫɿࣇಐ 1, ࣇಐ 2 อҭॴͷఆһɿA, B ͱ΋ 1 ʢSD ʹΑΔϚονϯάʣ ࣇಐ 1ʕอҭॴ A ࣇಐ 2 ʢผͷϚονϯάʣ ࣇಐ 1ʕอҭॴ B ࣇಐ 2ʕอҭॴ A ˠެฏతͰ͸ͳ͍͕ɺΞϯϚον͸ SD ΑΓগͳ͍ɻ ʢޮ཰తͰ͸ ͋Δʣ 28 / 30
29. ೥ྸؒͷఆһௐ੔ 0ʙ2 ࡀࣇΫϥε͸ఆһ͕ຬͨ͞Ε͍ͯͯ΋ɺ3 ࡀࣇҎ্Ϋϥ εͰ͸ఆһʹ༨༟͕͋Δ͜ͱ΋ଟ͍ɻ Ұ෦ͷ࣏ࣗମʢԣ඿ࢢͳͲʣͰ͸ɺϚονϯάޙʹɺ೥ྸؒ Ͱఆһ࿮Λ༥௨͠ɺ௥ՃతʹࣇಐΛड͚ೖΕ͍ͯΔɻ ˠΑΓʮେ͖ͳ໰୊ʯΛߟ͑Δ͜ͱͰɺঢ়گͷվળ͕Մೳɻ ͨͩ͠ɺԣ඿ࢢͷํ๏Ͱ͸ɺ ʮ௥Ճతʹड͚ೖΕΔࣇಐʯΛ ౰ॳͷϚονϯάͰΞϯϚονͱͳͬͨࣇಐʹݶఆ͍ͯ͠Δ ͨΊɺ࠷ऴతͳϚονϯάͰ͸ެฏੑ͕ຬͨ͞Εͳ͍Մೳੑ ͕͋Δɻ Okumura (2016) ͸ɺ೥ྸؒͷఆһௐ੔Λߟྀͭͭ͠ɺެฏ ੑͳͲͷ๬·͍͠ੑ࣭Λຬͨ͢ϚονϯάํࣜΛఏҊɻ 29 / 30
30. ࢀߟจݙ M. Balinski and T. S¨ onmez, A tale of two mechanisms: Student placement. Journal of Economic Theory, 84(1):73-94, 1999. A. Erdil and H. Ergin, Two-sided matching with indifferences. unpublished manuscript, 2015. D. Gale and L. S. Shapley, College admissions and the stability of marriage. American Mathematical Monthly, 69(1):9-15, 1962. G. Haeringer and F. Klijn, Constrained school choice. Journal of Economic Theory, 144(5):1921-1947, 2009. Y. Okumura, School choice with general constraints: A market design approach for the nursery school waiting list problem in Japan. unpublished manuscript, 2016. Y. Sasaki and M. Ura, Serial Dictatorship and Unmatch Reduction: A Problem of Japan’s Nursery School Choice, Economics Letters, 147:38-41, 2016. L. G. Svensson, Strategy-proof allocation of indivisible goods. Social Choice and Welfare, 16(4):557-567, 1999. 30 / 30