第１回予測市場勉強会資料・予測市場の概要と理論

by Yuya-Furusawa

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༧ଌࢢ৔ͷ֓ཁͱཧ࿦ ༧ଌࢢ৔ษڧձୈ̍ճ ݹᖒ ༏໵ 2019/06/24

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Table of Contents • ࣗݾ঺հ • ༧ଌࢢ৔ʹ͍ͭͯ • ༧ଌࢢ৔ͷཧ࿦ • ͓ΘΓʹ • Q&A

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ࣗݾ঺հ • ݹᖒ ༏໵ • ౦େܦࡁM2 • ઐ໳ɿήʔϜཧ࿦ɺωοτϫʔΫཧ࿦ • ؔ৺ɿ༧ଌࢢ৔ɺ҉߸௨՟ɺҼՌਪ࿦ • ༧ଌࢢ৔αʔϏε”Eagna”ΛӡӦɾ։ൃͯ͠·͢

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༧ଌࢢ৔ʹ͍ͭͯ

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༧ଌͷॏཁੑ • কདྷͷ༧ଌ͸ඇৗʹॏཁ དྷ݄ͷऩೖˠࠓ೔ͷങ͍෺ ঎඼ͷधཁˠઃඋ౤ࢿ ਺೥ޙͷੈք৘੎ˠݱࡏͷ੓ࡦ

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༧ଌͱ͍͏ӦΈ • ੈͷதʹࢄΒ͹͍ͬͯΔ৘ใΛू໿ͯ͠ɺকདྷ ʹؔ͢Δ৘ใΛಋ͘ߦҝ • Ͱ͸ͲͷΑ͏ʹ৘ใΛू໿͢Ε͹͍͍ͷ͔ʁ • ޮ཰త͔ͭ௿ίετͳू໿ํ๏ͩͱخ͍͠

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༧ଌखஈ̍ɿઐ໳Ոʹฉ͘ • Pros • ૊৫ʹೲಘײΛੜΉ • Cons • ίετߴ͍(ۚમతɺ࣌ؒత) • ਖ਼௚ʹ౴͑ΔΠϯηϯςΟϒ͸ʁ • ਫ਼౓ͦΜͳʹߴ͘ͳ͍͔΋͠Εͳ͍ɺɺɺ

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༧ଌखஈ̎ɿଟ਺ܾʢ౤ථʣ • Pros • ؆୯ʹ࣮ߦͰ͖Δ • ࢀՃऀ͕ฏ౳ʹѻΘΕΔ • Cons • ਖ਼௚ʹ౤ථ͢ΔΠϯηϯςΟϒ͕ແ͍ • ৘ใΛ͍࣋ͬͯΔਓͱ࣋ͬͯͳ͍ਓ͕ฏ౳ʹѻΘΕ ͯ͠·͏ • ౤ථऀͷແؾྗԽ(Voter Apathy)

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༧ଌखஈ̏ɿAIͰ༧ଌ • Pros • ༧ଌਫ਼౓͕ඇৗʹߴ͍ • Cons • ๲େͳσʔλ͕ඞཁ • σʔλ͕ͳ͍͜ͱͷ༧ଌ͸೉͍͠

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໰୊఺ 1. ༧ଌΛਖ਼௚ʹݴ͏ΠϯηϯςΟϒ͕ແ͍ 2. ࣌ؒతɾۚમతίετ͕ߴ͍ 3. େྔ͔࣭ͭͷߴ͍σʔλ͕ඞཁ

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ޮ཰తʹਫ਼౓ͷߴ͍༧ଌ͕͍ͨ͠ʂʂʂ

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༧ଌࢢ৔ Prediction Market • ܈ऺͷӥஐͱࢢ৔ϝΧχζϜΛ༻͍ͨ௿ίε τ͔ͭޮ཰తͳ৘ใू໿ϝΧχζϜ • ଟ਺ͷࢀՃऀ͕ࣗ෼ͷ༧૝ʹैͬͯɺূ݊Խ ͞Εͨ༧૝Λചങ͢Δ • ೔ຊͰ͸͋·Γ஌ΒΕͯ·ͤΜͶɺɺɺ

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܈ऺͷӥஐ Wisdom of Crowds • 1ਓͷ༏Εͨఱ࠽͕Լ͢൑அΑΓ΋ɺී௨ͷਓ ͔Β੒Δूஂ͕Լ͢൑அͷํ͕༏Ε͍ͯΔͱ ͍͏ݱ৅ • ྫɿΰϧτϯڭतͱ༤ڇͷମॏ౰ͯେձ

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ࢢ৔ϝΧχζϜ Market Mechanism • ܦࡁతΠϯηϯςΟϒʹΑΓޮ཰తͳ഑෼Λ ୡ੒ • ʮൃݟతखଓ͖ͱͯ͠ͷڝ૪ʯbyϋΠΤΫ • ৘ใू໿ϝΧχζϜͱͯ͠ͷࢢ৔

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༧ଌࢢ৔ͷ࢓૊Έ • τϥϯϓͱώϥϦʔͷͲͪΒ͕উ͔ͭΛ༧ଌ ͢Δ༧ଌࢢ৔Λߟ͑·͠ΐ͏ʂ

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༧ଌࢢ৔ͷ࢓૊Έ 1. τϥϯϓτʔΫϯͱώϥϦʔτʔΫϯΛൃߦ τϥϯϓ $1 $0 τϥϯϓউར τϥϯϓഊ๺ ώϥϦʔ $1 $0 ώϥϦʔউར ώϥϦʔഊ๺

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༧ଌࢢ৔ͷ࢓૊Έ 2. τʔΫϯͷചങΛ͢Δ • উͭͱ༧૝͢ΔํͷτʔΫϯΛങ͏ τϥϯϓ ώϥϦʔ τϥϯϓ͕উͭ ͱࢥ͏ͳΒ… ώϥϦʔ͕উͭ ͱࢥ͏ͳΒ…

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༧ଌࢢ৔ͷ࢓૊Έ 2. τʔΫϯΛചങ͢Δ • ޷͖ͳτʔΫϯΛ޷͖ͳ͚ͩങ͑Δ τϥϯϓ ώϥϦʔ ×̑ ×̑ ൒ʑ͘Β͍ͩͱ ࢥ͏ͳΒ…

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༧ଌࢢ৔ͷ࢓૊Έ 2. τʔΫϯΛചങ͢Δ • ༧૝͕มԽͨ͠ΒͦΕʹԠͯ͡ചങ τϥϯϓ ώϥϦʔ ώϥϦʔ͕উͪͦ͏ͩ ͱͳͬͨΒ…

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༧ଌࢢ৔ͷ࢓૊Έ 3. ݁Ռ͕ܾ·ͬͨͷͪɺ෷͍໭͕͠ߦΘΕΔ τϥϯϓ ώϥϦʔ

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Ձ֨ͱ༧ଌ • Ձ͕֨ߴ͍ʹΈΜͳ͕༧૝͍ͯ͠Δ • Ձ֨ʹࢢ৔ͷ༧ଌ • ܦࡁతΠϯηϯςΟϒ͕༧ଌΛ΋ͨΒ͢

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͍͢͝ͱ͜Ζ 1. ༧ଌ͕ਖ਼֬ “Prediction Markets”, Wolfers and Zitzewitz

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“Prediction Markets”, Wolfers and Zitzewitz

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͍͢͝ͱ͜Ζ 2. දݱͷଟ༷ੑ • ෳ਺બ୒ࢶͷ༧ଌ • ਺஋ͷ༧ଌ • ৚݅෇͖ͷ༧ଌ

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͍͢͝ͱ͜Ζ 3. ϦΞϧλΠϜੑ • Ձ֨(ʹ༧ଌ)ͷมԽ͕Θ͔Δ • χϡʔεͳͲͰ༧ଌ͕DynamicʹมԽ • ଞͷ༧ଌखஈʹ͸ݟΒΕͳ͍ಛੑ

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༧ଌࢢ৔ͷՄೳੑ • ʮްੜ࿑ಇলͷ౷ܭʹෆਖ਼͕͋Δ͔ʁʯ ɹˠ಺෦ͷਓͷࠂൃΛಋ͚Δ͔΋ʢʁʣ • ʮ೔ຊͷ෺Ձ্ঢ཰͸˓%Λ௒͑Δ͔ʁʯ ɹˠਓʑͷظ଴Λ਺஋Խ͠੓ࡦʹ࢖͑Δ͔΋ʢʁʣ

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μϝͳͱ͜Ζ 1. ϚʔέοτͷσβΠϯ͕೉͍͠ 2. ๏తͳ໰୊ • ೔ຊͩͱṌത๏ͰΞ΢τͰ͢^^ 3. ྲྀಈੑͷ֬อɺ؅ཧऀͷଛࣦ 4. ݁Ռͷղऍ͕೉͍͠

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༧ଌࢢ৔͸ઈରతʹ༏Εͨ༧ଌखஈͰ͸ͳ͍ Ή͠Ζଞͷ༧ଌखஈͱิ׬తͳؔ܎

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༧ଌࢢ৔ͷཧ࿦

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༧ଌࢢ৔ͷϝΧχζϜ • Ͳ͏΍ͬͯՁ֨ΛܾΊΕ͹͍͍ͷ͔ʁ • Ձ͕֨༧ଌΛදͯ͠΄͍͠ • ͦͷ༧ଌ͸ਖ਼֬ͳ΋ͷͰ͋ͬͯ΄͍͠ • ࣗ෼ͷ༧ଌ௨Γʹਖ਼௚ʹചങͯ͠΄͍͠

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࿈ଓμϒϧΦʔΫγϣϯํࣜ Continuous Double Auction Mechanism • ূ݊Λചങ • Πϕϯτ͕ൃੜͨ͠ͱ͖ʹ$1΋Β͑Δূ݊ • ചΓ஫จͱങ͍஫จΛͦΕͧΕఏग़ • ৚͕݅Ϛον͢Ε͹໿ఆ • גࣜࢢ৔ɺҝସࢢ৔ͳͲͱಉ͡΍Γํ • ͜ͷͱ͖Ձ͕֨֬཰Λදͯ͘͠ΕΔʂ(Why?)

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࿈ଓμϒϧΦʔΫγϣϯํࣜ Continuous Double Auction Mechanism • Thin Market Problem • ಛʹબ୒ࢶ͕ଟ͘ͳΔͱ૬ख͕ݟ͔ͭΒͳ ͍Մೳੑ • No Trade Theorem • ૬ख͕औҾ͠Α͏ͱ͢ΔͳΒʹͦΕʹԠ͡ ͳ͍ํ͕ྑ͍

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ϚʔέοτϝΠΧʔํࣜ Automated Market Maker Mechanism • ࢢ৔ͷ؅ཧऀͱऔҾΛߦ͏ • ؅ཧऀ͔ΒτʔΫϯΛߪೖ͠ɺ؅ཧऀ͕ใु Λࢧ෷͏ • Ձ֨ΛͲ͏ܾΊΕ͹ྑ͍͔ʁ →ϞσϧԽ͠·͠ΐ͏ʂ

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είΞϦϯάϧʔϧ Scoring Rule • ֬཰Λਃࠂ͢Δɿ • είΞϦϯάϧʔϧ • ਃࠂ͞Εͨ֬཰ʹର͢ΔใुͷׂΓ౰ͯϧʔϧ S = {s1 (r), ⋯, sn (r)} r = {r1 , ⋯, rn } ͸ si (r) r i Λਃࠂ͠Πϕϯτ ͕ൃੜͨ͠৔߹ʹ΋Β͑Δใु 1͸20%, 2͸25%, …

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ϓϩύʔείΞϦϯάϧʔϧ Proper Scoring Rule • ࣗ෼ͷຊ౰ͷ༧૝ɿ • ϓϩύʔείΞϦϯάϧʔϧ • ਖ਼௚ʹਃࠂ͢Δ͜ͱͰظ଴ใु͕࠷େԽ͞ ΕΔΑ͏ͳείΞϦϯάϧʔϧ ̂ r = { ̂ r1 , ⋯, ̂ rn } ̂ r ∈ arg max r n ∑ i=1 ̂ ri Si (r)

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ϓϩύʔείΞϦϯάϧʔϧͷྫ • Logarithmic Scoring Rule • Quadratic Scoring Rule si (r) = ai + b log(ri ) si (r) = ai + 2bri − b n ∑ j=2 r2 j

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ϚʔέοτείΞϦϯάϧʔϧ Market Scoring Rule • Scoring Rule͚ͩͩͱ̍ճਃࠂͯ͠ऴΘΓɺෳ ਺ਓͷਃࠂΛѻ͑ͳ͍ • ஞ࣍తʹείΞϦϯάϧʔϧΛద༻ • ਃࠂΛɹɹɹɹɹɹɹͱ͍͏Α͏ʹࢀՃऀશ ମͰมԽ͍ͤͯ͘͞ r0 → r1 → ⋯ → r

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ϚʔέοτείΞϦϯάϧʔϧ Market Scoring Rule • ਃࠂΛม͑ͨ࣌ͷใु • ࢀՃऀ͸࠷ऴతʹɹɹɹɹɹ͚ͩ΋Β͏ • ؅ཧऀ͸ଛΛ͢ΔՄೳੑ si (r) − si (r0) rold rnew ਃࠂΛ ͔Β ʹมߋͨ͠৔߹ɺ i Πϕϯτ ͕ൃੜͨ࣌͠ʹ si (rnew) − si (rold)Λࢧ෷͏ Proper Scoring Rule

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LMSR • είΞϦϯάϧʔϧʹLogarithmic Scoring Rule Λ༻͍Δ৔߹ɺ Logarithmic Market Scoring Rule (LMSR) ͱݺ͹ΕΔ • Ұ൪Α͘࢖ΘΕΔϧʔϧ

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ίετؔ਺ͱϚʔέοτϝΠΧʔ Cost-function-based Market Maker • ΑΓʮࢢ৔Β͘͠ʯ͍ͨ͠ʂ ূ݊ͷചങͱ͍͏Θ͔Γ΍͍͢ܗʹ • ূ݊ Πϕϯτɹ͕ൃੜͨ࣌͠ʹˈ̍ͦΕҎ֎͸ˈ̌ • ֤ূ݊ͷ૯ൃߦྔϕΫτϧ i i q = {q1 , ⋯, qn }

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MSRͷ࠶ղऍ • ɹɹ͸ʮɹΛ༧૝ͨ࣌͠ʹ֤τʔΫϯ͕͍ͭ͘໯ ͑Δ͔ʯʹରԠ͍ͯ͠Δ • ͭ·Γɹɹ͸ɹʹରԠ͢Δ • औҾʹΑͬͯɹɹɹɹɹɹɹɹͱมԽ͍ͯ͘͠ • ɹͷมԽ͸ɹͷมԽΛ΋ͨΒ͢ • ɹ͸ɹɹɹͰมԽ͍ͯ͘͠ q0 → q1 → ⋯ → q q s(r) r s(r) q r r s−1(q)

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MSRͷ࠶ղऍ • Ձ֨ɹ͸ɹͱҰக͢ΔΑ͏ʹऔҾ͞ΕΔ • ͭ·ΓՁ͕֨ͪΌΜͱ༧ଌΛදͯ͘͠ΕΔʂ • Ձ֨͸ɹɹɹɹɹͰܾఆ͞ΕΔ • औҾͷࡍͷࢧ෷ֹ͍͸Ձ֨ؔ਺ͷੵ෼ • ͬ͘͟Γͱɹɹɹɹɹɹɹͭ·Γ • ίετؔ਺ɹɿՁ֨ؔ਺ͷݪ࢝ؔ਺ r p = s−1(q) C C(qnew) − C(qold) p ∫ qnew qold p(q)dq

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ίετؔ਺ with LMSR • LMSRͷ৔߹ɺ ίετؔ਺ Ձ֨ C(q) = b log n ∑ j=1 exp ( qj − aj b ) pi = exp ( qi − ai b ) ∑n j=1 exp ( qj − aj b )

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͓ΘΓʹ

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΋ͬͱ஌Γ͍ͨਓ͸ • ʮී௨ͷਓͨͪΛ༬ݴऀʹม͑Δʰ༧ଌࢢ৔ʱͱ͍ ͏৽ઓུʯɺυφϧυɾτϯϓιϯ • ʮʰΈΜͳͷҙݟʱ͸Ҋ֎ਖ਼͍͠ʯɺδΣʔϜζɾ εϩ΢ΟοΩʔ • “Prediction Market : Theory and Application”, Leighton Vaughan Williams

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Eagna • ”Eagna”ͱ͍͏αʔϏεΛӡӦɾ։ൃͯ͠·͢ • PCɺεϚϗͷϒϥ΢β্Ͱ༧ଌࢢ৔ΛແྉͰ ମݧͰ͖·͢ʢsign upඞཁʣ • Ϛʔέοτ͝ͱʹίΠϯΛ഑෍͢ΔͷͰɺͦ ΕΛͨ͘͞Μ૿΍͍ͯͩ͘͠͞ʂ

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Eagna • ใु΋͋Γ·͢ʂ • ֫ಘͨ͠ίΠϯʹൺྫͯ֬͠཰తʹίʔώʔͷΪ ϑτ݊Λ഑Γ·͢ • eagna.ioͰݕࡧʂ • ϑΟʔυόοΫେ׻ܴͰ͢ʂ

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༧ଌࢢ৔ษڧձ • ೔ຊͷ༧ଌࢢ৔ίϛϡχςΟͱͯ͠ຖ݄ߦͬ ͍ͯ͘༧ఆͰ͢ • ݄̓΋݄຤͘Β͍ʹߦ͍·͢ • ೔࣌ɺձ৔ɺςʔϚ͸connpass౳Ͱʂ • ੋඇ࣍ճ΋͝ࢀՃԼ͍͞ʂ