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第1回予測市場勉強会資料・予測市場の概要と理論
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Yuya-Furusawa
June 24, 2019
Science
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230
第1回予測市場勉強会資料・予測市場の概要と理論
第1回予測市場勉強会で使用したスライドです。
Eagna(
https://eagna.io/
)
Yuya-Furusawa
June 24, 2019
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Transcript
༧ଌࢢͷ֓ཁͱཧ ༧ଌࢢษڧձୈ̍ճ ݹᖒ ༏ 2019/06/24
Table of Contents • ࣗݾհ • ༧ଌࢢʹ͍ͭͯ • ༧ଌࢢͷཧ •
͓ΘΓʹ • Q&A
ࣗݾհ • ݹᖒ ༏ • ౦େܦࡁM2 • ઐɿήʔϜཧɺωοτϫʔΫཧ • ؔ৺ɿ༧ଌࢢɺ҉߸௨՟ɺҼՌਪ
• ༧ଌࢢαʔϏε”Eagna”ΛӡӦɾ։ൃͯ͠·͢
༧ଌࢢʹ͍ͭͯ
༧ଌͷॏཁੑ • কདྷͷ༧ଌඇৗʹॏཁ དྷ݄ͷऩೖˠࠓͷങ͍ ͷधཁˠઃඋࢿ ޙͷੈքˠݱࡏͷࡦ
None
༧ଌͱ͍͏ӦΈ • ੈͷதʹࢄΒ͍ͬͯΔใΛूͯ͠ɺকདྷ ʹؔ͢ΔใΛಋ͘ߦҝ • ͰͲͷΑ͏ʹใΛू͢Ε͍͍ͷ͔ʁ • ޮత͔ͭίετͳूํ๏ͩͱخ͍͠
༧ଌखஈ̍ɿઐՈʹฉ͘ • Pros • ৫ʹೲಘײΛੜΉ • Cons • ίετߴ͍(ۚમతɺ࣌ؒత) •
ਖ਼ʹ͑ΔΠϯηϯςΟϒʁ • ਫ਼ͦΜͳʹߴ͘ͳ͍͔͠Εͳ͍ɺɺɺ
༧ଌखஈ̎ɿଟܾʢථʣ • Pros • ؆୯ʹ࣮ߦͰ͖Δ • ࢀՃऀ͕ฏʹѻΘΕΔ • Cons •
ਖ਼ʹථ͢ΔΠϯηϯςΟϒ͕ແ͍ • ใΛ͍࣋ͬͯΔਓͱ࣋ͬͯͳ͍ਓ͕ฏʹѻΘΕ ͯ͠·͏ • ථऀͷແؾྗԽ(Voter Apathy)
༧ଌखஈ̏ɿAIͰ༧ଌ • Pros • ༧ଌਫ਼͕ඇৗʹߴ͍ • Cons • େͳσʔλ͕ඞཁ •
σʔλ͕ͳ͍͜ͱͷ༧ଌ͍͠
1. ༧ଌΛਖ਼ʹݴ͏ΠϯηϯςΟϒ͕ແ͍ 2. ࣌ؒతɾۚમతίετ͕ߴ͍ 3. େྔ͔࣭ͭͷߴ͍σʔλ͕ඞཁ
ޮతʹਫ਼ͷߴ͍༧ଌ͕͍ͨ͠ʂʂʂ
༧ଌࢢ Prediction Market • ܈ऺͷӥஐͱࢢϝΧχζϜΛ༻͍ͨίε τ͔ͭޮతͳใूϝΧχζϜ • ଟͷࢀՃऀ͕ࣗͷ༧ʹैͬͯɺূ݊Խ ͞Εͨ༧Λചങ͢Δ •
ຊͰ͋·ΓΒΕͯ·ͤΜͶɺɺɺ
܈ऺͷӥஐ Wisdom of Crowds • 1ਓͷ༏Εͨఱ࠽͕Լ͢அΑΓɺී௨ͷਓ ͔ΒΔूஂ͕Լ͢அͷํ͕༏Ε͍ͯΔͱ ͍͏ݱ • ྫɿΰϧτϯڭतͱ༤ڇͷମॏͯେձ
ࢢϝΧχζϜ Market Mechanism • ܦࡁతΠϯηϯςΟϒʹΑΓޮతͳΛ ୡ • ʮൃݟతखଓ͖ͱͯ͠ͷڝ૪ʯbyϋΠΤΫ • ใूϝΧχζϜͱͯ͠ͷࢢ
༧ଌࢢͷΈ • τϥϯϓͱώϥϦʔͷͲͪΒ͕উ͔ͭΛ༧ଌ ͢Δ༧ଌࢢΛߟ͑·͠ΐ͏ʂ
༧ଌࢢͷΈ 1. τϥϯϓτʔΫϯͱώϥϦʔτʔΫϯΛൃߦ τϥϯϓ $1 $0 τϥϯϓউར τϥϯϓഊ ώϥϦʔ $1
$0 ώϥϦʔউར ώϥϦʔഊ
༧ଌࢢͷΈ 2. τʔΫϯͷചങΛ͢Δ • উͭͱ༧͢ΔํͷτʔΫϯΛങ͏ τϥϯϓ ώϥϦʔ τϥϯϓ͕উͭ ͱࢥ͏ͳΒ… ώϥϦʔ͕উͭ
ͱࢥ͏ͳΒ…
༧ଌࢢͷΈ 2. τʔΫϯΛചങ͢Δ • ͖ͳτʔΫϯΛ͖ͳ͚ͩങ͑Δ τϥϯϓ ώϥϦʔ ×̑ ×̑ ʑ͘Β͍ͩͱ
ࢥ͏ͳΒ…
༧ଌࢢͷΈ 2. τʔΫϯΛചങ͢Δ • ༧͕มԽͨ͠ΒͦΕʹԠͯ͡ചങ τϥϯϓ ώϥϦʔ ώϥϦʔ͕উͪͦ͏ͩ ͱͳͬͨΒ…
༧ଌࢢͷΈ 3. ݁Ռ͕ܾ·ͬͨͷͪɺ͍͕͠ߦΘΕΔ τϥϯϓ ώϥϦʔ
Ձ֨ͱ༧ଌ • Ձ͕֨ߴ͍ʹΈΜͳ͕༧͍ͯ͠Δ • Ձ֨ʹࢢͷ༧ଌ • ܦࡁతΠϯηϯςΟϒ͕༧ଌΛͨΒ͢
͍͢͝ͱ͜Ζ 1. ༧ଌ͕ਖ਼֬ “Prediction Markets”, Wolfers and Zitzewitz
“Prediction Markets”, Wolfers and Zitzewitz
͍͢͝ͱ͜Ζ 2. දݱͷଟ༷ੑ • ෳબࢶͷ༧ଌ • ͷ༧ଌ • ͖݅ͷ༧ଌ
͍͢͝ͱ͜Ζ 3. ϦΞϧλΠϜੑ • Ձ֨(ʹ༧ଌ)ͷมԽ͕Θ͔Δ • χϡʔεͳͲͰ༧ଌ͕DynamicʹมԽ • ଞͷ༧ଌखஈʹݟΒΕͳ͍ಛੑ
༧ଌࢢͷՄೳੑ • ʮްੜ࿑ಇলͷ౷ܭʹෆਖ਼͕͋Δ͔ʁʯ ɹˠ෦ͷਓͷࠂൃΛಋ͚Δ͔ʢʁʣ • ʮຊͷՁ্ঢ˓%Λ͑Δ͔ʁʯ ɹˠਓʑͷظΛԽ͠ࡦʹ͑Δ͔ʢʁʣ
μϝͳͱ͜Ζ 1. ϚʔέοτͷσβΠϯ͕͍͠ 2. ๏తͳ • ຊͩͱṌത๏ͰΞτͰ͢^^ 3. ྲྀಈੑͷ֬อɺཧऀͷଛࣦ 4.
݁Ռͷղऍ͕͍͠
༧ଌࢢઈରతʹ༏Εͨ༧ଌखஈͰͳ͍ Ή͠Ζଞͷ༧ଌखஈͱิతͳؔ
༧ଌࢢͷཧ
༧ଌࢢͷϝΧχζϜ • Ͳ͏ͬͯՁ֨ΛܾΊΕ͍͍ͷ͔ʁ • Ձ͕֨༧ଌΛදͯ͠΄͍͠ • ͦͷ༧ଌਖ਼֬ͳͷͰ͋ͬͯ΄͍͠ • ࣗͷ༧ଌ௨Γʹਖ਼ʹചങͯ͠΄͍͠
࿈ଓμϒϧΦʔΫγϣϯํࣜ Continuous Double Auction Mechanism • ূ݊Λചങ • Πϕϯτ͕ൃੜͨ͠ͱ͖ʹ$1Β͑Δূ݊ •
ചΓจͱങ͍จΛͦΕͧΕఏग़ • ͕݅Ϛον͢Εఆ • גࣜࢢɺҝସࢢͳͲͱಉ͡Γํ • ͜ͷͱ͖Ձ͕֨֬Λදͯ͘͠ΕΔʂ(Why?)
࿈ଓμϒϧΦʔΫγϣϯํࣜ Continuous Double Auction Mechanism • Thin Market Problem •
ಛʹબࢶ͕ଟ͘ͳΔͱ૬ख͕ݟ͔ͭΒͳ ͍Մೳੑ • No Trade Theorem • ૬ख͕औҾ͠Α͏ͱ͢ΔͳΒʹͦΕʹԠ͡ ͳ͍ํ͕ྑ͍
ϚʔέοτϝΠΧʔํࣜ Automated Market Maker Mechanism • ࢢͷཧऀͱऔҾΛߦ͏ • ཧऀ͔ΒτʔΫϯΛߪೖ͠ɺཧऀ͕ใु Λࢧ͏
• Ձ֨ΛͲ͏ܾΊΕྑ͍͔ʁ →ϞσϧԽ͠·͠ΐ͏ʂ
είΞϦϯάϧʔϧ Scoring Rule • ֬Λਃࠂ͢Δɿ • είΞϦϯάϧʔϧ • ਃࠂ͞Εͨ֬ʹର͢ΔใुͷׂΓͯϧʔϧ S
= {s1 (r), ⋯, sn (r)} r = {r1 , ⋯, rn } si (r) r i Λਃࠂ͠Πϕϯτ ͕ൃੜͨ͠߹ʹΒ͑Δใु 120%, 225%, …
ϓϩύʔείΞϦϯάϧʔϧ Proper Scoring Rule • ࣗͷຊͷ༧ɿ • ϓϩύʔείΞϦϯάϧʔϧ • ਖ਼ʹਃࠂ͢Δ͜ͱͰظใु͕࠷େԽ͞
ΕΔΑ͏ͳείΞϦϯάϧʔϧ ̂ r = { ̂ r1 , ⋯, ̂ rn } ̂ r ∈ arg max r n ∑ i=1 ̂ ri Si (r)
ϓϩύʔείΞϦϯάϧʔϧͷྫ • Logarithmic Scoring Rule • Quadratic Scoring Rule si
(r) = ai + b log(ri ) si (r) = ai + 2bri − b n ∑ j=2 r2 j
ϚʔέοτείΞϦϯάϧʔϧ Market Scoring Rule • Scoring Rule͚ͩͩͱ̍ճਃࠂͯ͠ऴΘΓɺෳ ਓͷਃࠂΛѻ͑ͳ͍ • ஞ࣍తʹείΞϦϯάϧʔϧΛద༻
• ਃࠂΛɹɹɹɹɹɹɹͱ͍͏Α͏ʹࢀՃऀશ ମͰมԽ͍ͤͯ͘͞ r0 → r1 → ⋯ → r
ϚʔέοτείΞϦϯάϧʔϧ Market Scoring Rule • ਃࠂΛม͑ͨ࣌ͷใु • ࢀՃऀ࠷ऴతʹɹɹɹɹɹ͚ͩΒ͏ • ཧऀଛΛ͢ΔՄೳੑ
si (r) − si (r0) rold rnew ਃࠂΛ ͔Β ʹมߋͨ͠߹ɺ i Πϕϯτ ͕ൃੜͨ࣌͠ʹ si (rnew) − si (rold)Λࢧ͏ Proper Scoring Rule
LMSR • είΞϦϯάϧʔϧʹLogarithmic Scoring Rule Λ༻͍Δ߹ɺ Logarithmic Market Scoring Rule
(LMSR) ͱݺΕΔ • Ұ൪Α͘ΘΕΔϧʔϧ
ίετؔͱϚʔέοτϝΠΧʔ Cost-function-based Market Maker • ΑΓʮࢢΒ͘͠ʯ͍ͨ͠ʂ ূ݊ͷചങͱ͍͏Θ͔Γ͍͢ܗʹ • ূ݊ Πϕϯτɹ͕ൃੜͨ࣌͠ʹˈ̍ͦΕҎ֎ˈ̌
• ֤ূ݊ͷ૯ൃߦྔϕΫτϧ i i q = {q1 , ⋯, qn }
MSRͷ࠶ղऍ • ɹɹʮɹΛ༧ͨ࣌͠ʹ֤τʔΫϯ͕͍ͭ͘ ͑Δ͔ʯʹରԠ͍ͯ͠Δ • ͭ·ΓɹɹɹʹରԠ͢Δ • औҾʹΑͬͯɹɹɹɹɹɹɹɹͱมԽ͍ͯ͘͠ • ɹͷมԽɹͷมԽΛͨΒ͢
• ɹɹɹɹͰมԽ͍ͯ͘͠ q0 → q1 → ⋯ → q q s(r) r s(r) q r r s−1(q)
MSRͷ࠶ղऍ • Ձ֨ɹɹͱҰக͢ΔΑ͏ʹऔҾ͞ΕΔ • ͭ·ΓՁ͕֨ͪΌΜͱ༧ଌΛදͯ͘͠ΕΔʂ • Ձ֨ɹɹɹɹɹͰܾఆ͞ΕΔ • औҾͷࡍͷࢧֹ͍Ձ֨ؔͷੵ •
ͬ͘͟Γͱɹɹɹɹɹɹɹͭ·Γ • ίετؔɹɿՁ֨ؔͷݪ࢝ؔ r p = s−1(q) C C(qnew) − C(qold) p ∫ qnew qold p(q)dq
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 )
͓ΘΓʹ
ͬͱΓ͍ͨਓ • ʮී௨ͷਓͨͪΛ༬ݴऀʹม͑Δʰ༧ଌࢢʱͱ͍ ͏৽ઓུʯɺυφϧυɾτϯϓιϯ • ʮʰΈΜͳͷҙݟʱҊ֎ਖ਼͍͠ʯɺδΣʔϜζɾ εϩΟοΩʔ • “Prediction Market
: Theory and Application”, Leighton Vaughan Williams
Eagna • ”Eagna”ͱ͍͏αʔϏεΛӡӦɾ։ൃͯ͠·͢ • PCɺεϚϗͷϒϥβ্Ͱ༧ଌࢢΛແྉͰ ମݧͰ͖·͢ʢsign upඞཁʣ • Ϛʔέοτ͝ͱʹίΠϯΛ͢ΔͷͰɺͦ ΕΛͨ͘͞Μ૿͍ͯͩ͘͠͞ʂ
Eagna • ใु͋Γ·͢ʂ • ֫ಘͨ͠ίΠϯʹൺྫͯ֬͠తʹίʔώʔͷΪ ϑτ݊ΛΓ·͢ • eagna.ioͰݕࡧʂ • ϑΟʔυόοΫେܴͰ͢ʂ
None
༧ଌࢢษڧձ • ຊͷ༧ଌࢢίϛϡχςΟͱͯ͠ຖ݄ߦͬ ͍ͯ͘༧ఆͰ͢ • ݄݄̓͘Β͍ʹߦ͍·͢ • ࣌ɺձɺςʔϚconnpassͰʂ • ੋඇ࣍ճ͝ࢀՃԼ͍͞ʂ
Q&A
͋Γ͕ͱ͏͍͟͝·ͨ͠ʂ