1 Gabatarwa
Tare da fiye da cryptocurrencies 4,000 da ke yawo da darajar sama da tiriliyan $1 da kuma ɗimbain aikace-aikacen da ba su da tushe da ke gudana akan su, fasahohin blockchain suna jawo hankali sosai. Duk da haka, rashin tabbas game da kwanciyar hankalinsu da dorewar dogon lokaci ya kasance shamaki ga ƙarin amfani. Fahimtar waɗannan abubuwan yana da mahimmanci ga blockchain marasa izini da kuma karɓar cryptocurrency a matsayin hanyar mu'amalar kuɗi ta ko'ina.
Ma'adinai suna taka muhimmiyar rawa a kwanciyar hankalin yanayin blockchain ta hanyar samar da albarkatu masu tsada (ikon lissafi a cikin Proof of Work ko raka'a cryptocurrency na asali a cikin Proof of Stake) don tabbatar da yarjejeniya. Suna aiki ne da son kai, ba su da tushe kuma suna iya shiga ko barin hanyoyin sadarwa a kowane lokaci, suna karɓar lada daidai da albarkatun da suka bayar.
2 Samfuri da Tsari
2.1 Samfurin Tattalin Arzikin Ma'adinai
Muna nazarin samfurin ka'idar wasa na tattalin arzikin ma'adinai wanda ya ƙunshi blockchain ɗaya ko da yanda ke zaune tare. Samfurin ya ginu akan aikin da ya gabata wanda ke samar da keɓaɓɓun rabon Nash Equilibrium a ƙarƙashin tsare-tsaren lada daidai wanda aka saba da shi a yawancin ka'idojin Proof of Work da Proof of Stake.
Muhimman abubuwan da aka haɗa sun haɗa da:
- Ma'adinai masu nau'ikan haɗarin daban-daban
- Cryptocurrencies da yawa da za a iya haƙa su
- Ƙuntatawar motsin albarkatu tsakanin blockchains
- Hanyoyin ba da lada daidai
2.2 Abubuwan Cuta
An bayyana cuta a matsayin al'adar da mahalartan hanyar sadarwa ke cutar da wasu a ɗan ƙaramin farashi ga kansu. Muna ƙididdige wannan ta hanyar abubuwan cuta - ma'auni waɗanda ke auna asarar hanyar sadarwa dangane da asarar mai karkata kansa.
An ayyana ma'aunin cuta $GF_i$ don ma'adinai $i$ kamar haka:
$GF_i = \frac{\sum_{j \neq i} \Delta \pi_j}{\Delta \pi_i}$
inda $\Delta \pi_j$ ke wakiltar canjin lada ga ma'adinai $j$ kuma $\Delta \pi_i$ shine canjin lada ga ma'adinan da ya karkata.
3 Nazarin Ka'idoji
3.1 Nazarin Nash Equilibrium
A rabon Nash Equilibrium, ma'adinai masu aiki suna ci gaba da samun kwarin gwiwa don karkata ta hanyar ƙara albarkatu don cimma mafi girman lada dangane. Duk da cewa ba su da kyau a cikin sharuɗɗan lada cikakke, asarar da ma'adinan da suka karkata ke samu an biya ta fiye da yawa ta hanyar haɓakar kaso na kasuwa da manyan asarar da aka yi wa sauran ma'adinai da hanyar sadarwa gabaɗaya.
Ka'idar 1 ta tabbatar da wanzuwa da keɓancewar Nash Equilibrium a ƙarƙashin daidaitattun tsare-tsaren lada daidai.
3.2 Kwanciyar Hankali na Juyin Halitta
Cuta yana da alaƙa da ra'ayoyin kwanciyar hankali na juyin halitta. Muna ƙaddamar da kwanciyar hankali na juyin halitta zuwa ga yawan jama'a marasa iri ɗaya ta amfani da abubuwan cuta, yana ba da tushen ka'ida ga abubuwan da aka gani kamar ɓarnatar da albarkatu, ƙarfafa iko, da manyan shingayen shiga cikin ma'adinan blockchain.
Ka'idar 6 da Corollary 7 sun tsara alaƙar tsakanin halin cuta da rashin kwanciyar hankali na juyin halitta a cikin tattalin arzikin ma'adinai.
4 Ka'idar Amsa Daidai
4.1 Ƙirar Algorithm
Yayin da hanyoyin sadarwa suka girma, hulɗar ma'adinai suna kama da tattalin arzikin samarwa ko kasuwannin Fisher. Don wannan yanayin, mun samo ka'idar sabuntawa ta Amsa Daidai (PR) wacce ke haɗuwa zuwa ma'auni na kasuwa inda cuta ta zama maras muhimmanci.
Ka'idar PR tana sabunta rabon albarkatu daidai da ƙimar amfanin gefe:
$x_i^{(t+1)} = x_i^{(t)} \cdot \frac{\partial u_i}{\partial x_i} / \left( \frac{1}{n} \sum_{j=1}^n \frac{\partial u_j}{\partial x_j} \right)$
inda $x_i$ ke wakiltar rabon albarkatu na ma'adinai $i$ kuma $u_i$ aikin amfaninsu ne.
4.2 Siffofin Haɗuwa
Ka'idar Amsa Daidai tana haɗuwa zuwa ma'auni na kasuwa ga faɗin nau'ikan haɗarin ma'adinai da matakan motsin albarkatu daban-daban tsakanin blockchains tare da fasahohin haƙa daban-daban. Haɗuwa yana riƙe ƙarƙashin zato na gaskiya game da halayen ma'adinai da yanayin hanyar sadarwa.
5 Sakamakon Ƙwaƙwalwar Aiki
5.1 Nazarin Shari'a: Cryptocurrencies Guda Hudu
Mun gudanar da nazarin ƙwaƙwalwar aiki ta amfani da bayanai daga cryptocurrencies huɗu da za a iya haƙa su. Binciken ya bincika tsare-tsaren rabon albarkatu, yaɗuwar halin cuta, da ma'aunin kwanciyar hankali a cikin yanayin hanyar sadarwa daban-daban da yawan ma'adinai.
Muhimman Bincike:
- An lura da halin cuta a cikin kashi 68% na tafkunan ma'adinai da aka bincika
- Matsakaicin ma'aunin cuta: 1.42 (yana nuna cutar hanyar sadarwa ta wuce farashin mai karkata)
- Ka'idar PR ta rage abubuwan da suka faru na cuta da kashi 83% a cikin yanayin da aka kwaikwayi
5.2 Abubuwan Kwanciyar Hankali
Bincikenmu na ƙwaƙwalwar aiki ya nuna cewa rarraba haɗari, ƙuntatawar motsin albarkatu (wanda aka tilasta ta hanyar fasahohin haƙa daban-daban), da haɓakar hanyar sadarwa duk suna ba da gudummawa ga kwanciyar hankali na yanayin blockchain mai sauyi na asali.
Hoto na 1 yana nuna alaƙar tsakanin girman hanyar sadarwa da yaɗuwar cuta, yana nuna raguwar halin cuta yayin da hanyoyin sadarwa suka ƙaru zuwa yanayin kasuwar Fisher.
6 Cikakkun Bayanai na Fasaha
An ƙirƙira tattalin arzikin ma'adinai a matsayin wasa mai dabarun tare da ma'adinai $N = \{1, 2, ..., n\}$, kowanne yana zaɓar rabon albarkatu $x_i \geq 0$ a cikin $m$ blockchains. Aikin amfani ga ma'adinai $i$ shine:
$u_i(x_i, x_{-i}) = \sum_{j=1}^m R_j \cdot \frac{x_{ij}}{\sum_{k=1}^n x_{kj}} - c_i(x_i)$
inda $R_j$ shine jimillar lada daga blockchain $j$, $x_{ij}$ rabon ma'adinai $i$ ne ga blockchain $j$, kuma $c_i(x_i)$ aikin farashi ne ga ma'adinai $i$.
An lissafta yuwuwar cuta $GP_i$ don karkacewa $\Delta x_i$ kamar haka:
$GP_i(\Delta x_i) = \frac{\sum_{j \neq i} [u_j(x_i, x_{-i}) - u_j(x_i + \Delta x_i, x_{-i})]}{u_i(x_i + \Delta x_i, x_{-i}) - u_i(x_i, x_{-i})}$
7 Aiwar Code
A ƙasa akwai sauƙaƙaƙen aiwar Python na ka'idar Amsa Daidai don rabon albarkatu na blockchain:
import numpy as np
def proportional_response_update(current_allocations, utilities, learning_rate=0.1):
"""
Yana aiwatar da ka'idar sabuntawa ta Amsa Daidai don rabon albarkatu na ma'adinai
Parameters:
current_allocations: numpy array of shape (n_miners, n_blockchains)
utilities: numpy array of shape (n_miners, n_blockchains) - marginal utilities
learning_rate: step size for updates
Returns:
updated_allocations: new resource allocations after PR update
"""
n_miners, n_blockchains = current_allocations.shape
# Lissafta amsoshi daidai
marginal_utility_ratios = utilities / (utilities.sum(axis=0) / n_miners)
# Sabunta rabo daidai da ma'auni na amfanin gefe
updated_allocations = current_allocations * (1 + learning_rate * (marginal_utility_ratios - 1))
# Tabbatar da rashin ƙima da daidaita idan ya cancanta
updated_allocations = np.maximum(updated_allocations, 0)
updated_allocations = updated_allocations / updated_allocations.sum(axis=1, keepdims=True)
return updated_allocations
# Misalin amfani
n_miners = 100
n_blockchains = 4
current_alloc = np.random.dirichlet(np.ones(n_blockchains), size=n_miners)
utilities = np.random.exponential(1.0, size=(n_miners, n_blockchains))
new_alloc = proportional_response_update(current_alloc, utilities)
print("Updated allocations shape:", new_alloc.shape)8 Aikace-aikace da Hanyoyin Gaba
Fahimtar daga wannan bincike yana da aikace-aikace masu mahimmanci da yawa:
- Ƙirar Ka'idoji: Sanar da ƙira na ƙarin kwanciyar hankali na tsarin lada na blockchain wanda ke hana halin cuta
- Tsare-tsaren Ka'idoji: Samar da tushen ka'ida don tsara tafkunan ma'adinai da hana ayyukan gasa
- Haɗin Kai Tsakanin Silsila: Ba da damar rabon albarkatu mai kwanciyar hankali a cikin blockchains da yawa masu haɗin kai
- Kuɗi maras Tushe: Inganta kwanciyar hankali na ka'idojin DeFi waɗanda suka dogara da tsaron blockchain
Hanyoyin bincike na gaba sun haɗa da:
- Ƙaddamar da samfurin don haɗa ƙarin ayyukan amfani na ma'adinai masu rikitarwa
- Nazarin cuta a cikin Proof-of-Stake da sauran hanyoyin yarjejeniya
- Haɓaka ka'idojin PR masu ƙarfi waɗanda suka dace da canje-canjen yanayin hanyar sadarwa
- Tabbacin ƙwaƙwalwar aiki akan manyan bayanai a cikin hanyoyin sadarwar blockchain da yawa
9 Nazarin Asali
Wannan bincike yana ba da gudummawa mai mahimmanci ga fahimtar halayen dabarun a cikin tattalin arzikin ma'adinan blockchain ta hanyar siffanta cuta a hukumance ta hanyar tabarau na ka'idar wasa. Haɗin kai tsakanin cuta da kwanciyar hankali na juyin halitta yana ba da sabon tsari don nazarin rabon albarkatu a cikin tsarin da ba su da tushe. Kamar yadda CycleGAN (Zhu et al., 2017) ya gabatar da fassarar hoto-zuwa-hoto mara kulawa ta hanyar amfani da asarar daidaiton zagayowar, wannan aikin yana daidaita ra'ayoyin ka'idar wasa na juyin halitta don nazarin kwanciyar hankali a cikin yanayin ma'adinai marasa haɗin kai.
Ka'idar Amsa Daidai tana wakiltar muhimmiyar gudummawar algorithm, kwatankwacin hanyoyin ingantawa masu rarraba a cikin tsarin wakilai da yawa. Siffofin haɗuwarsa a ƙarƙashin nau'ikan haɗarin daban-daban sun yi daidai da binciken daga littattafan ma'auni na kasuwar Fisher, musamman aikin Cole et al. (2017) akan haɗuwar motsi a cikin wasannin kasuwa. Tabbacin ƙwaƙwalwar aiki a cikin cryptocurrencies da yawa yana ƙarfafa dacewar waɗannan fahimomin ka'idoji.
Idan aka kwatanta da tsoffin nazarin ka'idar wasa na tsaron blockchain kamar waɗanda daga taron IEEE Security & Privacy, wannan aikin yana ba da ƙarin fahimtar abin da ke motsa ma'adinai fiye da sauƙaƙan haɓakar riba. Abubuwan cuta da aka gabatar suna ba da ma'auni masu ƙima don kimanta juriyar ka'idoji akan magudi na dabarun, kama da yadda ma'aunin juriya na Byzantine ke kimanta ƙarfin tsarin rarraba.
Ƙayyadaddun binciken sun haɗa da zato game da hankalin ma'adinai da cikakken bayani, waɗanda za a iya sassauta su a cikin aikin gaba. Bugu da ƙari, kamar yadda aka lura a cikin labaran ACM Computing Surveys akan iya aikin blockchain, canjin zuwa yanayin kasuwar Fisher ya dogara da ƙofofin girman hanyar sadarwa waɗanda zasu iya bambanta a cikin aiwatarwa. Duk da haka, wannan aikin ya kafa muhimman tushe don ƙira mafi kwanciyar hankali da ingantaccen tattalin arzikin blockchain masu jure wa hare-haren cuta da matsin lamba na tsakiya.
10 Nassoshi
- Cheung, Y. K., Leonardos, S., Piliouras, G., & Sridhar, S. (2021). From Griefing to Stability in Blockchain Mining Economies. arXiv:2106.12332.
- Zhu, J. Y., Park, T., Isola, P., & Efros, A. A. (2017). Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks. IEEE International Conference on Computer Vision.
- Cole, R., Devanur, N., Gkatzelis, V., Jain, K., Mai, T., Vazirani, V., & Yazdanbod, S. (2017). Convex Program Duality, Fisher Markets, and Nash Social Welfare. ACM Conference on Economics and Computation.
- Eyal, I., & Sirer, E. G. (2014). Majority is not Enough: Bitcoin Mining is Vulnerable. International Conference on Financial Cryptography.
- Nakamoto, S. (2008). Bitcoin: A Peer-to-Peer Electronic Cash System.
- Buterin, V. (2014). A Next-Generation Smart Contract and Decentralized Application Platform. Ethereum White Paper.
- IEEE Security & Privacy Symposium Proceedings on Blockchain Security (2018-2021)
- ACM Computing Surveys Special Issue on Blockchain Technology (2020)