Alexey Savvateev: Game-theoretic modhi yesocial cleavage (+ ongororo panginx)

Hei Habr!
Ini ndinonzi Asya. Ndakawana hurukuro inotonhorera, handigone kubatsira asi kuigovana.

Ini ndinounza kwauri pfupiso yehurukuro yevhidhiyo pamusoro pemakakatanwa emagariro mumutauro wenyanzvi dzemasvomhu. Iyo yakazara hurukuro inowanikwa pane iyi link: Modhi yesocial cleavage: mutambo weternary sarudzo pane yekudyidzana network (A.V. Leonidov, A.V. Savvateev, A.G. Semenov). 2016.

Alexey Vladimirovich Savvateev - Mumiriri weEconomic Sayenzi, Chiremba wePhysical uye Mathematical Sayenzi, Purofesa paMIPT, Anotungamira Muongorori paNES.

Muhurukuro iyi ndichataura pamusoro pekuti nyanzvi dzemasvomhu uye theorists vanotarisa sei chiitiko chinowanzoitika chevanhu, chinoratidzirwa nevhoti yeEngland kubva muEuropean Union (Shona Brexit), chiitiko chekuparadzana kwakadzika kwemagariro muRussia mushure Maidan, Sarudzo dzeUS nemhedzisiro inonakidza. 

Ungatevedzera sei mamiriro ezvinhu akadaro kuti ave nemaungira echokwadi? Kuti unzwisise chiitiko, zvakakosha kuti udzidze zvizere, asi hurukuro iyi ichapa muenzaniso.

Social schism zvinoreva

Izvo zviitiko zvitatu izvi zvakafanana ndezvekuti munhu anowira mumusasa mumwe chete kana kuramba kutora chikamu uye kukurukura sarudzo dzavo. Avo. Sarudzo yemunhu wega wega ndeye ternary - kubva kune matatu maitiro: 

• 0-ramba kubatanidzwa mukukonana;
• 1 - kutora chikamu mukukonana kune rumwe rutivi; 
• -1 - kutora chikamu mukukonana kune rimwe divi.

Pane mhedzisiro yakananga inoenderana nemafungiro ako kune kukonana muchokwadi. Pane fungidziro yekuti munhu wese ane imwe mhando yepfungwa yekutanga yekuti ndiani ari pano. Uye ichi ndicho chinoshanduka chaicho. 

Semuenzaniso, kana munhu asinganyatso nzwisisa kuti ndiani ari right, poindi yacho iri pamutsetse wenhamba pane imwe nzvimbo yakatenderedza zero, semuenzaniso pa0,1. Kana munhu aine chokwadi che100% kuti mumwe munhu akarurama, ipapo parameter yake yemukati inenge yatova -3 kana +15, zvichienderana nesimba rezvaanotenda. Ndiko kuti, pane imwe parameter yezvinhu iyo munhu ane mumusoro make, uye inoratidza mafungiro ake pamusoro pemakakatanwa.

Izvo zvakakosha kuti kana ukasarudza 0, saka izvi hazvibatanidze chero mhedzisiro kwauri, hapana kuhwina mumutambo, wasiya kupokana.

Kana ukasarudza chimwe chinhu chisingaenderani nechinzvimbo chako, ipapo minus ichaonekwa pamberi vi, semuenzaniso vi = - 3. Kana nzvimbo yako yemukati ichienderana nedivi rekupokana kwaunotaura, uye chinzvimbo chako chiri σi = -1, zvino vi = +3. 

Ipapo mubvunzo unomuka, ndezvipi zvikonzero iwe dzimwe nguva unofanirwa kusarudza rutivi rwakashata rwezviri mumweya wako? Izvi zvinogona kuitika pasi pekumanikidzwa kubva munharaunda yako yemagariro. Uye ichi ndicho chirevo.

Iyo postulate ndeyokuti iwe unofurirwa nemhedzisiro yausingakwanisi kudzora. Izwi rekuti aji parameter chaiyo yedhigirii uye chiratidzo chesimba pauri kubva j. Iwe uri nhamba i, uye munhu anokufurira munhu nhamba j. Zvadaro pachava nematrix yose yeji yakadaro. 

Munhu j uyu anogona kutokufurira zvisina kunaka. Semuenzaniso, iyi ndiyo nzira yaungatsanangura nayo kutaura kwemunhu wezvematongerwo enyika wausingade kune rimwe divi rekukonana. Paunotarisa mutambo wofunga: "Iyi idiot, uye tarisa zvaanotaura, ndakuudza kuti idiot." 

Nekudaro, kana isu tikafunga pesvedzero yemunhu ari padyo kana anoremekedzwa newe, zvino zvinoita kunge mutambi mumwe j pane vese vatambi i. Uye pesvedzero iyi inowedzerwa nekusangana kana kusawirirana kwezvinzvimbo zvakagamuchirwa. 

Avo. kana σi, σj iri yechiratidzo chakanaka, uye panguva imwe cheteyo aji iri yechiratidzo chakanaka, saka uku ndiko kuwedzera kune yako yekukunda basa. Kana iwe kana munhu akakosha kwauri akatora zero chinzvimbo, saka izwi iri harisipo.  

Nokudaro, takaedza kufunga nezvese zvinokonzerwa nemagariro evanhu.

Inotevera ndiyo pfungwa inotevera. Kune akawanda mamodheru akadaro ekudyidzana kwevanhu, anotsanangurwa kubva kumativi akasiyana (chikumbaridzo-yekuita sarudzo mhando, akawanda ekunze mamodheru). Vanotarisa pachiyero chepfungwa mumutambo wemutambo unonzi Nash equilibrium. Pane kusagutsikana kwakadzama nepfungwa iyi yemitambo ine nhamba huru yevatori vechikamu, senge UK uye US mienzaniso yakataurwa pamusoro apa, i.e. mamirioni mazhinji avanhu.   

Mumamiriro ezvinhu aya, mhinduro chaiyo yedambudziko inopfuura kuburikidza nekufungidzira uchishandisa inoenderera. Nhamba yevatambi ndeimwe rudzi rwekuenderera mberi, "gore" rinotamba, rine imwe nzvimbo yezvipimo zvakakosha. Pane dzidziso yemitambo inoenderera, Lloyd Shapley

"Zvinorehwa nemitambo isiri yeatomu". Iyi inzira yekubatana kwemutambo dzidziso. 

Iko hakuna dzidziso isiri yemubatanidzwa yemitambo ine nhamba inoenderera yevatori vechikamu sedzidziso zvakadaro. Kune makirasi akaparadzana ari kudzidzwa, asi ruzivo urwu haruna kuumbwa kuita dzidziso huru. Uye chimwe chezvikonzero chikuru chekusavapo kwayo ndechekuti mune iyi kesi iyo Nash equilibrium haina kururama. Chaizvoizvo pfungwa isiriyo. 

Chii zvino chiri pfungwa yakarurama? Mumakore mashoma apfuura kwave nekumwe kubvumirana kuti pfungwa yakagadziridzwa mumabasa Palfrey naMcKelvey zvinonzwika se"Quantal response equilibrium", kana"Discrete Response Equilibrium", sekududzira kwandakaita naZakharov. Shanduro yacho ndeyedu, uye sezvo pasina akanga aishandurira muchiRussia pamberi pedu, takaisa iyi shanduro kunyika inotaura chiRussia.

Zvataitaura nezita iri ndezvekuti munhu wega wega haatambe zano rakasanganiswa, anotamba rakachena. Asi munharaunda iyi ye "gore" inomuka umo imwe kana imwe yakachena inosarudzwa, uye mukupindura, ndinoona kuti munhu anotamba sei, asi ini handizivi kuti ari kupi mugore iri, i.e. kune ruzivo rwakavanzika ipapo, ini ona munhu ari mu "gore" semukana waachazoenda neimwe nzira. Iyi ipfungwa yenhamba. Iyo inopfumisa symbiosis yefizikisi uye vatambi vedzidziso, zvinoita kwandiri, ichatsanangura dzidziso yemutambo yezana ramakore rechi21. 

Isu tinogadzirisa chiitiko chiripo mukuenzanisira mamiriro ezvinhu akadaro neasinganamate zvachose data rekutanga uye tinonyora hurongwa hwemaequation hunoenderana nekuenzana kwemhinduro yakasarudzika. Ndizvo zvese; kuenderera mberi, kugadzirisa equations, zvinodikanwa kuita fungidziro inonzwisisika yemamiriro ezvinhu. Asi zvese izvi zvichiri kumberi; iyi igwara rakakura musainzi.

Discrete response equilibrium ndiyo yakaenzana yatinotamba nayo hameno kuti ndiani. Muchiitiko ichi, ε inowedzerwa kune mubhadharo kubva kune yakachena zano. Kune matatu akahwina, dzimwe nhamba nhatu zvinoreva "kunyura" kune rimwe divi, "kunyura" kune rimwe divi uye kurega, uye kune ε, iyo inowedzerwa kune vatatu ava. Uyezve, musanganiswa weizvi ε hauzivikanwe. Iko kusanganiswa kunogona kungofungidzirwa a priori, uchiziva mukana wekugovera we ε. Muchiitiko ichi, mikana yekubatanidzwa ε inofanira kutaurirwa nesarudzo dzemunhu pachake, kureva, kuongorora kwake kwevamwe vanhu uye kufungidzira kwezvingaitika zvavo. Kuwirirana uku ndiko kuenzana kwemhinduro yakasarudzika. Tichadzokera kuchinhu ichi.

Kugadzira kuburikidza ne discrete mhinduro yakaenzana

Hezvino izvo winnings dzinotaridzika sei mune iyi modhi:

Inounganidza mumabhuraketi pesvedzero yese inoonekwa pauri kana wakasarudza chero divi, kana kuti ichawedzerwa ne zero kana usina kusarudza chero divi. Uyezve zvichave ne “+” chiratidzo kana σ1 = 1, uye ne “-” chiratidzo kana σ1 = -1. Uye ε inowedzerwa kune izvi. Kureva kuti, σ inowedzerwa nemamiriro ako emukati, uye nevanhu vese vanokufurira. 

Panguva imwecheteyo, munhu chaiye anogona kupesvedzera mamirioni avanhu, seizvo vanhu vezvenhau, vatambi, kana kunyange mutungamiri wenyika achifurira mamirioni avanhu. Zvinoitika kuti pesvedzero matrix inotyisa asymmetrical; yakatwasuka inogona kuve nenhamba huru yeasiri zero ekupinda, uye yakatwasuka, kubva pamamiriyoni mazana maviri evanhu munyika, semuenzaniso, zana asiri-zero nhamba. Kumunhu wese, kuwana uku ndiko kuwanda kwenhamba diki yematemu, asi aij (pesvedzero yemunhu pane mumwe munhu) inogona kunge isiri zero yenhamba huru j, uye pesvedzero yeji (pesvedzero yemumwe munhu pamunhu) haina kudaro. huru, kazhinji inogumira kuzana. Apa ndipo panomuka asymmetry yakakura kwazvo. 

Mienzaniso yevatori vechikamu network

Takaedza kududzira data yekutanga yemuenzaniso mumagariro evanhu. Semuenzaniso, ndiani "conformist careerist"? Uyu ndiye munhu asingabatanidzi mukati mukukonana, asi kune vanhu vanomukurudzira zvikuru, semuenzaniso, mukuru.

Zvinokwanisika kufanotaura kuti sarudzo yake yakabatana sei nesarudzo yemukuru mune chero kuenzana.

Uyezve, “mudikani” munhu ane kupwiswa kwakasimba kwomukati kudivi rerwisano. 

Aij yake (pesvedzero pamunhu) yakakura, kusiyana neshanduro yapfuura, apo aji (pesvedzero yemumwe munhu pamunhu) yakakura.

Uyezve, "autist" munhu asingatori mumitambo. Zvaanotenda zvava pedyo ne zero, uye hapana anomufurira.

Uye pakupedzisira, "anopenga" munhu anozviita hapana zvachose haina kukanganisa. 

Izwi razvino rinogona kunge risiri iro kubva pamaonero emitauro, asi pachine basa rinofanira kuitwa munzira iyi.

Izvi zvinoratidza kuti, kufanana ne "chido," vi yake yakakura zvikuru kupfuura zero, asi aji = 0. Ndapota cherechedza kuti "munhu ane chido" anogona kuva "anonyanyisa" panguva imwe chete. 

Isu tinofungidzira kuti mukati menode dzakadaro zvichave zvakakosha kuti sarudzo ipi iyo "inoshuva / inopenga" inoita, sezvo sarudzo iyi ichapararira segore. Asi iyi haisi ruzivo, asi kungofungidzira. Parizvino hatigone kugadzirisa dambudziko iri mune chero fungidziro.

Uye kune zvakare TV. Chii chinonzi TV? Uku ndiko kushanduka kwemukati mako, rudzi rwe "magnetic field".

Uyezve, pesvedzero yeTV, mukusiyana neiyo yemuviri "magnetic field" pane ese "social molecules," inogona kunge yakasiyana zvese muhukuru uye chiratidzo. 

Ndingatsiva TV neInternet here?

Asi, Indaneti ndiyo muenzaniso chaiwo wekudyidzana unoda kukurukurwa. Ngatitii iyo yekunze sosi, kana isiri yeruzivo, ipapo yerumwe rudzi rweruzha. 

Ngatitsanangure nzira nhatu dzinobvira dze σi=0, σi=1, σi=-1:

Kudyidzana kunoitika sei? Pakutanga, vatori vechikamu vese "makore", uye munhu wese anongoziva nezvemumwe munhu wese kuti iyi i "gore", uye anotora kugovera kwekutanga mukana we "makore" aya. Pakarepo apo munhu chaiwo anotanga kutaurirana, anodzidza pamusoro pake katatu ε, i.e. pfungwa chaiyo, uye panguva iyo munhu anoita sarudzo inomupa nhamba yakakura (yeiyo iyo ε inowedzerwa kune yakahwina, anosarudza iyo yakakura kupfuura mamwe maviri), vamwe vese havazivi kuti ipfungwa ipi. iye aripo, saka havagone kufanotaura . 

Tevere, munhu anosarudza (σi=0/ σi=1/ σi=-1), uye kuti asarudze, anofanira kuziva σj kune wese wese. Ngatiteererei kubhuraketi; mubhuraketi mune chirevo [∑ j ≠ i aji σj], i.e. chinhu chisingazivikanwi nemunhu. Anofanira kufanotaura izvi mukuenzanisa, asi mukuenzana haaone σj senhamba, anozviona sezvingangoitika. 

Ichi ndicho musimboti wemusiyano uripo pakati peiyo discrete response equilibrium neNash equilibrium. Munhu anofanirwa kufanotaura zvingangoitika, saka hurongwa hwekugona kuenzana hunomuka. Ngatimbofungidzirai hurongwa hwemaequation evanhu 100 miriyoni, wedzera neimwe 2. sezvo paine mukana wekusarudza “+”, mukana wekusarudza “-” (mukana wekusiiwa hauna kuverengerwa, sezvo ichi chiri parameter inotsamira). Nekuda kweizvozvo, kune 200 mamirioni akasiyana. Uye 200 mamiriyoni equations. Hazvina musoro kugadzirisa izvi. Uye zvakare hazvibviri kuunganidza ruzivo rwakadaro chaizvo. 

Asi nyanzvi dzezvemagariro evanhu dzinotiudza kuti: “Mira, shamwari, tichakuudza kuti ungataipa sei nzanga.” Vanobvunza kuti marudzi mangani ematambudziko atinogona kugadzirisa. Ini ndinoti, isu ticharamba tichigadzirisa makumi mashanu equation, komputa inogona kugadzirisa hurongwa uko kune makumi mashanu equation, kunyangwe zana hapana. Vanoti hazvina dambudziko. Zvino vakabva vanyangarika, varasha. 

Isu takanga tine musangano wakarongwa nevanodzidza nezvepfungwa uye vezvemagariro evanhu kubva kuHSE, vakati tinogona kunyora purojekiti yekuchinja, muenzaniso wedu, data yavo. Uye havana kuuya. 

Kana iwe uchida kundibvunza kuti sei zvinhu zvose zviri kuitika zvakashata, ini ndichakuudza, nokuti nyanzvi dzepfungwa nemagariro evanhu havauye kumisangano yedu. Kudai taiungana, taifambisa makomo.

Nekuda kweizvozvo, munhu anofanira kusarudza kubva pamatatu angaite mazano, asi haagone, nekuti haazive σj. Zvadaro tinoshandura σj kune zvingangoitika.

Kuwana mune discrete mhinduro yakaenzana

Pamwe chete neisingazivikanwe σj isu tinotsiva mutsauko mumikana yekuti munhu anotora rimwe kana rimwe divi mukukonana. Kana tichiziva kuti nderipi vhekita ε tinosvika papi munzvimbo ine mativi matatu. Panguva idzi (winnings) "makore" anooneka, uye tinogona kuabatanidza uye kuwana uremu hweumwe neumwe we "makore" matatu.

Somugumisiro, tinowana mikana kubva kune mucherechedzi wekunze kuti mumwe munhu achasarudza izvi kana izvo asati aziva nzvimbo yake yechokwadi. Kureva, iyi ichave fomula ichapa yayo p mukupindura ruzivo rwemamwe ese p. Uye fomula yakadaro inogona kunyorwa kune yega yega i uye kusiya kubva mairi hurongwa hweequation huchave hunozivikanwa kune avo vakashanda paIsing uye Potz modhi. Statistical physics inotaura zvakasimba kuti aij = aji, kupindirana hakugoni kuva asymmetrical.

Asi pane mamwe "mashura" pano. Masvomhu "zvishamiso" ndezvekuti mafomula anenge achienderana nemafomu kubva kumhando dzinoenderana dzenhamba, kunyangwe hazvo pasina kupindirana kwemutambo, asi kune mashandiro anogadziridzwa pamhando dzakasiyana siyana.

Nekupokana kwekutanga data, modhi inoita sekunge mumwe munhu ari kugadzirisa chimwe chinhu mairi. Mienzaniso yakadaro inonzi "inogona mitambo" kana tichitaura nezveNash equilibrium. Kana mutambo wakagadzirwa nenzira yekuti Nash equilibria inotemerwa nekugadzirisa zvimwe zvinoshanda panzvimbo yesarudzo dzese. Chii chinogona kuitika mukuenzanisa kwemhinduro yakasarudzika haisati yagadzirwa. (Kunyangwe Fyodor Sandomirsky angakwanisa kupindura mubvunzo uyu. Izvi zvingava budiriro). 

Izvi ndizvo zvinoita iyo yakazara system ye equations inotaridzika se:

Mikana yaunosarudza nayo iyi kana iyo inopindirana nekufanotaura kwako. Pfungwa iyi yakafanana neyemuNash equilibrium, asi inoshandiswa kuburikidza nezvinobvira. 

Kugovera kwakakosha ε, kureva kugovera kweGumbel, inova nzvimbo yakatarwa yekutora huwandu hwehuwandu hwehuwandu hwakazvimiririra hwakasiyana. 

Kugovera kwakajairika kunowanikwa neavhareji yenhamba huru yezvakazvimiririra zvisina tsarukano zvinosiyana zvine musiyano mukati mehukoshi hunogamuchirwa. Uye kana tikatora huwandu kubva kunhamba huru yezvakazvimiririra zvimiro zvakasiyana, tinowana kugovera kwakakosha kwakadaro. 
Nenzira, iyo equation yakasiya parameter yemhirizhonga muzvisarudzo zvakaitwa, λ, ndakakanganwa kuinyora.

Kunzwisisa nzira yekugadzirisa iyi equation kunobatsira iwe kunzwisisa maitiro ekuunganidza nzanga. Muchikamu chedzidziso, kugona kwemitambo kubva pamaonero eiyo discrete mhinduro equation. 

Iwe unofanirwa kuyedza iyo chaiyo social graph, iyo ine akasiyana seti yezvivakwa: 

• diki dhayamita;
• mutemo wesimba wekugovera madhigirii e vertices;
• high clustering. 

Ndokunge, iwe unogona kuedza kunyora zvakare zvivakwa zveiyo chaiyo social network mukati meiyi modhi. Hapana akambozviedza, pamwe chimwe chinhu chichabuda ipapo.

Zvino ndinogona kuedza kupindura mibvunzo yenyu. Pamwe ndinogona kunyatsovateerera.

Izvi zvinotsanangura sei maitiro eBrexit uye sarudzo dzeUS?

Saka ndizvozvo. Izvi hazvitsananguri chinhu. Asi zvinopa zano rekuti sei vavhoti vachigara vachiita kuti zvavanofungidzira zvisizvo. Nekuti vanhu vanopindura pachena izvo nharaunda yavo yemagariro inoda kuti vapindure, asi vari vega vanovhotera kutendiswa kwavo kwemukati. Uye kana tikakwanisa kugadzirisa iyi equation, chii chichava mumhinduro ndicho chatakapihwa neongororo yezvemagariro evanhu, uye vi ndizvo zvichange zviri muvhoti.

Uye mune iyi modhi, zvinokwanisika kufunga kwete munhu, asi hukama hwemagariro sechinhu chakasiyana?

Izvi ndizvo chaizvo zvandinoda kuita. Asi isu hatizivi chimiro chesocial strata. Ichi ndicho chikonzero tiri kuedza kufambirana nenyanzvi dzezvemagariro evanhu uye vepfungwa.

Ko modhi yako ingashandiswe neimwe nzira kutsanangura maitiro emhando dzakasiyana dzematambudziko emagariro anoonekwa muRussia? Ngatibvumirei mutsauko pakati pemigumisiro yemasangano epamutemo?

Kwete, handizvo zvazvinoreva. Izvi ndizvo chaizvo zvekukonana kuri pakati pevanhu. Handifungi kuti dambudziko remasangano pano rinogona kutsanangurwa nenzira ipi zvayo. Pamusoro pechinyorwa ichi, ndine yangu pfungwa yekuti masangano akagadzirwa nevanhu akaomesesa, haakwanise kuchengetedza dhigirii rakadaro rekuomarara uye achamanikidzwa kudzikisira. Uku ndiko kunzwisisa kwangu kwechokwadi.

Zvinoita here kuti neimwe nzira kudzidza chiitiko chepolarization yenzanga? Iwe watove nev yakavakwa mune izvi, zvakanaka sei kune chero munhu ...

Kwete chaizvo, tine TV ipapo, v + h. Uku ndiko kuenzanisa statics.

Hongu, asi polarization inoitika zvishoma nezvishoma. Zvandinoreva ndezvokuti kubatanidzwa kwevanhu vane chimiro chakasimba ndeye 10% v-positive, 6% v-negative, uye gaka riri kuwedzera kuwedzera pakati pezvikoshi izvi.

Handizivi kuti chii chichaitika mumasimba zvachose. Mumasimba chaiwo, sezviri pachena, v ichatora kukosha kweiyo yapfuura σ. Asi ini handizive kana mhedzisiro iyi ichashanda. Iko hakuna panacea, hapana muenzaniso wepasirese wenzanga. Iyi modhi ndeimwe maonero anogona kubatsira. Ndinotenda kuti kana tikagadzirisa dambudziko iri, tichaona kuti sarudzo dzepfungwa dzinoramba dzichisiyana sei kubva kune chokwadi chekuvhota. Pane mhirizhonga huru munzanga. Kunyangwe kuyera imwe parameter inopa mhinduro dzakasiyana. 

Izvi zvine chekuita ne classical matrix game theory?

Iyi mitambo yematrix. Kungoti matrices pano ane 200 miriyoni ne 200 miriyoni muhukuru. Uyu mutambo wemunhu wese nemunhu wese, iyo matrix yakanyorwa sebasa. Izvi zvakabatana nemitambo yematrix seizvi: mitambo yematrix mitambo yevanhu vaviri, asi pano vari kutamba mamiriyoni 200. Nokudaro, iyi tensor ine chiyero chemamiriyoni 200. Haisi kunyange matrix, asi cube ine dimension. emamiriyoni 200. Asi vanorangarira pfungwa isina kujairika yemhinduro.

Pane pfungwa yemutengo wemutambo here?

Mutengo wemutambo unongogoneka mumutambo unopikisa wevatambi vaviri, i.e. ne zero sum. Izvi kweteAntagonistic game yevatambi vakawanda. Panzvimbo pemutengo wemutambo, kune mibairo yakaenzana, kwete mukuenzanisa kweNash, asi mune discrete mhinduro yakaenzana.

Zvakadini nepfungwa ye "strategy"?

Mazano acho ndeaya, 0, -1, 1. Izvi zvinobva muchirevo chekare cheNash-Bayes equilibrium, equilibrium. mitambo ine ruzivo rusina kukwana. Uye mune iyi kesi, iyo Bayes-Nash equilibrium yakavakirwa pane data kubva kumutambo wenguva dzose. Izvi zvinoguma nemusanganiswa unonzi discrete response equilibrium. Uye izvi zviri kure kwazvo nemitambo yematrix yepakati pezana remakore rechiXNUMX.

Hazvina chokwadi kuti iwe unogona kuita chero chinhu nevatambi vane miriyoni ...

Uyu ndiwo mubvunzo wekuti ungabatanidza sei nzanga; hazvibviri kugadzirisa mutambo nevatambi vakawanda, wakarurama.

Zvinyorwa pane zvine hukama nzvimbo mune statistical fizikisi uye sociology

1. Dorogovtsev SN, Goltsev AV, uye Mendes JFF Zvinetso zvakakosha mumatanho akaomarara // Ongororo yeMazuvano Fizikisi. 2008. Vol. 80. pp. 1275-1335.
2. Lawrence E. Blume, Steven Durlauf Equilibrium Concepts for Social Interaction Models // International Game Theory Ongororo. 2003. Vol. 5, (3). pp. 193-209.
3. Gordon MB et. al., Sarudzo Dzakasarudzika pasi peKufurira Kwemagariro: Maonero akajairwa // Mathematical Models uye nzira muApplied Sayenzi. 2009. Vol. 19. pp. 1441-1381.
4. Bouchud J.-P. Matambudziko uye Kubatanidzwa Kwemagariro-Economic Phenomena: Mienzaniso Yakareruka uye Zvinetso // Chinyorwa cheStatic Physics. 2013. Vol. 51(3). pp. 567-606.
5. Sornette D. Fizikisi uye hupfumi hwemari (1776-2014): mapuzzle, lsing, uye agent-based modhi // Mishumo yeKufambira mberi muFizikisi. 2014. Vol. 77, 6). pp. 1-287

 

Vashandisi vakanyoresa chete ndivo vanogona kutora chikamu muongororo. Nyorera mu, Munogamuchirwa.

(chaizvo semuenzaniso) Chinzvimbo chako maererano naIgor Sysoev:

• 62,1%+1 (tora chikamu mukukonana kudivi raIgor Sysoev)175

• 1,4%-1 (tora chikamu mukukonana kune rimwe divi)4

• 28,7%0 (ramba kupindira mukukonana)81

• 7,8%edza kushandisa kukonana kuti uzvibatsire22

282 vashandisi vakavhota. 63 vashandisi vakaramba.

Source: www.habr.com