khel siddhaant

khel siddhaant ya game theory (game theory) vyavahaarik ganit ki ek shaakha hai jiska prayog samaaj vigyaan, arthashaastr, jeev vigyaan, engineering, raajaneeti vigyaan, antarraashtreeya sambandh, computer science aur darshan mein kiya jaata hai. khel siddhaant kootaneetik paristhitiyon mein (jismein kisi ke dvaara vikalp chunane ki safalta doosaron ke chayan par nirbhar karti hai) vyavahaar ko boojhane ka prayaas karta hai. yooain to shuroo mein ise un pratiyogitaaon ko samajhne ke liye viksit kiya gaya tha jinmein ek vyakti ka doosare ki galatiyon se faayda hota hai (zero sam gems), lekin iska vistaar aisi kai paristhitiyon ke liye kara gaya hai jahaaain alag-alag kriyaaon ka ek-doosare par asar padta ho. aaj, "game theory" samaaj vigyaan ke taarkik paksh ke liye ek chhatari ya 'yooneefaaid field' theory ki tarah hai jismein 'saamaajik' ki vyaakhya maanav ke saath-saath doosare khilaadiyon (kampyutar, jaanavar, paudhe) ko sammilit kar ki jaati hai.(Aumann 1987)

game theory ke paaramparik anuprayogon mein in gemon mein saamyaavasthaaen khojane ka prayaas kiya jaata hai. saamyaavastha mein game ka pratyek khilaadi ek neeti apanaata hai jo vah sanbhavat: naheen badalta hai. is vichaar ko samajhne ke liye saamyaavastha ki kai saari avadhaaranaaen viksit ki gayi hain (sabse prasiddh naish ikvilibriym). saamyaavastha ke in avadhaaranaaon ki abhiprerana alag-alag hoti hai aur is baat par nirbhar karti hai ki ve kis kshetr mein prayog ki ja raheen hain, haalaaainki unke maayane kuchh had tak ek doosare mein mile-jule hote hain aur mel khaate hain. yeh paddhati aalochna rahit naheen hai aur saamyaavastha ki vishesh avadhaaranaaon ki upayuktata par, saamyavaasthaaon ki upayuktata par aur aamtaur par ganiteeya modelon ki upayogita par vaad-vivaad jaari rahate hain.

haalaaainki iske pehle hi is kshetr mein kuchh vikaas chuke the, game theory ka kshetr John vaun nyumann aur oscar maurganastarn ki 1944 ki pustak theory of gems aind ikonomik biheviar ke saath aastitv mein aaya. is siddhaant ka vikaas bade paimaane par 1950 ke dashak mein kai vidvaanon dvaara kiya gaya. baad mein game theory spashtataya 1970 ke dashak mein jeev vigyaan mein prayukt kiya gaya, haalaaainki aisa 1930 ke dashak mein hi shuroo ho chuka tha. game theory ki pehchaan vyaapak roop se kai kshetron mein ek mahatvapoorn upakaran ke roop mein ki gayi hai. aath game thyorists arthashaastr mein Nobel puraskaar jeet chuke hain aur John menaard smith ko game theory ke jeev vigyaan mein prayog ke liye krafoord puraskaar se sammaanit kiya gaya.

anukram

gemon ka niroopan

inhein bhi dekhein: List of games in game theory

game theory mein avalokit game spashtataya paribhaashit ganiteeya 'objekts'hote hain. ek game khilaadiyon ke ek set, khilaadiyon ke paas upalabdh chaalon (neetiyon) ke ek set aur neetiyon ke pratyek sanyojan ke laabh ke nirdhaaran se bana hota hai. adhikaansh 'kooparetiv game'(paraspar sahayog vaale game) vishesh fankshan form mein niroopit kiye jaate hain, jabki eksateinsiv aur naurmal form ka prayog naunakooparetiv gemon (game jinmein paraspar sahayog naheen hota) ko paribhaashit karne mein hota hai.

eksateinsiv form

vyaapak roop ka ek khel

eksateinsiv form ka prayog kuchh mahatvapoorn anukram vaale gemon ko 'faurmalaaij' karne mein kiya ja sakta hai. ismein game aksar 'treej' ke roop mein niroopit kiye jaate hain (jaisa ki baayeen taraf ki tasveer mein dikhaaya gaya hai) yahaan pratyek varteks (shikhar) (ya nod) ek khilaadi ke liye vikalp ki ek bindu darshaata hai. khilaadi 'varteks' dvaara soocheebaddh ek sankhya dvaara nirdisht kiya jaata hai. varteks se baahar nikli rekhaaen us khilaadi ke ek sanbhaavya kriya ko darshaati hain. laabh (parinaam) tri ke nichle hisse mein nirdisht kiye jaate hain.

yahaan chitrit game mein do khilaadi dikhaae gaye hain. khilaadi 1 pehle chaal chalta hai aur ya to F ya U chunata hai. khilaadi 2 khilaadi 1ki chaal ko dekhta hai aur fir ya (or) to A ya R chunata hai . maanein ki khilaadi 1 U chunata hai aur fir khilaadi 2 A chunata hai, tab khilaadi 1, 8 paata hai aur khilaadi 2, 2 paata hai .

eksateinsiv form, vaise game jinmein donon chaalein ek saath naheen chali jaateen aur aise game jinme jaankaari pakki naheen hoti, in do prakaar ke gemon ki bhi vyaakhya kar sakta hai. ise niroopit karne ke liye vibhinn vartekson ko- unhein ek hi soochana set ka hissa dikhaane ke liye (yaani khilaadi yeh naheen jaante ki vo kis bindu par hain)- ya to ek bindeedaar (dauted) rekha se joda jaata hai, ya unke daramyaan ek band (klojd) rekha kheenchi jaati hai.

naurmal form

Player 2
chooses Left
Player 2
chooses Right
Player 1
chooses Up
4, 3 –1, –1
Player 1
chooses Down
0, 0 3, 4
Normal form or payoff matrix of a 2-player, 2-strategy game

naurmal (ya streteejik form) aamtaur par ek metriks ke dvaara niroopit kiya jaata hai jismein khilaadi, chaalein aur laabh ankit rahate hain (daayeen aur sthit udaaharan ko dekhein). aam taur par yeh kisi aise fankshan ke dvaara niroopit kiya ja sakta hai jo pratyek khilaadi ke chaalon ke sabhi sanyojanon ke laabh se sambaddh rahata hai. saath mein diye gaye udaaharan mein do khilaadi hain; ek ro ka chayan karta hai aur doosra column ka. pratyek khilaadi ke paas do rananeetiyaan hain jo ro aur kaulamon ki sankhya ke dvaara nirdisht ki gain hain. laabh andar mein diye gaye hain. pehli sankhya ro vaale khilaadi (hamaare udaaharan mein khilaadi 1) ko praapt laabh hai; doosari sankhya column vaale khilaadi (hamaare udaaharan mein khilaadi 2) ko praapt laabh hai. maanein ki agar khilaadi 1 oopar chalta hai khilaadi 2 baaen chalta hai. tab khilaadi 1 ko 4 laabh praapt hota hai aur khilaadi 2 ko 3 praapt hota hai.

jab ek khel naarmal form mein prastut kiya jaata hai, yeh maana jaata hai ki pratyek khilaadi ek saath chaal chalte hain ya kam se kam doosare ke chaalon se anbhigya hote hain. yadi khilaadiyon ko ek doosare ke vikalpon ki koi jaankaari hoti hai to game ko aam taur par eksateinsiv form mein prastut kiya jaata hai.

kairektaristik fankshan form

hastaantaraneeya upayogita vaale 'kooparetiv' gemon mein koi bhi svatantr alag laabh naheen diye rahate hain. iske bajaay, kairektaristik fankshan pratyek gathabandhan ke liye laabh nirdhaarit karta hai. maanak dhaarana yeh hai ki khaali gathabandhan ko 0 laabh praapt hota hai.

is form ka praarambhik srot vaun nyumann aur maurganastarn ki aadhaarbhoot pustak se praapt hota hai. unhonne koalishnal (gathabandhaneeya) naurmal form gemon ka adhyayan karte samay yeh maana (kalpana kiya) ki jab ek gathabandhan C banta hai, yeh sanpoorak gathabandhan (N\setminus C) ke virooddh khelta hai jaise ki vo 2 khilaadiyon wala game khel rahe hon. C ka saamyaavastha laabh kairektaristik hota hai. ab naurmal form gemon se koalishnal (gathabandhaneeya) maan nikaalne ke liye vibhinn model hain, par kairektaristik form ke saare game naurmal form gemon se vyuttpann naheen kiye ja sakte.

niymaanusaar, ek kairektaristik fankshan form game (TU-game naam se bhi gyaat) ek peyar ke roop mein niroopit kiya jaata hai jahaaain khilaadiyon ke ek set ko vyakt karta hai aur ek kairektaristik fankshan hota hai.

kairektaristik fankshan form bina hastaantaraneeya upayogita ke anumaargan vaale gemon mein saamaanyeekrut kiya gaya hai.

paarteeshan fankshan form

kairektaristik fankshan form 'koalishn' (gathabandhan) ke gathan ke sanbhaavya 'eksatarnaleeteej' ko najrandaaj kar deta hai. paarteeshan fankshan form mein 'koalishn' (gathabandhan) ka laabh sirf iske sadasyon par hi nirbhar naheen karta balki is par bhi nirbhar karta hai ki baaki khilaadi kis roop mein vibhaajit hain(Thrall & Lucas 1963).

anuprayog aur chunautiyaan

game theory ka prayog maanav aur pashu ke vividh vyavahaaron ke vistrut adhyayan mein kiya gaya hai. shuroo mein yeh arthashaastr mein aarthik vyavahaar ke ek bade sangrah ko samajhne ke liye viksit kiya gaya tha, jinmein companiyon, baajaaron aur upabhogem theory ke vyavahaar shaamil hain. saamaajik vigyaan mein game theory ka upayog aur vistrut hua hai aur game theory raajaneetik, saamaajik aur manovaigyaanik vyavahaaron ke adhyayan mein bhi prayukt hua hai.

game theory aadhaarit vishleshan ka upayog shuroo mein 1930 ke dashak mein ronaald fishr ne pashuon ke vyavahaar ka adhyayan karne ke liye kiya tha (yadyapi Charles daarvin tak ne bhi kuchh anaupachaarik game theory aadhaarit vaktavya diye hain). yeh kaam "game theory" ke naam ke aastitv mein aane se pehle ka hai, lekin iski aur game theory ki kai visheshataaen samaan hain. arthashaastr mein hue iske vikaas ka baad mein jeev vigyaan mein prayogJohn menard smith ne apni pustak ivolyooshan aind the theory of gems mein kiya.

vyavahaar ke anumaan aur vyaakhya ke alaava game theory ka prayog naitik ya maanak vyavahaar ke siddhaanton ko viksit karne ke prayaas mein bhi kiya gaya hai. arthashaastr aur darshanashaastr mein, vidvaanon ne game theory ko achhe ya uchit vyavahaar ko samajhne mein bhi prayukt kiya hai. agar ham peechhe jaaen to dekh sakte hai ki game theory aadhaarit is prakaar ke bhaavaarth ko pleto ne bhi prastut kiya tha.[1]

raajaneeti vigyaan

raajaneeti vigyaan mein game theory ka prayog nishpaksh vibhaajan, [[raajaneetik arthavyavastha, saarvajanik chayan/vikalp, yuddh saudebaaji, sakaaraatmak raajaneetik siddhaant aur saamaajik pasand siddhaant|raajaneetik arthavyavastha[[, saarvajanik chayan/vikalp, yuddh saudebaaji, sakaaraatmak raajaneetik siddhaant aur saamaajik pasand siddhaant]]]] ke ativyaapi kshetron par kendrit hai. in kshetron mein se pratyek mein, shodhakartaaon ne game theory aadhaarit modelon ko viksit kiya hai jinmein khilaadi aksar matadaata, raajya, special intarest group aur raajaneetijnya hote hain.

raajaneeti vigyaan mein prayukt game theory ke aaranbhik udaaharanon ke liye enthani daauns ka kaarya dekhein. apni pustak ain ikonomik theory of demokrasisaaaincha:Harvard citations/core mein unhonne 'hotaling farm lokeshan (sthiti) model'ko raajaneetik pranaali mein prayukt kiya hai. daaunasiyn model mein, raajaneetik ummeedavaar siddhaanton ke prati ek aayaami neeti 'space' mein pratibaddh hote hain. siddhaantakaar darshaate hain ki kis tarah se raajaneetik ummeedavaar ausat matadaataaon ki pasandeeda vichaaradhaara ki or abhisrit honge. bilkul taaja udaaharanon ke liye steven braams, George tsebelis, jeen M. grausamain aur elhaanan helpamain ki ya David osten-smith aur jefri S. bainks ki pustakein dekhein.

lokataantrik shaanti ki ek khel-saiddhaantik vyaakhya yeh hai ki janta aur lokatantr ki mukt bahas apne iraadon se sambandhit spasht aur vishvasaneeya jaankaari doosare raajyon ko bhejate hain. iske vipreet, gair-lokataantrik netaaon ke iraadon ka pata lagaana kathin hai ki kaun-kaun si riyaayatein laagoo hongi aur kya vaadon ko poora kiya jaaega. is tarah riyaayatein pradaan karne ke prati avishvaas aur anichha hogi yadi vivaadaadheen dalon mein se kam se kam ek dal gair-lokataantrik saaaincha:Harvard citations/core hai.

arthashaastr aur vyaapaar

arthashaastri bahut lambe samay se game theory ka prayog neelaamiyon, mol-bhaav, dvayaadhikaaron, nyaayapoorn vibhaajan, alpaadhikaaron, saamaajik network ke nirmaan aur matadaan tantron sahit aarthik tathyon ki vyaapak shreniyon ke vishleshan ke liye karte rahe hain. yeh anusandhaan saamaanyat: rananeetiyon ke vishisht samuchchayon par keindrit hota hai, jinhein khelon mein santulan kehte hain. ye “asamaadhaan avadhaaranaayein” saamaanyat: taarkikta ke niyamon ki aavashyakataaon par aadhaarit hoti hain. gair-sahakaari khelon mein, naish santulan inmein se sabse prasiddh hai. rananeetiyon ka ek samuchchaya yadi anya rananeetiyon ke prati sarvashreshth pratikriya ka pratinidhitv karta ho, to vah naish santulan hai. isaliye yadi sabhi khilaadi apni chaalein naish santulan mein chal rahe hain, to unke beech path se hatne ke liye koi ekatarafa pralobhan naheen hoga, choonki unki rananeeti sarvashreshth hai, at: ve vah kar sakte hain, jo anya khilaadi kar rahe hon.

khilaadiyon ki vyaktigem theory upayogita ka pratinidhitv karne ke liye saamaanyat: khel ke munaafe ko liya jaata hai. aadarsh sthitiyon mein munaafa aksar dhan ka pratinidhitv karta hai, jo sanbhavat: kisi vyakti ki upayogita se sambandhit hota hai. haalaaainki yeh dhaarana trutipoorn ho sakti hai.

arthashaastr mein game theory par ek pratimaanaatmak shodhapatr kisi aise khel ki prastuti ke dvaara praarambh hota hai, jo kisi vishisht aarthik sthiti ka sankshepan ho. ek ya ek se adhik samaadhaan avadhaaranaayein chuni jaati hain aur lekhak yeh pradarshit karta hai ki prastut khel mein rananeeti ke kaun-se samuchchaya upayukt prakaar ke santulan mein hain. svaabhaavik roop se hamein yeh aashcharya ho sakta hai ki is jaankaari ka kya upayog kiya jaae. arthashaastri aur vyaapaarik professor do praathamik upayogon ka sujhaav dete hain: varnanaatmak aur aadeshaatmak.

varnanaatmak

teen charanon wala ek shatapad khel

pehla gyaat upayog is baat ko varnit karna hai ki maanav aabaadi kis prakaar ka vyavahaar karti hai. kuchh vidvaan maanate hain ki khelon ke santulanon ki khoj kar lene par ve is baat ka poorvaanumaan kar sakte hain ki jis khel ka adhyayan kiya ja raha hai, usamein varnit sthitiyon jaisi sthitiyon se saamana hone par vaastavik maanav aabaadi kis prakaar ka vyavahaar karegi. game theory ka yeh vishisht drushtikon naveenatam aalochna ka saamana kar raha hai. sabse pehle, iski aalochna is baat ko lekar ki jaati hai ki game thyoreekaaron dvaara banaai gayi dhaaranaaon ka aksar ullanghan hota hai. game thyoreekaar yeh maan sakte hain ki khilaadi apni vijyon ko pratyaksh roop se adhiktam star tak badhaane ke liye sadaiv ek hi prakaar se kaarya karte hain (homo ikaunaumiks model), lekin vyavahaarik taur par, maanav svabhaav aksar is model se bhinn hota hai. is tathya ki anek vyaakhyaayein hain: tarkaheenata, vivechana ke naye model, ya yahaaain tak ki vibhinn prerak (jaise paryaayavaad). pratyuttar mein game thyoreekaar apni dhaaranaaon ki tulana bhautik-shaastr mein prayukt dhaaranaaon ke saath karte hain. is prakaar haalaaainki unki dhaaranaayein sadaiv sahi saabit naheen hoteen, lekin ve game theory ko bhautik-shaastriyon dvaara prayukt pratimaanon ke samaan vaigyaanik aadarsh ke roop mein prayog kar sakte hain. haalaaainki is game theory ke prayog par kuchh atirikt aalochna bhi laadi jaati hai kyonki kuchh adhyayanon ne yeh pradarshit kiya hai ki vyakti santulan rananeetiyon ka prayog naheen karte. udaaharan ke liye shatapad khel (centipede game) mein, ek ausat khel ka 2/3 bhaag anumaan par aadhaarit hota hai aur taanaashaah khel (Dictator game) mein log niyamit roop se naish santulanon ke dvaara naheen khelte. in adhyayanon ke mahatva ke sandarbh mein bahas jaari hai.[2]

vaikalpik roop se, kuchh lekhak daava karte hain ki naish santulan maanav aabaadiyon ke liye poorvaanumaan naheen pradaan karte, balki ve is baat ki vyaakhya karte hain ki naish santulanon se khelne waali aabaadiyaan us avastha mein hi kyon bani rahateen hain. haalaaainki yeh savaal fir bhi khula rahata hai ki aabaadiyaan us bindu tak kaise pahuainchateen hain.

apni chintaaon ke samaadhaan ke liye kuchh siddhaantakaar vikaasavaadi game theory ki or mud gaye hain. ye pratimaan ya to khilaadiyon ke liye koi taarkikta naheen maanate ya paribddh taarkikta maanate hain. apne naam ke baavajood vikaasavaadi game theory aavashyak roop se jaivik arth mein praakrutik chayan ko naheen maanata. vikaasavaadi game theory jaivik aur saath hi saanskrutik vikaas tatha vyaktigem theory shiksha ke pratimaan (udaaharanaarth kaalpanik khel game theory ivijnyaaan) donon ko shaamil karta hai.

aadeshaatmak ya nirdeshaatmak vishleshan

Cooperate Defect
Cooperate -1, -1 -10, 0
Defect 0, -10 -5, -5
The Prisoner's Dilemma

doosari or, kuchh vidvaan game theory ko manushyon ke vyavahaar ke liye ek bhavishyasoochak upakaran ke roop mein naheen, balki is baat ke ek sujhaav ke roop mein dekhte hain ki logon ko kis prakaar ka vyavahaar karna chaahiye. choonki kisi khel ka ek naish santulan anya khilaadiyon ki game theory vidhiyon ke prati vyakti ki sarvashreshth pratikriya ka nirmaan karta hai, at: aisi chaal chalana upayukt prateet hota hai, jo naish santulan ka ek bhaag ho. haalaaainki, game theory ke liye yeh prayog bhi aalochna ke antargem theory aa gaya hai. sabse pehle, kuchh maamalon mein gair-santulan rananeeti ka prayog karna tab upayukt hota hai, jab vyakti ko anya khilaadiyon dvaara bhi ek gair-santulan rananeeti ka prayog karne ki ummeed ho. ek udaaharan ke liye, ausat ka 2/3 anumaan dekhein.

doosra, kaidi ka asamanjas (Prisoner's dilemma) ek anya sambhaavit prati-udaaharan prastut karta hai. kaidi ka asamanjas mein, apne svaarth ki poorti ka prayaas karte hue pratyek khilaadi donon khilaadiyon ko usase buri sthiti mein le aata hai, jismein ve apne svaarth ki poorti ka prayaas na karne par rahe hote.

jeevavijnyaaan

Hawk Dove
Hawk v−c, v−c 2v, 0
Dove 0, 2v v, v
The hawk-dove game

arthashaastr ke vipreet, jeevavijnyaaan mein khelon ke liye laabh ki vyaakhya aksar yogyata ke sambandh mein ki jaati hai. iske atirikt taarkikta ke vichaar se sambandhit santulanon par kam aur vikaasavaadi shaktiyon dvaara banaaye rakhe ja sakane vaale santulanon par zyaada dhyaan keindrit kiya jaata raha hai. jeevavijnyaaan mein gyaat sarvashreshth santulan ko vikaasavaadi sthir rananeeti (Evolutionary Stable Strategy [athva ESS]) ke roop mein jaana jaata hai aur ise sabse pehle (Smith & Price 1973) mein prastut kiya gaya tha. haalaaainki iski praarambhik prerana mein naish santulan ki koi bhi maanasik aavashyakta shaamil naheen thi, lekin pratyek ESS ek naish santulan hota hai.

jeev vigyaan mein game theory ka upayog anek bhinn tathyon ko samajhne mein kiya gaya hai. sabse pehle iska upayog 1:1 ling anupaat ki utpatti (aur sthirta) ki vyaakhya karne ke liye kiya gaya tha.(Fisher 1930) ne yeh sujhaav diya ki 1:1 ling anupaat un vyaktiyon par kaarya kar rahi vikaasavaadi shaktiyon ka parinaam hai, jinhein apne pautron ki sankhya ko adhiktam star tak badhaane ka prayaas karne vaalon ke roop mein dekha ja sakta hai.

iske atirikt, jeev-vijnyaaaniyon ne vikaasavaadi game theory aur ESS ka upayog pashuon ke beech sanpreshan ke aavirbhaav ki vyaakhya karne ke liye kiya hai.(Harper & Maynard Smith 2003) sanket khelon aur anya sanpreshan khelon ke vishleshan ne pashuon ke beech sanpreshan ki utpatti ki kuchh jaankaari pradaan ki hai. udaaharan ke liye, pashuon ki anek prajaatiyon, jinmein shikaari jaanvaron ki ek badi sankhya kisi bade parabhakshi par hamla karti hai, mein saamoohik aakraman ka vyavahaar sahaj roop se utpann sangathan ka ek udaaharan prateet hota hai.

kshetreeyata aur ladaai ke vyavahaar ka vishleshan karne ke liye jeev-vijnyaaaniyon ne choojon ke khel ka prayog kiya hai.[krupaya uddharan jodein]

khelon ki utpatti aur siddhaant (Evolution and the theory of Games) ki prastaavana mein menaard smith likhte hain, “[vi]rodhaabhaasi roop se, yeh paaya gaya hai ki game theory arthashaastreeya vyavahaar ke kshetr, jiske liye vah mool roop se banaaya gaya tha, ki bajaay jeevavijnyaaan par zyaada achhi tarah laagoo hota hai”. vikaasavaadi game theory ka prayog prakruti mein asangem theory prateet hone vaale anek tathyon ki vyaakhya karne ke liye kiya jaata raha hai.[3]

aise hi ek tathya ko jaivik paropakaarita kehte hain. yeh ek aisi sthiti hai, jismein ek jeev aisi paddhati se kaarya karta hua dikhaai deta hai, jo anya jeevon ke liye laabhadaayak aur swayam uske liye ahitkar hoti hai. yeh paropakaarita ki paaramparik dhaarana se bhinn hai, kyonki aise kaarya sachetan naheen hote, balki sakal yogyata ko badhaane ke liye vikaasavaadi anukoolan ke roop mein dikhaai dete hain. iske udaaharan pishaach chamagaadadon, jo raat ke shikaar se haasil kiye gaye khoon ko ugalakar apne samooh ke un sadasyon ko de dete hain, jo shikaar kar paane mein asafal rahe hon, se lekar karmi madhumakkhiyon, jo aajeevan raani madhumakkhi ki seva karti hain aur kabhi milan naheen karateen, se lekar varvet bandaron, jo samooh ke sadasyon ko shikaari ke aagaman ki chetaavani dete hain, bhale hi isse unka swayam ka jeevan khtare mein pad jaaye, tak mein paaye ja sakte hain.[4] inmein se sabhi kaarya ek samooh ki sakal yogyata ko badhaate hain, lekin aisa karne ke liye ek jeev ko apni jaan ganvaani padti hai.

vikaasavaadi game theory is paropakaarita ki vyaakhya sanbandhiyon ke chayan ke vichaar ke roop mein karta hai. paropakaari jeev un praaniyon ke beech bhed-bhaav karte hain, jinki ve sahaayata karte hain aur ve apne sanbandhiyon ka paksh lete hain. haimiltan ka niyam is chayan ke peechhe vikaasavaadi tark ki vyaakhya sootr c<b*r ke dvaara karta hai, jahaaain paropakaari ko laganevaali laagem theory (c) praaptakarta ko milnevaale laabh (b) va sanbaddhata ke gunaank (r) ke gunanafal se kam honi chaahiye. do jeevon ke beech niktata jitni adhik hogi, paropakaarita ki ghatanaayein bhi utani hi badh jaaengi kyonki unke anek jinetik tatv (alleles) samaan honge. iska arth yeh hai ki paropakaari jeev, is baat ko sunishchit karte hue ki uske nikat sanbandhiyon ke jenetik tatv aage prasaarit hote hain, (usaki santaan ke dvaara), swayam ki santaan ko janm dene ke vikalp ka tyaag kar sakta hai kyonki samaan sankhya mein jenetik tatv aage prasaarit hue hain. udaaharanaarth, kisi sahodar ki sahaayata karne ka gunaank 1/2 hota hai kyonki jeev apne sahodar ki santaan mein 1/2 jenetik tatv saajha karta hai. is baat ko sunishchit kar lena ki kisi sahodar ki santaanon ki paryaapt sankhya vayask hone tak jeevit rahati hai, paropakaari vyakti ke liye swayam ki santaan utpann karne ki aavashyakta ko samaapt kar deta hai.[4] gunaank maan khel ke maidaan ke daayare par atyadhik aashrit hote hain: udaaharanaarth, jinke prati pakshapaat karna hai, unke chunaav mein yadi sabhi jenetik jeevit vastuen, keval sambandhi naheen, shaamil hon, to ham maanate hain ki sabhi manushyon ke beech antar khel ke maidaan mein vividhta ka lagbhag 1% hota hai, jo gunaank ek chhote kshetr mein 1/2 tha, vah 0.995 ho jaata hai. isi prakaar yadi is par vichaar kiya jaaye ki jenetik svaroop ki kisi soochana ke atirikt koi anya soochana (uda. epijenetiks, dharm, vigyaan aadi) samay ke saath bani rahati hai, to khel ka maidaan aur bada va bhed-bhaav chhote ho jaate hain.

computer vigyaan aur tark

tark aur computer vigyaan mein game theory ek badhti hui mahatvapoorn bhoomika nibhaane laga hai. anek taarkik siddhaanton ka aadhaar khel arthavijnyaaan mein hai. iske atirikt, computer vaigyaaniko ne anek ant:kriyaatmak gananaaon ka nirmaan karne ke liye khelon ka prayog kiya hai. saath hi, game theory bahu-abhikrta tantron ke kshetr ka ek saiddhaantik aadhaar pradaan karta hai.

pruthak roop se, game theory ne online elgorithm mein bhi bhoomika nibhaai hai. vishishtat:, k-sarvar samasya, jiska ullekh ateet mein chal-laagem theory vaale khel (games with moving costs) aur nivedan-uttar khel (request-answer games) ke roop mein kiya jaata tha.saaaincha:Harvard citations/core yaao ka siddhaant yaadruchhikrut elgorithm aur visheshat: online elgorithm, ki gananaatmak jatilta ki nichli seemaaon ko siddh karne ke liye ek khel-saiddhaantik takaneek hai.

elgorithmik game theory ka kshetr jatilta aur elgorithm ki rachana ki computer vigyaan ki avadhaaranaaon ko game theory aur aarthik siddhaant ke saath sanyojit karta hai. Internet ke udbhav ne khelon, baajaaron, gananaatmak neelaamiyon, peeyar-se-peeyar tantron aur suraksha tatha soochana baajaar mein santulanon ki khoj karne ke liye elgorithm ke vikaas ko prerit kiya hai.[5]

darshanashaastr

Stag Hare
Stag 3, 3 0, 2
Hare 2, 0 2, 2
Stag hunt

darshanashaastr mein game theory ke anek upayog hain. saaaincha:Harvard citations/core dvaara prastut do shodh-patron par pratikriya dete hue, Lewis (1969) ne sammelan ki ek daarshanik samajh viksit karne ke liye game theory ka prayog kiya. aisa karte hue, unhonne saamaanya gyaan ka praarambhik vishleshan pradaan kiya aur taal-mel sambandhi khelon mein khel ke vishleshan ke liye iska prayog kiya. iske atirikt, pehle unhonne yeh sujhaav diya ki vyakti arth ko sanket khelon ke sandarbh mein samajh sakta hai. luis ke baad anek daarshanikon dvaara is sujhaav ka prayog kiya gaya hai (Skyrms (1996),saaaincha:Harvard citations/core). sammelanon ke khel-saiddhaantik Lewis (1969) ke baad, ulmain maargelit (1977) aur bicheri (2006) ne saamaajik niyamon ke aise siddhaant viksit kiye hain, jo unhein ek mishrit-uddeshya vaale khel ko ek taal-mel sambandhi khel mein roopaantarit karne ke parinaamasvaroop praapt hone vaale naish santulanon ke roop mein paribhaashit karte hain.[6]

game theory daarshanikon ko ant:kriyaatmak jnyaaanameemaansa ke sambandh mein sochane ki chunauti bhi deta hai: kisi samooh ke liye samaan vishvaason ya gyaan ka kya arth hota hai aur abhikrtaaon ki ant:kriya ke kaaran milnevaale saamaajik parinaamon par is gyaan ka kya prabhaav padta hain. is kshetr mein kaarya karne vaale daarshanikon mein bicheri (1989, 1993),[7] skirms (1990),[8] tatha staalanekar (1999)[9] shaamil hain.

neetishaastr mein, kuchh lekhakon ne, Thomas haubs dvaara shuru ki gayi, svaarth se naitikta praapt karne ki pariyojana ka anusaran karne ka prayaas kiya hai. choonki kaidi ka asamanjas naitikta aur svaarth ke beech ek aabhaaseeya sangharsh ko prastut karta hai, at: is baat ki vyaakhya karna is pariyojana ka ek mahatvapoorn ghatak hai ki svaarth ke liye sahakaarita ki aavashyakta kyon hoti hai. yeh saamaanya rananeeti raajanaitik darshanashaastr mein saamaanya saamaajik anubandh ke drushtikon ka ek ghatak hoti hai (udaaharan ke liye, Gauthier (1986) tatha Kavka (1986) dekhein).[10]

anya lekhakon ne naitikta ke prati maanaveeya drushtikon ke udbhav tatha is sambandh mein pashuon ke vyavahaaron ki vyaakhya karne ke liye vikaasavaadi game theory ka prayog karne ka prayaas kiya hai. ye lekhak kaidi ka asamanjas (Prisoner's dilemma), baarahasinge ka shikaar (Stag hunt) sahit vibhinn khelon aur naish saudebaaji khel (Nash bargaining game) ko naitikta ke drushtikon ke udbhav ki vyaakhya pradaan karanevaalon ke roop mein dekhte hain (uda.saaaincha:Harvard citations/core tatha saaaincha:Harvard citations/core dekhein).

game theory ke kuchh bhaagon mein prayukt kuchh poorvaanumaanon ko darshanashaastr mein chunauti di gayi hai; manovaigyaanik ahanbhaav kehta hai ki taarkikta svaarth ko kam karti hai-ek daava, jo daarshanikon ke liye bahas ka vishay hai. (manovaigyaanik ahanbhaav#aalochana dekhein)

khelon ke prakaar

sahakaari ya gair-sahakaari

ek khel sahakaari hota hai, yadi khilaadi bandhanakaari pratibddhataaon ka nirmaan kar paane mein saksham hon. udaaharan ke liye kaanooni tantr unke liye apne vachanon ka paalan karna aavashyak banaata hai. gair-sahakaari khelon mein yeh sambhav naheen hota.

aksar aisa maana jaata hai ki sahakaari khelon mein khilaadiyon ke beech samvaad ki anumati di jaati hai, lekin gair-sahakaari khelon mein naheen. yeh vargeekaran do dviaadhaari kasautiyon ke aadhaar par asveekaar kar diya gaya hai.(Harsanyi 1974)

khel ke do prakaaron mein se, gair-sahakaari khel sarvashreshth vivranon tak paristhitiyon ke pradarshan mein saksham hote hain aur sateek parinaam utpann karte hain. sahakaari khel vyaapak roop se khel par keindrit hote hain. in do maargon ko jodne ke lakshaneeya prayaas kiye gaye hain. tathaakathit naish-program[tathya vaanchhit] ne pehle hi anek sahakaari sthitiyon ko gair-sahakaari santulanon ke roop mein sthaapit kar diya hai.

sankarit khelon mein sahakaari va gair-sahakaari tatv hote hain. udaaharan ke liye sahakaari khelon mein khilaadiyon ke gathabandhan banaaye jaate hain, lekin ve ek gair-sahakaari shaili mein khelte hain.

samamit aur asamamit

E F
E 1, 2 0, 0
F 0, 0 1, 2
An asymmetric game

ek samamit khel aisa khel hota hai, jismein kisi vishisht rananeeti ke anusaar khelne ka laabh keval anya prayukt rananeetiyon par nirbhar karta hai, na ki unhein khelanevaalon par. yadi rananeetiyon se milnevaale munaafe ko badle bina khilaadiyon ki pehchaan badli ja sakti ho, to khel samamit hota hai. saamaanyat: adhyayan kiye jaane vaale 2 × 2 khelon mein se anek samamit hote hain. chikn, kaidi ka asamanjas aur baarahasinge ka shikaar ke maanak pradarshan sabhi samamit khel hain. kuchh vidvaan in khelon ke udaaharanon ke roop mein vibhinn asamamit khelon par vichaar kar sakte hain. haalaaainki inmein se pratyek khel ke liye sarvaadhik prachalit laabh samamit hote hain.

sarvaadhik adhyayan kiye jaane vaale asamamit khel ve khel hote hain, jinmein donon khilaadiyon ke liye rananeetiyon ke samaan samuchchaya naheen hote. udaaharan ke liye, altimet game aur diktetar game mein pratyek khilaadi ke liye bhinn rananeetiyaan hoti hain. haalaaainki, yeh bhi sambhav hai ki kisi khel mein donon khilaadiyon ke liye ek samaan rananeetiyaan hon aur fir bhi vah asamamit ho. udaaharan ke liye, donon khilaadiyon ke liye rananeetiyon ke samaan samuchchaya hone ke baavajood bhi daahini or chitrit khel asamamit hai.

shoonya-raashi aur gair-shoonya-raashi

A B
A –1, 1 3, –3
B 0, 0 –2, 2
A zero-sum game

shoonya-raashi khel sthir-raashi khelon ke vishesh udaaharan hain, jinmein khilaadiyon dvaara kiye gaye chayan upalabdh sansaadhanon ko na to badhaate hain aur na hi ghataate hain. shoonya-raashi khelon mein, rananeetiyon ke pratyek sanyojan ke liye, khel ke sabhi khilaadiyon ko milnevaale kul laabh ka yogafal shoonya hota hai (adhik anaupachaarik roop se, ek khilaadi ko hone wala laabh anya khilaadiyon ki utani hi haani ke dvaara hota hai). pokar ka khel ek shoonya-raashi khel ka udaaharan prastut karta hai (kisi ghar mein katauti ki sambhaavana ki anadekhi karte hue) kyonki koi bhi khilaadi theek utani hi rakm jeetata hai, jitni uske pratidvandvi haarate hain. anya shoonya-raashi khelon mein sikkon ka Milan (matching pennis) aur go tatha shataranj sahit adhikaansh shaastreeya board khel shaamil hain.

game thyoreekaaron dvaara jin khelon ka adhyayan kiya gaya hai, unamein se adhikaansh (prasiddh kaidi ka asamanjas sahit) gair-shoonya-raashi khel hain kyonki unamein se kuchh praaptiyon ke sakal parinaam shoonya se zyaada ya kam hote hain. anaupachaarik roop se, gair-shoonya-raashi khelon mein, kisi ek khilaadi ko milnevaala laabh aavashyak taur par kisi anya khilaadi ko hone waali haani se juda naheen hota.

sthir-raashi khel chori aur jue jaisi game theory vidhiyon se sambandhit hote hain, lekin us moolabhoot aarthik paristhiti se naheen, jismein vyaapaar se laabh sambhaavit hote hain. ek atirikt nakali khilaadi (jise aksar "board" kaha jaata hai), jiski haaniyaan khilaadi ke shuddh laabh ki kshatipoorti karti hain, ko jodkar kisi bhi khel ko ek (sanbhavat: asamamit) shoonya-raashi khel mein roopaantarit kar paana sambhav hota hai.

samakaalik aur aanukramik

samakaalik khel aise khel hote hain, jinmein donon khilaadi apni chaal ek saath chalte hain, ya yadi ve ek saath chaal naheen chalte, to baad vaale khilaadi pehle khelne vaale khilaadiyon ki chaal se anbhigya hote hain (jo unhein prabhaavi roop se samakaalik banaata hai). aanukramik khel (ya game theory sheel khel) aise khel hote hain, jinmein baad mein khelne vaale khilaadiyon ko poorvavarti chaalon ki kuchh jaankaari hoti hai. yeh aavashyak roop se poorvavarti khilaadiyon ki pratyek game theory vidhi ki poorn jaankaari naheen hoti; yeh bahut thodi jaankaari ho sakti hai. udaaharan ke liye, sambhav hai ki koi khilaadi yeh jaanta ho ki kisi poorvavarti khilaadi ne koi vishisht chaal naheen chali thi, jabki vah yeh na jaanta ho ki pehle khilaadi ne anya upalabdh chaalon mein se vastut: kaun-si chaal chali thi.

samakaalik aur aanukramik khelon mein mukhya antar oopar charchit vibhinn pradarshanon mein sammilit kiye gaye hain. aksar, samakaalik khelon ko darshaane ke liye saamaanya roop ka aur aanukramik khelon ko darshaane ke liye vistrut roop ka prayog kiya jaata hai; haalaaainki, takaneeki roop se yeh koi sakht niyam naheen hai.

poorn jaankaari aur apoorn jaankaari

apoorn jaankaari wala ek khel (bindeedaar rekha khilaadi 2 ki or se ajnyaaanata ka pratinidhitv karta hai)

aanukramik khelon ka ek mahatvapoorn up-samuchchaya poorn jaankaari se milkar bana hota hai. ek khel poorn jaankaari se yukt hota hai, yadi sabhi khilaadi anya khilaadiyon dvaara pehle chali gayi chaalon ke baare mein jaante hon. is prakaar, keval aanukramik khel hi poorn jaankaari vaale ho sakte hain kyonki samakaalik khelon mein pratyek khilaadi anya khilaadiyon ki chaalon ko naheen jaanta. game theory mein adhyayan kiye jaane vaale adhikaansh khel apoorn-jaankaari vaale khel hote hain, haalaaainki, altimet game aur shatapad khel sahit poorn-jaankaari vaale khelon ke kuchh rochak udaaharan upalabdh hain. poorn-jaankaari vaale khelon mein shataranj, go, mainkala aur arima shaamil hain.

poorn jaankaari ko aksar samast jaankaari samajh liya jaata hai, jo ek sadrush avadhaarana hai. samast jaankaari ke liye pratyek khilaadi ko anya khilaadiyon ki rananeetiyon va praaptiyon ki jaankaari hona aavashyak hai, lekin unki game theory vidhiyon ki jaankaari hona aavashyak naheen hai.

aseemit roop se lambe khel

arthashaastriyon aur vaastavik-vishv ke khilaadiyon dvaara adhyayan kiye jaane vaale khel saamaanyat: chaalon ki seemit sankhya mein samaapt ho jaate hain. shuddh ganitjnya utane baadhya naheen hote aur samuchchaya siddhaantakaar vishishtat: un khelon ka adhyayan karte hain, jo chaalon ki aseemit sankhya tak jaari rahate hain aur unamein vijeta (ya anya laabh) un sabhi chaalon ki samaapti ke baad tak gyaat naheen hota.

saamaanyat: dhyaan is baat par zyaada keindrit naheen hota ki aise khelon ko khelne ki sarvashreshth vidhi kya hai, balki keval is par hota hai ki kya kisi khilaadi ke paas jeetne ki rananeeti hai. (chayan ke siddhaant ka prayog karke yeh siddh kiya ja sakta hai ki aise khel hote hain- yahaaain tak ki poorn jaankaari ke saath aur jahaaain parinaam keval "jeet" ya "haar" hote hain- jinke liye kisi khilaadi ke paas jeetne ki rananeeti naheen hoti). nipunata se rachit khelon ke liye varnanaatmak samuchchaya siddhaant mein aisi rananeetiyon ke astitv ke mahatvapoorn prabhaav hote hain.

asatat aur satat khel

game theory ka adhikaansh bhaag seemit, asatat khelon se sambandhit hota hai, jinmein khilaadiyon, chaalon, ghatnaaon, parinaamon aadi ki sankhya seemit hoti hai. haalaaainki anek avadhaaranaaen vistaarit ki ja sakti hain. satat khel apne khilaadiyon ko ek satat rananeeti samuchchaya mein se kisi rananeeti ka chayan karne ki anumati dete hain. udaaharan ke liye, kaurnat pratiyogita ki rachana vishisht roop se is prakaar ki gayi hai ki khilaadiyon ki rananeetiyaan koi gair-nakaaraatmak maatraaen, bhinnaatmak maatraaon sahit, hoti hain.

antareeya khel, jaise kantinyuas parsyut end ivejan khel satat khel hain.

ek-khilaadi aur anek-khilaadiyon vaale khel

vyaktigem theory nirnaya samasyaaon ko kabhi-kabhi "ek-khilaadi vaale khel" maana jaata hai. haalaaainki ye sthitiyaan khel saiddhaantik naheen hain, lekin unki rachana nirnaya siddhaant ke niyamon ke antargem theory unheen upakaranon mein se anek ka prayog karke ki jaati hai. keval do ya do se adhik khilaadiyon ke hone par hi koi samasya khel saiddhaantik banti hai. aksar betarateeb dhng se khelne wala koi khilaadi joda jaata hai, jo "avasaravaadi chaalein" chalta hai, jinhein "svaabhaavik chaalon" ke roop mein bhi jaana jaata hai.(Osborne & Rubinstein 1994) do-khilaadiyon vaale kisi khel mein is khilaadi ko teesara khilaadi naheen maana jaata, balki khel mein jahaaain aavashyak ho, vahaaain vah keval paase ki bhoomika nibhaata hai. khilaadiyon ki aseemit sankhya vaale khelon ko aksar n-vyakti khel kaha jaata hai.(Luce & Raiffa 1957)

metaakhel

ye ve khel hain jinhein khelna kisi anya khel, lakshya ya vishay khel, ke liye niyamon ka vikaas karna hota hai. metaakhel viksit kiye gaye niyamon ke samooh ke upayogita maan ko adhiktam star tak badhaane ka prayaas karte hain. metaakhelon ka siddhaant kriyaavidhi rachana siddhaant se sambandhit hota hai.

itihaas

game theory ki pehli gyaat charcha 1713 mein James vaaldegrev dvaara likhit ek patra mein hui. is patra mein vaaldegrev taash ke khel le har ke do-vyaktiyon vaale sanskaran ke samaadhaan ke liye ek minimaiks mishrit siddhaant pradaan karte hain.

James medisn ne usaka nirmaan kiya, jise ab ham is baat ke khel-saiddhaantik vishleshan ke roop mein jaante hain ki karaaropan ke vibhinn tantron ke antargem theory avasthaaon se kis prakaar ka vyavahaar karne ki apeksha ki ja sakti hai.[11][12]

entoni ogastin kaurnat dvaara 1838 mein Recherches sur les principes mathéaamatiques de la théaaorie des richesses (dhan ke siddhaant ke ganiteeya siddhaanton mein anusandhaan) ka prakaashan kiye jaane tak kisi saamaanya khel saiddhaantik vishleshan ka anusaran naheen kiya jaata tha. is kaarya mein kaurnat ne ek dvayaadhikaar par vichaar kiya hai aur ek samaadhaan prastut kiya hai, jo naish santulan ka ek seemit sanskaran hai.

haalaaainki kaurnat ka vishleshan vaaldegrev ke vishleshan se adhik saamaanya hai, lekin John vaun nyoomain dvaara 1928 mein shodh-patron ki ek shrunkhala ka prakaashan kiye jaane se poorv tak ek adviteeya kshetr ke roop mein game theory ka vastut: koi astitv naheen tha. haalaaainki fraanseesi ganitjnya emili borel ne khelon par kuchh praarambhik kaarya kiya, lekin vaun nyoomain ko game theory ka aavishkaarak hone ka shreya uchit roop se diya ja sakta hai. vaun nyoomain ek buddhimaan ganitjnya the, jinka kaarya samuchchaya siddhaant se lekar unki gananaaon, jo anu va haaidrojan bamon donon ke vikaas ki kunji theen aur antat: sanganakon ke vikaas ke unke kaarya tak vyaapak roop se faila hua tha. game theory mein vaun nyoomain ka kaarya 1944 mein vaun nyoomain aur oscar maurgenstem ki kitaab Theory of Games and Economic Behavior (khelon aur aarthik vyavahaar ka siddhaant) mein apne charam par pahuncha. is gahan kaarya mein do-vyaktiyon vaale shoonya-raashi khelon ke liye paraspar sangem theory samaadhaanon ki khoj karne hetu vidhiyaan shaamil hain. is samayaavadhi ke dauraan, game theory par kaarya praathamik roop se sahakaari game theory par keindrit tha, jo vyaktiyon ke samooh ke liye yeh maanate hue ishtatam rananeetiyon ka vishleshan karta hai ki ve upayukt rananeetiyon ke baare mein apne beech sahamati laagoo kar sakte hain.

1950 mein, kaidi ka asamanjas prakat hua aur RAND corporation mein is khel par ek prayog kiya gaya. isi samay ke aas-paas, John naish ne khilaadiyon ki rananeetiyon ki paraspar sangem theory ta ke liye ek maapdand viksit kiya, jise naish santulan ke roop mein jaana jaata hai aur jo vaun nyoomain aur maurgenstem dvaara prastaavit maapdand ki tulana mein khelon ki ek vyaapak shreni par laagoo hota hai. yeh santulan paryaapt roop se itna saamaanya hai ki yeh sahakaari khelon ke atirikt gair-sahakaari khelon ke vishleshan ki anumati bhi deta hai.

1950 ke dashak mein game theory ne game theory vidhiyon ki ek halachal ka anubhav kiya, jis samay ke dauraan mool, gahan svaroop ke khel, kaalpanik khel, doharaaye gaye khelon aur shepale (Shapley) maan ki avadhaaranaaen viksit huin. iske atirikt, isi samay ke dauraan darshanashaastr aur raajaneeti vigyaan mein game theory ko pehli baar laagoo kiya gaya.

1965 mein, reenahaard seltan ne upakhel poorn santulanon (subgame perfect equilibria) ki apni samaadhaan avadhaarana prastut ki, jisne naish santulan ko aur adhik parishkrut kiya (baad mein unhein [[kaanpate haath ka anubhav [trembling hand perception]]] bhi prastut karna tha). 1967 mein, John harsenyi ne sampoorn soochana aur baayesiyn khelon ki avadhaaranaaen viksit keen. aarthik game theory mein unke yogadaan ke liye naish, seltan aur harsenyi 1994 mein arthashaastr ke Nobel puraskaar vijeta bane.

1970 ke dashak mein, mukhyat: John menaard smith aur unki vikaasavaadi roop se sthir rananeeti ke kaarya ke falasvaroop game theory ko jeevavijnyaaan mein gahan roop se laagoo kiya gaya. iske atirikt sahasanbaddh santulan, kaanpate haath ka anubhav aur saamaanya gyaan ki avadhaaranaaen[13] prastut ki gain aur unka vishleshan kiya gaya.

2005 mein, game thyoreekaaron Thomas sheling aur Robert omain ne Nobel vijetaaon ke roop mein naish, seltan aur harsenyi ka anusaran kiya. sheling ne game theory vikaasasheel pratimaanon par kaarya kiya, jo vikaasavaadi game theory ke praarambhik udaaharan the. omain ne ek santulan kathorata, sahasanbaddh santulan, prastut karke aur saamaanya gyaan aur iske prabhaavon ke anumaanon ka ek gahan aupachaarik vishleshan viksit karke santulan vichaaradhaara mein adhik yogadaan diya.

san 2007 mein, Roger maayarsan ko lionid harvij aur erik maskin ke saath "kriyaavidhi rachana siddhaant ki neenv rakhane ke liye" arthashaastr mein Nobel puraskaar se sammaanit kiya gaya. maayarsan ke yogadaanon mein upayukt santulan ka vichaar aur ek mahatvapoorn snaatak paathyapustak: Game Theory, Analysis of Conflict (game theory, takaraavon ka vishleshan), shaamil hain.(Myerson 1997)

inhein bhi dekhein

  • mishrit game theory
  • game theory ki shabdaavali
  • game theory mein khelon ki soochi
  • kvaantam game theory
  • aatm santulan ki pushti
  • chenastor virodhaabhaas

nots

  1. Ross, Don. "Game Theory". The Stanford Encyclopedia of Philosophy (Spring 2008 Edition). Edward N. Zalta (ed.). http://plato.stanford.edu/archives/spr2008/entries/game-theory/. abhigman tithi: 2008-08-21.
  2. game theory ke prayogaatmak kaarya ke kai naam hain, praayogik arthashaastr, vyavahaarik arthashaastr aur vyavahaarik game theory kai hain. is kaaryakshetr par haal hi mein ki gayi charcha ke liye Camerer (2003) dekhein.
  3. vikaasavaadi game theory (stainaford inasaaiklopeediya of filausfi)
  4. a aa jaiv paropakaarita (stainaford inasaaiklopeediya of filausfi)
  5. Algorithmic Game Theory. http://www.cambridge.org/journals/nisan/downloads/Nisan_Non-printable.pdf.
  6. E. ulaman margaalit, the emarajeins of naurms, Oxford university press, 1977. si. bikchiyeri, the graamar of society: saamaajik maanadandon ki prakruti aur game theory ki, Cambridge university press, 2006
  7. "self refyuting thyorij of straitejik interaikshan: saamaanya gyaan ka ek virodhaabhaas", erkenatnis, 1989: 69-85. samajhadaari aur samanvaya bhi dekhein, Cambridge university press, 1993.
  8. the daayanaamiks of raishanal delibereshan, Harvard university press, 1990.
  9. "khelon mein gyaan, vishvaas aur pratitthyaatmak tark." kristeena bikchiyeri, richrd jefari aur Brian skyarms, ke sanskaranon mein, the laujik of straiteji. New York: Oxford university press, 1999.
  10. neetishaastr mein game theory ke istemaal ki adhik vistrut charcha ke liye stainaford inasaaiklopeediya of filausfi ki pravishti game theory aur neetishaastr dekhein.
  11. James medisn, sanyukt raajya America ki raajanaitik vyavastha ke dosh, April 1787. link
  12. Jack rakov, "James maidisn aur samvidhaan", history naau, ank 13 sitmbar 2007. link
  13. haalaaainki saamaanya gyaan ki charcha sabse pehle 1960 ke dashak ke ant mein daarshanik David levis ne apne shodh prabandh (aur baad mein pustak) kanveinshan mein ki thi, lekin 1970 ke dashak mein Robert oman ki kruti tak arthashaastriyon ne is par vyaapak roop se vichaar naheen kiya.

sandarbh

Wiktionary-logo-en.png
game theory ko vikshanari,
ek mukt shabdakosh mein dekhein.

paathyapustikaaen aur saadhaaran sandarbh

  • Aumann, Robert J. (1987), "game theory,", The New Palgrave: A Dictionary of Economics, 2, pa॰ 460–82 .
  • (2008). the new palagrev dikshanari of ikaunomiks, dviteeya sanskaran:
Robert J. oman ki "game theory", kaalpanik.
Robert liyonaard ki "game theory in ikaunomiks, orijins of," kaalpanik.
faaruk gul ki "biheviyral ikaunomiks aind game theory". kaalpanik.
  • Dutta, Prajit K. (1999), Strategies and games: theory and practice, MIT Press, aai॰aऍsa॰abee॰aऍna॰ 978-0-262-04169-0 . poorvasnaatak aur bijnas chhaatron ke liye upayukt.
  • Fernandez, L F.; Bierman, H S. (1998), Game theory with economic applications, Addison-Wesley, aai॰aऍsa॰abee॰aऍna॰ 978-0-201-84758-1 . uchch-stareeya poorvasnaatakon ke liye upayukt.
  • Gibbons, Robert D. (1992), Game theory for applied economists, Princeton University Press, aai॰aऍsa॰abee॰aऍna॰ 978-0-691-00395-5 . unnat poorvasnaatakon ke liye upayukt.
  • Robert Gibbons (2001), A Primer in Game Theory, London: Harvester Wheatsheaf, aai॰aऍsa॰abee॰aऍna॰ 978-0-7450-1159-2 ke roop mein Europe mein prakaashit.
  • Gintis, Herbert (2000), Game theory evolving: a problem-centered introduction to modeling strategic behavior, Princeton University Press, aai॰aऍsa॰abee॰aऍna॰ 978-0-691-00943-8
  • Green, Jerry R.; Mas-Colell, Andreu; Whinston, Michael D. (1995), Microeconomic theory, Oxford University Press, aai॰aऍsa॰abee॰aऍna॰ 978-0-19-507340-9 . snaatak star ke liye upayukt game theory ko aupachaarik tareeke se prastut karta hai.
  • Isaacs, Rufus (1999), Differential Games: A Mathematical Theory With Applications to Warfare and Pursuit, Control and Optimization, New York: Dover Publications, aai॰aऍsa॰abee॰aऍna॰ 978-0-486-40682-4
  • Miller, James H. (2003), Game theory at work: how to use game theory to outthink and outmaneuver your competition, New York: McGraw-Hill, aai॰aऍsa॰abee॰aऍna॰ 978-0-07-140020-6 . saadhaaran darshakon ke liye upayukt.
  • Osborne, Martin J. (2004), An introduction to game theory, Oxford University Press, aai॰aऍsa॰abee॰aऍna॰ 978-0-19-512895-6 . poorvasnaatak paathyapustika.
  • Osborne, Martin J.; Rubinstein, Ariel (1994), A course in game theory, MIT Press, aai॰aऍsa॰abee॰aऍna॰ 978-0-262-65040-3 . snaatak star ki ek aadhunik prastaavana.
  • Poundstone, William (1992), Prisoner's Dilemma: John von Neumann, Game Theory and the Puzzle of the Bomb, Anchor, aai॰aऍsa॰abee॰aऍna॰ 978-0-385-41580-4 . game theory aur game thyoritishiyans ka ek saadhaaran itihaas.

aitihaasik drushti se mahatvapoorn pustikaaen

  • oman, aar.J. aur sheple, L.S. (1974), vailyooj of naun-etaumik gems, prinsatan university press
  • Cournot, A. Augustin (1838), "Recherches sur les principles mathéaamatiques de la théaaorie des richesses", Libraire des sciences politiques et sociales (Paris: M. Rivièare & C.ie)
  • Edgeworth, Francis Y. (1881), Mathematical Psychics, London: Kegan Paul
  • Fisher, Ronald (1930), The Genetical Theory of Natural Selection, Oxford: Clarendon Press
  • pun:mudrit sanskaran: R.A. Fisher ; edited with a foreword and notes by J.H. Bennett. (1999), The Genetical Theory of Natural Selection: A Complete Variorum Edition, Oxford University Press, aai॰aऍsa॰abee॰aऍna॰ 978-0-19-850440-5
  • Luce, R. Duncan; Raiffa, Howard (1957), Games and decisions: introduction and critical survey, New York: Wiley
  • pun:mudrit sanskaran: R. Duncan Luce ; Howard Raiffa (1989), Games and decisions: introduction and critical survey, New York: Dover Publications, aai॰aऍsa॰abee॰aऍna॰ 978-0-486-65943-5
  • Smith, John Maynard; Price, George R. (1973), "The logic of animal conflict", Nature 246: 15–18, doi:10.1038/246015a0
  • sheple, L.S. (1953), N-vyakti khelon ka ek maan, in: kantreebyooshans tu the theory of gems khand II, H. dablyoo. kuhan aur A.dablyoo. takar (sanskaran)
  • sheple, L.S. (1953), stochaastik gems, proseedings of naishanal aikadami of science khand 39, peepi. 1095-1100.
  • von Neumann, John; Morgenstern, Oskar (1944), Theory of games and economic behavior, Princeton University Press
  • Zermelo, Ernst (1913), "Üaber eine Anwendung der Mengenlehre auf die Theorie des Schachspiels", Proceedings of the Fifth International Congress of Mathematicians 2: 501–4

anya mudran sandarbh

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