
bheedbhaad vaale khelon mein arajakta kii keemat

arajakta (poa) kii keemat khel siddhant aur tantra design mein ack avadharana haye joe yeh maapati haye kii kaise ack pranali kaa samajik kalyan usake agents key swarthi vyavhaar key kaaran cumm hoe jaataa haye. iska vibhinn sandarbhon mein vyaapak roop seey adhyayan kiya gayaa haye, vishesh roop seey bheedbhaad vaale khelon (see. jee.) mein. 
udaaharan key liye.
bheedbhaad vaale khelon kii akshamta koo pahali baar 1920 mein pigo dwara nimnalikhit saral bheedbhaad vaale khel kaa upayog karke chitrit kiya gayaa thaa. maan leejiye kii dou sadaken hain joe bindu aeye seey bindu bee taka jaati hainh
maan leejiye kii 1000 chaalak hain jinhen aeye seey bee taka jaane kii aavashyakta haye. pratyek chaalak apani deree koo cumm karna chaahata haye, lekin sarkaar kull deree (sabhi chalakon kii deree kaa yog) koo cumm karna chaahegi. 
iss udaaharan mein, swarthi maarg kull deree kii or leey jaataa haye joe ishtatam seey 4/3 gunaa adhik haye, isaliye arajakta kii keemat 4/3 haye. samanya roop seey, arajakta kii keemat bheed key khel key prakaar, network kii sanrachana aur deree karyon key aadhar parr bhinn hoe sakati haye. vibhinn lekhakon ney vibhinn bheedbhaad vaale khelon mein poe parr oopari aur nichali seema kii ganana kii haye.
vilamb karyon kaa prabhaav.
poa parr vilamb karyon key prabhaav koo spasht karane key liye, uparokt udaaharan key ack prakaar parr vichaar karein jisamen sadak 1 mein deree abhee bhee 1 minut haye, lekin sadak 2 mein deree jaba "x" chaalak iska upayog karate hain tou yeh sootra _ 1 haye, kuchh d> 1 key liye. 
isaliye, arajakta kii keemat sootra _ 3 key roop mein anant taka pahunchati haye.
paribhaashaaen.
ack bheed khel (see. jee.) koo "sansadhanon" key ack samooh dwara paribhaashit kiya jaataa haye. udaaharan key liye, sadak network mein, pratyek sadak ack vyaktigat sansaadhan haye. pratyek key liye 
sansaadhan, ack "vilamb kaary" (urf "laagat kaary") haye. kaary sansaadhan mein bheed kii matra kaa maanchitran kartaa haye (ee.jee. sadak kaa upayog karane key liye chunane vaale chalakon kii sankhya) pratyek khilaadi dwara iska upayog karane mein honey vaali deree taka. ack khilaadi kii kull laagat vaha chunane vaale sabhi sansadhanon mein kull deree haye. pratyek khilaadi apani laagat koo cumm karane key liye ack ranneeti chunata haye. 
naish equilibirum ack aisee sthiti haye jisamen koee bhee khilaadi ektarafa roop seey apani pasand badalkar apani deree mein sudhaar naheen curr sakata haye. arajakta (poa) kii keemat naish santulan mein sabse badee deree aur samagr roop seey sabse chhoti sambhav deree key beach kaa anupaat haye. sthirata kii keemat (sthiti) naish santulan mein "sabse chhoti" deree (arthaath sabse achchha sambhav santulan), aur samagr roop seey sabse chhoti sambhav deree key beach kaa anupaat haye. poa aur pose kii ganana anya santulan avadhaaranaon key sambandh mein bhee kii jaa sakati haye, jaise kii mishrit santulan yaa sahsambaddh santulan.
bheedbhaad vaale khelon key kaee mukhya varg hainh
see. jee. aiss. kaa ack anya vargeekaran khilaadiyon key liye upalabdh ranneetiyon key sett parr adharit haih 
isake alaavaah
paramanu bheed khel.
christodolo aur kautsupias ney paramanu bharheen see. jee. aiss. kaa vishleshan kiya. unhone saabit kiya kii jaba sabhi vilamb kaary raikhik hotey hain tou poa bilkul 2.5 hotaa haye (arthaath poa hamesha adhikatam 2.5 hotaa haye, aur kuchh mamalon mein yeh bilkul 2.5 hotaa haye). unhone poe key liye oopari aur nichali seemaaen bhee deen jaba vilamb kaary seemit degree key bahupad hotey hain. ack anya pepper mein, christodolo aur kautsupias ney raikhik vilamb karyon key saath paramanu bharheen bheed-bhaad khelon key sthiti kaa vishleshan kiya. unhone saabit kiya kii sthiti adhikatam 1.6 haye, aur ack udaaharan dikhaaya jisamen sthiti 1.577 haye. unhone yeh bhee dikhaaya kii iss mamle mein sahsambaddh santulan kaa poa bilkul 2.5 bharheen khelon key liye aur thheek 2.618 vajan vaale khelon key liye haye.
everbooch, ajaar aur appstein ney vishleshan kiye gaye paramanu "bhaarit" see. jee. aiss. kaa vishleshan kiya. unhone saabit kiya kii jaba sabhi vilamb kaary raikhik hotey hain tou poa bilkul 2.618 hotaa haye. unhone yeh bhee dikhaaya kii jaba vilamb kaary degree "d" key bahupad hotey hain, tou poa sootra _ 10 mein hotaa haye.
alland, dumraf, garring, monien aur scopman ney paramanu see. jee. aiss. key liye sateek poa kii ganana kii, vilamb karyon key liye joe adhikatam "dee" degree key bahupad hainh
jaba bhee koee khilaadi ektarafa vichalan dwara apani "apekshit" laagat mein sudhaar naheen curr sakata haye tou vahee seemaaen hoti hain. isaliye, sabse kharaab sthiti mein shuddh naish santulan, mishrit naish santulan, sahsambaddh santulan aur motey sahsambaddh santulan key sambandh mein samaan hain. isake alawa, bharheen aur bhaarit "network" bheed-bhaad vaale khelon key liye seemaaen hain.
bawalkar, garring aur rufguarden vajan vaale see. jee. aiss. kaa vishleshan karate hain, aur yeh dikhaate hain kii laagat karyon key kissy bhee varg key liye poa kii ganana kaise kii jaae (aavashyak roop seey bahupad naheen). way yeh bhee dikhaate hain kii, sweekarya vilamb karyon parr halki paristhitiyon mein, shuddh naish equilibria, mishrit naish equilibria, sahsambaddh equilibria aur motey sahsambaddh equilibria key sambandh mein poa hamesha barabar hotaa haye. way yeh bhee dikhaate hain kii bahupad laagat karyon key saath, sabse kharaab sthiti poa ack saral network parr praapt kiya jaataa haye, jisamen kewal samanantar kinaaron kaa ack sett hotaa haye. way yeh bhee dikhaate hain kii samamit bharheen bheed-bhaad vaale khelon kaa poa hamesha asmamit khelon key barabar hotaa haye.
aage key parinam.
dee-jong aur uetz kramik see. jee. kaa adhyayan karate hain, jisamen khilaadi ack saath apani ranneetiyon koo kramik roop seey chunate hain. way upa-khel poorna santulan key poa kaa vishleshan karate hain. way dikhaate hain kii affine laagat karyon key saath anukramik poa dou khilaadiyon key liye bilkul 1.5 aur teen khilaadiyon key liye ± 2.13 haye, aur chaar khilaadiyon key liye cumm seey cumm 2.46 haye. ekal tunn bheed key liye, jaba n khilaadi hotey hain, tou anukramik poa adhikatam "n"-1 hotaa haye; jaba sootra _ 21 hotaa haye, tou anukramik poa cumm seey cumm 2 + 1/e ± 2.37 hotaa haye.
photakis raikhik-swatantra pathon key saath see. jee. aiss. key poa kaa adhyayan kartaa haye, joe samanantar link kii setting kaa ack vistaar haye.
kaanoon, huang aur liu sangyanatmak radio network mein see. jee. aiss. key poa kaa adhyayan karate hain.
garring, burkhard aur carsten khilaadi-vishisht raikhik vilamb karyon key saath see. jee. aiss. key poa kaa adhyayan karate hain.
mlichtaich paramanu cgs mein pne kii dakshata parr network topology key prabhaav kaa vishleshan kartaa haih
gair-paramanu bheed khel kaa poa.
khurdara garden aur tardos ney gair-paramanu see. jee. kaa vishleshan kiya. unhone dikhaaya kii, jaba vilamb kaary adhikatam "dee" degree key bahupad hotey hain, tou poa sootra _ 16 mein hotaa haye, joe paramanu khelon key poa seey kaafee chhota hotaa haye. vishesh roop seey, jaba "d" = 1, tou poa 4/3 haye; yeh darshaata haye kii raikhik vilamb karyon key liye pigau kaa saral udaaharan sabse kharaab mamla haye.
chau aur sima khurdara udyaan aur tardos key parinamon koo (1) samamit laagat maanchitron parr vichaar karke aur (2) lochdaar maangon koo shamil karke vistaarit karate hain.
koria, schulz aur steer-moos gair-paramanu see. jee. key liye poa parr parinamon key liye ack chhota, jyaamitiya pramaan prastut karate hain. way poe parr majboot seemaaen bhee dete hain jaba santulan laagat nirdhaarit laagat kii uchit seema key bheetar hoti haye.
blum, ivan-daar aur ligate ney dikhaaya kii yeye sabhi poe seemaaen apekshaakrit kamjor vyavhaar sambandhi dhaaranaon key tahat lagu hoti hainh yeh paryaapt haye kii sabhi upayogkarta khel key baar-baar khelane parr ausat afsos koo praapt karate hain.
poa key vishleshan mein ack upayogi avadharana "chiknai" haye. ack vilamb falan "d" koo sootra _ 23 kahaa jaataa haye yadi sabhi sootra _ 24 key liye, sootra _ 25. yadi vilamb sootra _ 23 chikna haye, sootra _ 27 ack naish santulan haye, aur sootra _ 28 ack ishtatam aavantan haye, tou sootra _ 29. dusare shabdon mein, arajakta kii keemat sootra _ 30 haye.
mlitchtich ney nimnalikhit atirikt visheshtaon key saath "singleton" gair-paramanu see. jee. aiss. kaa vishleshan kiyaah
aise khelon mein, santulan bhugtan hamesha advitiya aur pareto-kushal hotey hain, lekin upayogitaon key yog koo adhikatam naheen curr sakate hain. isake alaavaah
splitable congession games kaa poa.
rufguarden aur scopman ney splitable congession khelon kaa vishleshan kiya. unhone dikhaaya kii, jaba vilamb kaary adhikatam "dee" degree key bahupad hotey hain, tou poa sootra _ 35 mein hotaa haye. vishesh roop seey, jaba "dee" = 1, tou poa adhikatam 3/2 hotaa haye. vibhajan yogya khelon key liye poa paramanu khelon kii tulanaa mein chhota hotaa haye, lekin gair-paramanu khelon seey badaa hotaa haye. udaaharan key liyeh
paropkari khilaadiyon key saath poa.
buniyaadi see. jee. model yeh maanata haye kii khilaadi swarthi hain-way kewal apane swayam key bhugtan kii parwah karate hain. vaastav mein, khilaadi paropkari hoe sakate hain aur samajik laagat kii bhee parwah curr sakate hain. yeh yeh maanate hue model kiya jaa sakata haye kii pratyek khilaadi kii vaastavik laagat usaki apani deree aur kull deree kaa bhaarit ausat haye. paropkar kaa pranali kii dakshata parr aashcharyajanak prabhaav parh sakata haih
poa parr paropkar key prabhaav kaa adhyayan karane vaale anya shodh patra hain. dakshata parr paropkar key prabhaav koo maapane kaa ack vaikalpik tarika tulanaatmak sthiti key madhyam seey haih ack hii khel mein (jaruri naheen kii sabse kharaab sthiti mein), paropkar gunank koo badhaana samajik laagat koo kaise prabhaavit kartaa haye? see. jee. aiss. key kuchh vargon key liye, dakshata parr paropkar kaa prabhaav nakaratmak hoe sakata haye. 

