ALGORITHM MASU SANYA FARASHI SUNA HAƊA BAKI — BA TARE DA YI WA JUNA BARAZANA BA

Ana ƙara miƙa sanya farashi ga tsarin koyo. Wani sanannen bincike yana damun hukumomin gasa: shirye-shiryen koyon ƙarfafawa (reinforcement learning) masu sauƙi, kowanne an horar da shi kawai don ƙara ribarsa a cikin kasuwar kamfanoni biyu da aka kwaikwaya, suna ƙarewa da cajin farashin da ya wuce matakin gasa sosai. Wani babban bincike na 2020 na Emilio Calvano da abokan aikinsa a cikin American Economic Review ya ci gaba. Bayan tilasta wa shiri ɗaya ya rage farashinsa na lokaci ɗaya, sun ga abokin hamayya shi ma ya rage, sannan duka biyun suka koma tsoffin farashinsu. Sun fassara wannan a matsayin “tsarin lada da hukunci”: ka rage farashi a kaina zan rama, don haka yaudara ba ta taɓa biya.

Wannan fassarar, in ji Kauê Lopes de Moraes da Rodrigo De Losso na Jami’ar São Paulo, ita ce ta ba sakamakon nauyinsa a fagen manufofi. “Farashin da kawai ya yi sama abin ƙirƙira ne; farashin da ake karewa ta ramuwa cartel ne.” Tambayarsu taƙaitacciya ce: shin akwai tsarin hukunci a zahiri?

A fara maimaitawa, sannan a daskare

Marubutan sun sake gina kasuwar Calvano: kamfanoni biyu, farashi 15 masu yiwuwa, kowane shiri tebur ne na ƙimomi (tabular Q-learning) wanda ke tuna farashi biyu na baya — yanayi 225 masu yiwuwa. Sun horar da nau’i 1,024, matakai miliyan 2 kowanne. Sakamakon ya maimaitu: farashi suna daidaita a ma’aunin haɗa baki (collusion index) na 0.668, inda 0 shi ne farashin gasa (Nash) 1 kuma farashin mallaka ɗaya (monopoly).

Haka ma sanannen tsarin. Tilasta wa wakili ɗaya ya rage farashi, kuma a cikin nau’i 1,013 daga cikin 1,024 farashin abokin hamayya yana faɗuwa; a cikin kashi 98.2% na nau’ikan duka biyun suna komawa farashinsu na baya, yawanci cikin lokuta biyar.

Sannan muhimmin mataki: daskare shirye-shiryen da aka horar, kashe koyo, sannan a gwada abin da suke ɗauke da shi a zahiri.

Farashi bayan tilasta ragewa (sama) ko tilasta ɗagawa zuwa farashin mallaka ɗaya (ƙasa), ga nau’ikan da aka horar (hagu) da kuma ga wakilan da aka haɗa da baƙi (dama). — Hoto na 3, Lopes de Moraes da De Losso (2026), arXiv:2610.21867.

Bincike biyar, babu mai hukuntawa

Hanya ba ta da muhimmanci. Tilasta wa wakilin ya ɗaga farashinsa zuwa matakin mallaka ɗaya — motsi zuwa cartel — kuma abokin hamayya har yanzu yana rage farashinsa sannan ya farfaɗo, a cikin nau’i 960 daga cikin 1,024. Martanin da ke ɗaukar haɗin kai daidai kamar cin amana ba ƙa’ida ce da aka tsara don hana cin amana ba.

Babu samfurin abokin hamayya. Ka haɗa wakilan da aka horar da abokin hamayya da aka rubuta wa rubutu wanda yake hukuntawa da gaske — yana haɗa kai har sai an ci amanarsa, sannan ya yi farashin gasa har abada. Idan aka fara cikin haɗin kai, kashi 77% na wakilai suna rage farashi a kansa cikin lokuta huɗu kuma ba sa farfaɗowa.

Babu dabara a wajen hanyar da aka saba. Idan aka karanta su a matsayin ayyukan martani (reaction functions), teburorin da aka koya da ƙyar suke bin martani mafi kyau masu ma’ana (matsakaicin alaƙar matsayi 0.18, daga −0.70 zuwa 0.84).

Komawar tilas ce. A cikin nau’i 914 daga cikin 1,024, shirye-shirye biyu da aka daskare suna da abin jan hankali (attractor) guda ɗaya wanda ke jawo dukkan yanayi 225 masu yiwuwa. Suna komawa farashinsu na yau da kullum daga ko’ina, bayan kowace damuwa, saboda kowane dalili — kamar yadda ƙwallo ke birgima ta koma ƙasan kwano. Teburorin bazata suna yin haka ƙasa da kyau sosai, don haka horo yana ƙara sauri da wuri; amma ba zaɓi ba.

Ba iyakar tsarin ba ce. Marubutan sun gina da hannu ƙa’idojin hukunci na gaske — ɗaya mai yafewa, ɗaya wanda ba ya mantawa — a cikin teburin 225 × 15 ɗin nan ɗaya. Duka biyun suna aiki. Iyawar tana nan; koyo bai yi amfani da ita ba.

Al’adar nau’in biyu

Na gaba, gwajin “baƙo”. Ka haɗa wakili da ɗaya daga wani zagaye na horo daban, ƙa’ida ɗaya, ba su taɓa haɗuwa ba: ma’aunin haɗa baki yana faɗuwa daga 0.669 zuwa 0.134 — rushewa ta kashi 80%, tare da kashi 7.4% na haɗe-haɗe suna sanya farashi ƙasa da matakin gasa. Har ma nau’ikan da suka daidaita a farashi ɗaya suna warwarewa. “Haɗa baki a cikin wannan yanayi ba dabara ce da wakili yake da ita ba; al’ada ce da nau’i biyu ke kiyayewa.”

Ma’aunin haɗa baki tare da abokin horo (shuɗi) da kuma tare da abokin da ba a taɓa gani ba (lemu): 0.669 idan aka kwatanta da 0.134. — Hoto na 7, Lopes de Moraes da De Losso (2026), arXiv:2610.21867.

Kaucewar da babu wanda ke gwadawa

Marubutan sun tabbatar da binciken Calvano na kansa: rage farashi na lokaci ɗaya ba ya biya a cikin kashi 92% na nau’ikan. Amma wannan kaucewa ce ta wauta. Lissafa dabara mafi kyau mai yiwuwa gaba da kowane abokin tarayya da aka daskare, ta hanyar dynamic programming daidai, yana ba da ƙarin riba ta kashi 17.5% a matsakaici (har zuwa kashi 93.7%). Wakilai 124 kawai daga cikin 2,048 ne suke riga suna yin martaninsu mafi kyau. “Tsarin yana hana kaucewar da babu mai inganta riba (optimizer) da zai zaɓa kawai.”

Me ya sa? Yayin da bincike (exploration) ke dushewa a lokacin horo, kowane nau’i yana ziyartar ƙunƙuntar hanyar yanayi kawai. Duk sauran abubuwa a cikin teburorin suna kasancewa kusan ba a horar da su ba. Marubutan suna kiran sakamakon daidaito mai tabbatar da kansa (self-confirming equilibrium) — imanin da ke daidai a kan hanyar da aka bi kuma ba a taɓa gwada su a wajenta ba. Tace grid ɗin farashi daga matakai 15 zuwa 200, wanda ke yaɗa horo ɗaya a kan ƙarin yanayi, yana rage ma’aunin haɗa baki daga 0.64 zuwa 0.23, kamar yadda wannan hoton ya yi hasashe. Tare da nau’i 5 da aka horar daidai bisa ƙa’idar tsayawa ta Calvano, kowane sakamako yana tabbata, kaucewar mai riba tana raguwa zuwa kashi 10.4%.

Farashi har yanzu sama, magani daban

Matsalar masu saye ba ta tafi ba: farashi suna kasancewa sama da gasa sosai. Abin da ya canza shi ne ganewar asali. Marubutan suna jayayya cewa, ba tare da barazanar da ke dogara da yanayi ba, waɗannan nau’ikan ba su dace sosai da rukunonin shari’a irin na yarjejeniya ba — kuma dagula haɗe-haɗen (sabon mai shiga kasuwa, juyawa, sake horarwa) yana lalata haɗin kan shirye-shiryen da aka daskare. Suna kuma ba da gwaje-gwajensu a matsayin ma’auni kafin tura kowane tsarin sanya farashi. Iƙirarinsu ya shafi tabular Q-learning a cikin wannan kasuwa ɗaya kawai; ko wakilan koyon zurfi (deep learning) suna koyon barazana na gaske tambaya ce da aka gina ƙa’idarsu don ta amsa, ba don ta ɗauka ba.