Equilíbrio de Nash (Uma Mente Brilhante, John Nash): Definição, Explicação & Exemplos em Um Minuto
O que veremos neste artigo:
Neste vídeo, o conceito do equilíbrio de Nash é explicado de forma clara e concisa, utilizando um exemplo prático de estratégia de mercado. O equilíbrio de Nash é um conceito fundamental na teoria dos jogos, nomeado em homenagem ao matemático John Nash, que ficou conhecido pelo filme “Uma Mente Brilhante”.
O Exemplo de Bill e Rachel
No exemplo apresentado, os concorrentes Bill e Rachel vendem limonada por $1 por copo, com vendas diárias de 200 copos cada. Após despesas, ambos obtêm um lucro de $100. Se um deles reduzir o preço, terá que aumentar a quantidade de vendas para manter o mesmo lucro, o que levaria à reação competitiva do outro, resultando eventualmente em um ganho menor para ambos.
A Estratégia de Bill
Bill considera reduzir o preço para 80 centavos, o que aumentaria a quantidade de vendas necessárias para manter seu lucro. No entanto, isso resultaria em uma competição com Rachel, levando a uma redução no lucro de ambos.
A Reação de Rachel
Diante da redução de preço proposta por Bill, Rachel também reduziria os preços, iniciando uma batalha de preços que, no final das contas, resultaria em menor lucro para ambos.
O Equilíbrio de Nash
Nesse cenário, ambos os concorrentes percebem que manter o preço em $1 é a melhor estratégia, evitando uma competição que levaria a um menor lucro para ambos. Esse tipo de situação, na qual cada jogador, tomando as decisões dos outros como fixas, determina as próprias ações, é conhecido como equilíbrio de Nash.
Conclusão
O equilíbrio de Nash é um conceito essencial na teoria dos jogos, demonstrando como os participantes em uma interação estratégica podem chegar a uma situação na qual ninguém tem incentivos para mudar sua estratégia. Ao compreender o equilíbrio de Nash, é possível tomar decisões mais informadas em ambientes competitivos.
FAQ
O que é o equilíbrio de Nash?
O equilíbrio de Nash ocorre quando os participantes de um jogo interativo escolhem suas melhores estratégias, levando em conta as estratégias dos outros participantes, sem ter incentivos para mudar suas decisões.
Qual é a importância do equilíbrio de Nash na teoria dos jogos?
O equilíbrio de Nash é crucial na compreensão de situações competitivas e estratégicas, ajudando a prever as decisões dos jogadores e a entender as possíveis dinâmicas de competição e cooperação.
Fonte: O equilíbrio de Nash (Uma Mente Brilhante, John Nash): Definição, Explicação & Exemplos em Um Minuto
Hi loved your content, though I had a question. How do I differentiate between a case of Nash Equilibrium, prisoners dilemma and Game theory, I seem to have trouble doing that. Thanks
This is almost certainly happening with traditional retail as trading conditions are so volatile
And there is a Cartel!!
Can you make a video on Coase theorem?
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Exactly what the multibillion dollar industry are doing. Best example is 30% commission taken by Apple & Google on AppStore & PlayStore. Same in almost all gaming marketplace like Steam & GOG. Only when some new guy comes along and cuts down the cost, say Epic Games Store charging 12% instead of the Industry standard 30% set by the giants themselves, then these guys get angry.
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Like neighboring gas stations
o.O?? That's normal though. The market has a natural deflationary effect, everyone and their grandmother knows this. It's a natural part of the business cycle. Hollywood literally made an entire movie to promote market collusion as some high minded math equation?
Yet the US 2 party system argues 2 parties are enough to compete and offer the public what it wants.
If there was multiple parties like in Europe, then yes, they would have to compete to make the best offer to what the public wants. But, that's exactly what trying to be prevented.
It’s illegal for companies to collude to set prices with their competitors
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It sounds so simple, but everyone thinks they can beat the Nash Equilibrium. That's what really drives prices to where they are.
If Bill knows that Rachel will follow his pricing scheme, then they're not actually competing. It could be just as easily said that he could raise his price to $100 per glass of lemonade, and make 100 times more money because then Rachel would do the same.
The real calculation of equilibrium involves how much more or less lemonade would be sold at different prices. If lemonade is very expensive, less lemonade will be sold overall (consumers will opt for water). If lemonade is very cheap, more lemonade will be sold (consumers will be able to afford more, and choose lemonade over other beverages).
If Bill and Rachel are truly competing, and consumers have no reason to prefer one seller to another (i.e. every single consumer would only purchase from the seller who offered it cheaper), the sellers would both lower their prices to one cent above the price at which it would become not worth their time to produce and sell it. That's the equilibrium.
Here's the translation:
Thank you for your video. I believe it's important to emphasize that the Nash equilibrium of that problem (Bertrand Competition) is to have no profits and produce at cost price (https://en.wikipedia.org/wiki/Bertrand_competition). I think what you present as NE at the end of the video can be confusing for beginners.
You will play the following game with your classmates who are taking this exam at this moment: In the box provided below, you will write an integer from 0 to 100. (You can write 0 and 100.) The top-5 students with highest 5 numbers will earn bonus points according to the following formula: If a top-5 student’s number is 𝑥, he gets 100 − 𝑥 bonus points. To be precise, this is how I will proceed: I will order the integers written in the boxes. Let it be as follows: 𝑥1 ≥𝑥2 ≥𝑥3 ≥𝑥4 ≥𝑥5 ≥𝑥6 ≥⋯≥𝑥𝑛 • A student who has written a number 𝑥𝑖 > 𝑥6 is a winner. He earns 100 − 𝑥𝑖 bonus points. Remaining students earn no bonus points. So, write down your number in the box provided below. Note: In this question, a student can earn at most 30 bonus points. So, even if you earn 30+ bonus points, you will still get 30 bonus points. Also, if you do not write a number, I will assume that your number is 0.
The narrative of this content is impactful. A book with akin themes was transformative beyond words. "Game Theory and the Pursuit of Algorithmic Fairness" by Jack Frostwell
I have a feeling this was greatly simplified.