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Game Theory is Impossible Without These 5 Things
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- Опубліковано 17 сер 2024
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🔍 Ever wondered how our actions and decisions can be explained through mathematics? 🤔 Dive into the fascinating world of Game Theory with our latest video! 🎥✨
From the gambling days of the Renaissance with Gerolamo Cardano 🎲 to the breakthrough ideas of Blaise Pascal and Christiaan Huygens, we explore the birth of probability theory and its significance. Discover how calculating dice probabilities led to solving real-life problems! 📊🧠
Fast forward to the 20th century, where John von Neumann’s minimax theorem revolutionized zero-sum games like chess ♟️, paving the way for the famous Nash Equilibrium. Learn how strategic thinking can help you maximize gains and minimize losses! 📈💡
We’ll also unravel the mystery of utility theory, where John von Neumann and Oskar Morgenstern showed us how to rank preferences and make rational decisions under uncertainty. 🤓📚
But wait, there’s more! The Prisoner’s Dilemma 🕵️♂️🔗 demonstrates how rational choices can lead to worse outcomes for everyone. Discover how strategies like "Tit for Tat" can foster cooperation over time.
Perfect for students, math enthusiasts, or anyone curious about strategic decision-making, this video breaks down complex concepts into easy-to-understand insights. 📚💡
Join us on this journey through the evolution of Game Theory and see how it impacts our everyday decisions. Click to watch and level up your strategic thinking! 🚀🧠✨
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The way you go from a lecture style monologue to a short back and forth conversation feels a bit awkward. However, great format of video with the whole 'these things helped create (math field)' i loved this video overall, fantastic content
@@FishSticker thanks, truly, especially for the constructive criticism. The next video will still have these “awkward conversations” you talked about because we did not have time to change it, but since many people told us this, we are thinking about (starting from next week) presenting the content while looking at the camera and talking directly to the audience. What do you think about it?
You don't have a 2/3 chance of winning first to three if you already won two, you have a 1/2 chance of winning the next one, then a 1/4 chance of losing the next one, then winning the one after that, giving you a 3/4 chance.
Your math forgets that you ignore the fact that if you win the next game, there're two scenarios, one where you win the one after that and one where you lose, which ultimately don't change whether you won, first to three, but should be included in the count
Thanks for your comment! Let's clarify the probability of Player A winning the "best of five" series after already winning two games.
If Player A has won 2 games and Player B has won 1 game, Player A just needs one more win to take the series. Assuming both players have a 50% chance of winning any given game, the probabilities break down like this:
Player A wins the next game (4th game) and wins the series: 50% chance.
Player A loses the next game but wins the one after that (5th game): 25% chance (50% for losing the 4th game and 50% for winning the 5th game).
Adding these up, Player A has a 50% + 25% = 75% chance of winning the series.
So, with equal chances of winning each game, Player A indeed has a 75% chance of clinching the series after already winning two games. Hope this clears things up!
@@dibeos Sorry, you think you're teaching me something, I understand entirely. 75% is 3/4, not 2/3
Sorry about that! You are right. Now I see my mistake.
@@dibeos It's okay, it happens to us all
The application is in evaluating the practicality of law and ethics, The prisoners dilemma played out over unknown number of games tit for tat prevents psychopathic betrayal strategies from winning but it requires remembering the person, so one time interactions with anonymity psychopathy is the winning strategy but with modern technology of DNA evidence and cameras and forensic techniques and statistical pattern recognition and internet surveillance these it is significantly exponentially harder to get away with this as opposed to olden times where you could out smart people and skip town or elude the navy on the open seas as a pirate, basically tit for tat is the way to prevent psychopaths from stealing and murdering everyone because you can in general have a better quality of life working in a cooperative game system of society as long as it rewards contribution proportionally and is consistent and clear without hypocrisy or arbitrary whims and too difficult to trick/con the other players.
@@victorrolston6892 Thank you for such an insightful explanation! Your point about the importance of remembering individuals in tit-for-tat strategies and the impact of modern technology on enforcing ethical behavior is the coolest part in my opinion! 😎
I'm curious about your thoughts on the limitations of such technologies: Are there any scenarios where psychopathic strategies might still prevail despite these advancements? And also, how do you think societies can ensure that cooperative systems remain fair and transparent, especially in the face of ethical dilemmas? 🧐
@@dibeoswell there are ways to be anonymous with tor and privacy coins so people can still get away with stealing with crypto scams or blackmail, also you can trick people into believing you are doing them a service like con artistry tricking elderly to by cheap jewelry or false or manipulative advertisement to buy nonsense or if you are big enough manipulating credit and investments to over sell or falsify rates and ponzi schemes or pyramid schemes, basically there are cracks in our systems where these strategies can win in limited ways because of weaknesses in technology, law, financial, human psychology, etc. As for "fair" contracts this gets complicated but consistency and promotionate compensation are some of the things most can abstractly agree on and balanced unbiased enforcement of the rules, and transparency of rules and contacts and decisions seems important I, don't know about specifics maybe every public official while working is recorded with video uploaded to public access and audited from congressman to mayor to judges to police etc, and all contracts individuals to corporations on a public ledger like a blockchain, and all systems and laws are more open and clear with easier feed back like an open source software system with elected officials like administrators, etc I am mainly spit balling ideas also voting systems that are more representative like single transferable vote, and less arbitrary tax systems that are so complicated maybe a flat income tax with and land value tax and a value added consumption tax, also so basic decency and respect on some basic rights like sovereignty over one's body being paramount along with right to speech, defending one's self, privacy, property, speedy unbiased public trial, innocent until proven guilty, etc not having these under consistent attack and being undermined would be nice.
@@dibeoswell there are ways to be anonymous with tor and privacy coins so people can still get away with stealing with crypto scams or blackmail, also you can trick people into believing you are doing them a service like con artistry tricking elderly to by cheap jewelry or false or manipulative advertisement to buy nonsense or if you are big enough manipulating credit and investments to over sell or falsify rates and ponzi schemes or pyramid schemes, basically there are cracks in our systems where these strategies can win in limited ways because of weaknesses in technology, law, financial, human psychology, etc. As for "fair" contracts this gets complicated but consistency and promotionate compensation are some of the things most can abstractly agree on and balanced unbiased enforcement of the rules, and transparency of rules and contacts and decisions seems important I, don't know about specifics maybe every public official while working is recorded with video uploaded to public access and audited from congressman to mayor to judges to police etc, and all contracts individuals to corporations on a public ledger like a blockchain, and all systems and laws are more open and clear with easier feed back like an open source software system with elected officials like administrators, etc I am mainly spit balling ideas also voting systems that are more representative like single transferable vote, and less arbitrary tax systems that are so complicated maybe a flat income tax with and land value tax and a value added consumption tax, also so basic decency and respect on some basic rights like sovereignty over one's body being paramount along with right to speech, defending one's self, privacy, property, speedy unbiased public trial, innocent until proven guilty, etc not having these under consistent attack and being undermined would be nice. But I know this is a math channel but I don't know a way to specify use math to accomplish this but maybe I could answer your question better with a specific dilemma to solve.
@@dibeos This is getting off topic of your channel of math but there are plenty of ways these strategies persist in conartisty, cryptoscams, the dark web, legal loopholes, double standards, etc. Also could you give me specific ethical dilemma's to respond to other wise my answer is just a generic use of technology to be transparent with camera's and open debate in decisions, independent freelance media, ensuring representation and philosophy of open source and consistency and easy access to voting and records automatically made public, and ranked choice voting and less gaming systems like gerrymandering and minimum sentencing, ridiculous case law, qualified immunity, lobbyist bribery, etc. If you want you could talk about theoretical applications of math for building systems to accomplish this like cryptography, blockchain records, cloud storage, signal transmission fast fouier transform algorithms, Quantum computing and quantum cryptography, single transferable vote, etc.
Never change. Thanks for the free education ❤
@@alextrebek5237 you’re welcome, Alex!!! 😎
I got a physics question unrelated to the video. Can we call the gradient of a scalar point function as a vector derivative of that function with respect to space.
@@hazimahmed8713 Yes, we can call the gradient of a scalar point function a vector derivative of that function with respect to space. In physics and mathematics, the gradient of a scalar field φ(x,y,z) is a vector field that points in the direction of the greatest rate of increase of the scalar field, and its magnitude is the rate of increase in that direction. Mathematically, the gradient is represented as:
grad(φ) = ( ∂φ/∂x, ∂φ/∂y, ∂φ/∂z )
This vector is often referred to as the "vector derivative" of the scalar field with respect to spatial coordinates 😎 pretty cool, huh?!
Yay)
My one of most rubrik)
Firstly I love the song from start)
Secondly when you were in game, it was little laugh, bc is cool
And when you two not independently say 'If you like this video, like and subscribe" I laugh of cute)
I love this video, thanks, it was great!)
Love y'all, and your content, never stop going!)
You the best, you going by your path, I never see this type of video content!)
Thanks to reading it❤!)
I don’t think this format works. It looks like you are lecturing to your partner. Better to have both presenting with each speaking different paragraphs. But the content quality is great.
@@user-wr4yl7tx3w thanks for the constructive criticism, really. We decided to keep this format just for the next video but after that we will change it. Let us know then if it is better 😎
@@dibeos I personally love this format and I think you deserve many more subscribers!!! Anyway the topics themselves are very interesting so I guess the form in which you present them doesn't matter that much.
@@b1akk-b7p thanks, really. Yeah the format is important but I think the main focus must be in the content itself. If people are learning something from it (including Sofia and I in the process of researching and making the video) then all of that is worth it! 😎
Nah it’s fine the format works
@@B-0-K-1 yeah, that’s a great suggestion! Thanks for taking the time to tell me us how to improve that ;) we will eventually get to a PERFECT format! 😎
Video molto interessante. Ho un paio di suggerimenti:
Per utilizzare il metodo Socratico, Luca, dovresti essere tu a fare domande a Sofia, portandola a raggiungere le conclusioni del video.
Ad esempio avresti potuto cominciare chiedendo perchè la probabilità che esca croce per il tiro di una moneta è 50%. Da lì, dopo qualche altra domanda Sofia poteva arrivare alla probabilità dei dadi.
Per mostrare i limiti dell'approccio, le potresti fare qualche domanda che la guidi alla scoperta dell'equiprobabilità, ad esempio, non ho una probabilità su tre di battere Magnus Carlsen a scacchi.
@@thedude882 you’re right (I’m answering in English just because the channel is in English), indeed we are working on fixing it! Thank you for the comment! Next video will be more aligned with the Socratic Method (let us know in the comments your thoughts 😉) 😎
@@dibeos thanks guys, I don't want to come across as too negative though! I like your energy and passion and the production value is incredible. The videos are incredibly informative and precise. My background is in math as well, and oftentimes, when I watch these videos, I always find small imprecisions. Never happened with your channel so far.
@@thedude882 we sincerely see these kinds of comments as something positive. We’re trying to find our space on UA-cam so we welcome any constructive criticism. Please, keep on commenting and pushing us to improve our content more and more!
Love your work but clickbait title implies you will use TTT rhetorical strategy in presentation at some point--which you don't.
Easily fixed tho--think of this as a chance to make a vid that does that.
I encourage you nonetheless, the math content continuity is excellent
Such an important poinr at (8:00) that those numerals used really aren't magnitudes--more like program stubbs?
UTILITY THEORY'S PURPOSE IS TO HELP MATHVOLK THINK ABOUT HAPPINESS;--its not really to quantify it
Especially loved ghosthead imagery in prisoner dilemma explanation--such a pungent point! (Ye scoundrel, arr!🏴)
i am going to play gambling after learning game theory
@@Satisfiyingvideo-uu9pw yeah, let’s say your chances of winning just increased after watching this video 😎 (but I will want my share of it!)
@@dibeos by the way please give a video about unsolvabality of quintic formula
Unless you're the bank, you'll find that your expected win is negative. At least if you use money as the utility function.
@@__christopher__ why “unless you’re the bank”?