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Apr 15, 2024

Nash equilibrium

Posted by in categories: economics, entertainment

J. V. Neumann, Zur Theorie der Gesellschaftsspiele, 1928. Proved the existence of equilibrium in 2 players’ zero-sum games.

The birth of game theory.


The modern concept of Nash equilibrium is instead defined in terms of mixed strategies, where players choose a probability distribution over possible pure strategies (which might put 100% of the probability on one pure strategy; such pure strategies are a subset of mixed strategies). The concept of a mixed-strategy equilibrium was introduced by John von Neumann and Oskar Morgenstern in their 1944 book The Theory of Games and Economic Behavior, but their analysis was restricted to the special case of zero-sum games. They showed that a mixed-strategy Nash equilibrium will exist for any zero-sum game with a finite set of actions.[13] The contribution of Nash in his 1951 article “Non-Cooperative Games” was to define a mixed-strategy Nash equilibrium for any game with a finite set of actions and prove that at least one (mixed-strategy) Nash equilibrium must exist in such a game. The key to Nash’s ability to prove existence far more generally than von Neumann lay in his definition of equilibrium. According to Nash, “an equilibrium point is an n-tuple such that each player’s mixed strategy maximizes his payoff if the strategies of the others are held fixed. Thus each player’s strategy is optimal against those of the others.” Putting the problem in this framework allowed Nash to employ the Kakutani fixed-point theorem in his 1950 paper to prove existence of equilibria. His 1951 paper used the simpler Brouwer fixed-point theorem for the same purpose.[14]

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Apr 15, 2024

SpaceX Starbase Update: Upgrades for First Catch with Chopsticks

Posted by in category: space travel

SpaceX NASASpaceflight

Apr 15, 2024

DeepMind’s New AI Saw 15,000,000,000 Chess Boards!

Posted by in category: robotics/AI

DeepMind’s AI system achieved grandmaster-level chess playing ability by learning from playing against itself billions of times, challenging traditional AI development techniques and opening up possibilities for broader applications beyond chess Questions to inspire discussion What is the title of the video? —The title.

Apr 15, 2024

Apple’s Robotics Push Challenges Tesla’s Ambitions

Posted by in categories: Elon Musk, robotics/AI, transportation

Herbert Ong Brighter with Herbert.

Apr 15, 2024

A balanced quantum Hall resistor provides a new measurement method

Posted by in category: quantum physics

Researchers at the University of Würzburg have developed a method that can improve the performance of quantum resistance standards. It’s based on a quantum phenomenon called Quantum Anomalous Hall effect.

Apr 15, 2024

Polaris Dawn is getting closer and closer to being launch ready

Posted by in category: space travel

Things are slowly falling into place for the Polaris Program’s first mission, Polaris Dawn. The mission is nearing milestones that might finally give it a launch date that will actually hold.

Polaris Dawn, a private mission being paid for by Shift4 CEO Jared Issacman, who also paid for and flew on Inspiration4 in 2021. The goal of the mission is to fly higher than any human spaceflight since Apollo, perform the first private spacewalk, and conduct numerous science experiments in orbit.

Like Inspiration4, Polaris is partnering with SpaceX to complete this. Currently, SpaceX is the only company capable of this sort of feat. To do so, the company has modified its Dragon spacecraft to support spacewalk operations and develop an upgraded spacesuit to be used in the vacuum of space.

Apr 15, 2024

Tesla is laying off more than 10% of its workforce, memo shows

Posted by in categories: Elon Musk, sustainability, transportation

Tesla is the latest major company to lay off employees.

The company is eliminating “more than 10%” of staff globally, according to an internal memo sent by Elon Musk on Sunday, which was seen by Business Insider. The layoffs have come shortly after the carmaker posted lackluster delivery numbers.

Musk wrote in the email: “There is nothing I hate more, but it must be done. This will enable us to be lean, innovative and hungry for the next growth cycle.”

Apr 15, 2024

NASA’s New Solar Sail Spacecraft Will Shine So Bright We’ll See It From Earth

Posted by in category: space travel

\r The most recent piece of news on this front comes from American space agency NASA, which announced last week that it is getting ready to launch a new kind of solar sail that may revolutionize such technologies.

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Apr 15, 2024

The Universe Could Be Eternal, According to This Controversial Theory

Posted by in category: space

The idea of a static universe would mean our cosmos is eternal, and it isn’t expanding after all.

Apr 15, 2024

Martin Rees — Why Is There Anything At All?

Posted by in category: futurism

Follow us on X for news, fascinating articles, and discussions with other followers: https://shorturl.at/imHY9

Why is there a world, a cosmos, something, anything instead of absolutely nothing at all? If nothing existed, there would be, well, ‘nothing’ to explain. To have anything existing demands some kind of explanation. Of all the big questions, this is the biggest. Why anything? Why not nothing? What can we learn from the absence of nothing?

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