Nash Equilibrium Quotes

A Nash equilibrium is a combination of two conditions: i. Each player is choosing a best response to what he believes the other players will do in the game. ii. Each player’s beliefs are correct. The other players are doing just what everyone else thinks they are doing.

Nash’s equilibrium, when it exists, is that point where neither player can do any better, or have no regrets, given what the opponent has done. Neither can have regrets because of how the other person played the game. It may not be the best option for either player, but it’s the best under the circumstances. There isn’t always an equilibrium in a game, or a Nash equilibrium in a game theory matrix. However, if it exists, in many cases the Nash equilibrium is a far better outcome for both players than the von Neumann saddle point. In the Kelley apartment cleaning game-theory matrices above, the Nash equilibrium is for them both to clean. Consider his payoffs. He does much better if he cleans no matter what she decides to do (because 5.7 is much greater than -2.2). Now consider her payoffs. She also does better if she cleans no matter what he does (because 8.5 is much greater than -6.6). So they have a stable Nash equilibrium at the joint strategy = (Male Cleans, Female Cleans). Then neither of them can have regrets about that choice because with that choice neither of them can do any better, regardless of what the partner does. With the Nash equilibrium their strategy is to maximize one’s own gains even if it means maximizing the partner’s gains (as well as one’s own).

Why not simply allow them unlimited vacation? Anecdotal reports thus far are mixed—but from a game-theoretic perspective, this approach is a nightmare. All employees want, in theory, to take as much vacation as possible. But they also all want to take just slightly less vacation than each other, to be perceived as more loyal, more committed, and more dedicated (hence more promotion-worthy). Everyone looks to the others for a baseline, and will take just slightly less than that. The Nash equilibrium of this game is zero. As the CEO of software company Travis CI, Mathias Meyer, writes, “People will hesitate to take a vacation as they don’t want to seem like that person who’s taking the most vacation days. It’s a race to the bottom.

A NASH EQUILIBRIUM is a configuration of strategies where no player can improve his own result by changing his strategy alone.

Consider a guess-the-number game in which players must guess a number between 0 and 100. The person whose guess comes closest to two-thirds of the average guess of all contestants wins. That’s it. And imagine there is a prize: the reader who comes closest to the correct answer wins a pair of business-class tickets for a flight between London and New York. The Financial Times actually held this contest in 1997, at the urging of Richard Thaler, a pioneer of behavioral economics. If I were reading the Financial Times in 1997, how would I win those tickets? I might start by thinking that because anyone can guess anything between 0 and 100 the guesses will be scattered randomly. That would make the average guess 50. And two-thirds of 50 is 33. So I should guess 33. At this point, I’m feeling pretty pleased with myself. I’m sure I’ve nailed it. But before I say “final answer,” I pause, think about the other contestants, and it dawns on me that they went through the same thought process as I did. Which means they all guessed 33 too. Which means the average guess is not 50. It’s 33. And two-thirds of 33 is 22. So my first conclusion was actually wrong. I should guess 22. Now I’m feeling very clever indeed. But wait! The other contestants also thought about the other contestants, just as I did. Which means they would have all guessed 22. Which means the average guess is actually 22. And two-thirds of 22 is about 15. So I should … See where this is going? Because the contestants are aware of each other, and aware that they are aware, the number is going to keep shrinking until it hits the point where it can no longer shrink. That point is 0. So that’s my final answer. And I will surely win. My logic is airtight. And I happen to be one of those highly educated people who is familiar with game theory, so I know 0 is called the Nash equilibrium solution. QED. The only question is who will come with me to London. Guess what? I’m wrong. In the actual contest, some people did guess 0, but not many, and 0 was not the right answer. It wasn’t even close to right. The average guess of all the contestants was 18.91, so the winning guess was 13. How did I get this so wrong? It wasn’t my logic, which was sound. I failed because I only looked at the problem from one perspective—the perspective of logic. Who are the other contestants? Are they all the sort of people who would think about this carefully, spot the logic, and pursue it relentlessly to the final answer of 0?

Objective facts are Nash equilibrium points in the contest of competing wills.

Game theory is about exploring of freedom of choices and the equilibrium which comes from understanding the consequences of freedom. 24 Dec National Mathematics Day

The Nash equilibrium outcome in the nuclear arms race is not Pareto efficient because both countries would be better off if neither engaged in nuclear build-up. However, as Dresher and Flood argued, this couldn’t be an equilibrium. If the USA were to have stopped nuclear build-up, the USSR would have continued building its own arsenal to capture the “super-power” position. And it would not have been rational for the USA to stop nuclear build-up in the first place.

In the arena of love, we arrive at the Nash Equilibrium not by trying to “win” for ourselves but by thinking for two. This is one of the core habits of really successful couples—instead of thinking, What’s best for me in this situation? they’re thinking, What’s best for us?

Usually, when things suck, it’s because they suck in a way that’s a Nash equilibrium.