Nash equilibrium | Hacker News Reader

Nash equilibrium

en.wikipedia.org

20 pointsmilhouse13376 comments

Recently I've read an answer on Quora about why some shop say that they have guaranteed lowest prices. It turns out that the price is probably higher than the actual price, and that's a sign that other shops should follow them, set the same "high price", otherwise, that shop will lower the price and no one win. It's a good read, unfortunately, I can't find the link now.

Any suggestion for a good comprehensive book on game theory in economics?

The problem with game theory is it does not take into account human psychology and often assumes everyone has perfect knowledge. Some people will buy from the lowest priced shop even when they know they could have bought at the guaranteed price shop instead. They will knowingly walk straight past the guaranteed shop. Why? Because they are shy about asking for the lower price and do not want to make a fuss. So to avoid any possibility of conflict they made a longer and less convenient journey. Someone else might be cynical and avoid the guaranteed priced shop because they think these statements mark out the shop as underhanded. People are not always rational and do not have perfect knowledge.

I suggest you read Camerer's Behavioral Game Theory or even a book on Evolutionary Game Theory, the former does take psychology into account and the latter allows for learning. A standard game theory book also consider imperfect information, e.g. Bayesian games. The most comprehensive game theory text is probably the one by Maschler and Solan.

A fascinating related concept is incentive compatibility (one of his variants use the Nash equilibrium).

  « A mechanism is called incentive-compatible (IC) if every participant can achieve the best outcome to him/herself just by acting according to his/her true preferences. »

https://en.m.wikipedia.org/wiki/Incentive_compatibility

I use this mind tool very frequently being an incentive system architect.

One interesting technology that allow IC is the vickrey auction.

This can actually be used in all parts of life. The struggle is building the model around the problem you are trying to solve. The good news is the more you do it the more you can apply it to different situations. It’s been really useful in my web dev career. Resolving conflicts between business and technical requirements. I sometimes feel like this is the mathematical model for some of the philosophical teachings of Buddha.

One of the most remarkable thing to me is Nash's proof of the equilibrium.

The whole thesis is about 27 pages and the proof itself is 7/8 pages (double spaced) and use basic linear algebra. Even though it extends a previous result from Von Neumann (where N=2) significantly.

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