Top products from r/GAMETHEORY

The matching with women proposing would be: m1/w3, m2/w1, m3/w4, m4/w2

This is because in the first round, women will choose different men than vice-versa. You're totally correct that there will also be only one round.

Honestly, this example is really shitty/construed. There are no further rounds/rejections because

• There's no outside option. Every man is acceptable to every woman and vice-versa.
  
• In the first round, every proposer chooses a different man/woman.
  
  An interesting fact of stable two-sided matchings is the following: When men (women) propose, from all possible stable matchings, the one that is best for men (women) materializes. So the interests of men and women are exactly opposing (i.e. what's good for one men is also good for all other men, and bad for all women).
  
  Armed with this fact, we can conclude something else about this problem: Since m4/w2 are matched in both matchings (i.e. best for men and best for women), they are matched in every stable matching. You could also deduce this from the fact that they are each other's first choice, but that statement would hold even if they weren't.
  
  If you want to study this in detail, this is the book to read: https://www.amazon.com/Two-Sided-Matching-Econometric-Society-Monographs/dp/0521437881

As all-pay auctions are standard, you can derive the answer from the revenue equivalence principle.

Under all the usual assumptions and given that a bidder values the item under auction at x, the symmetric equilibrium is

β^AP (x) = ∫(0 to x) y g(y) dy

where g is the probability density of the bidder winning the auction with a bid of y.

I recommend Krishna - "Auction Theory" for more details

Edit: I should make clear what the assumptions for this equilibrium are:

You have n bidders where bidder i values the item at X_i, the X_i are drawn IID from a distribution F. Each bidder only knows n and F, but has no additional information about the X_i (except their own, which they of course know). All bidders are assumed to be risk-neutral, that is, they only want to maximise the expected value they gain out of this auction (value of the item minus price paid)

That's my next book project. =)

That aside, I'd recommend Thinking Strategically and The Logic of Life.

There is some hyperbole in each. The subtitle of Thinking Strategically makes me lol, and half of The Logic of Life is "academics were clueless for decades until an economist looked at the problem for a half hour and solved it." But I enjoyed both of them for what they are.

Edit: I guess my book on bargaining and my book on war are somewhat like that. But the big difference is that Thinking Strategically and The Logic of Life are very light on the actual formalization, whereas mine are not.

I cant speak to your specific problem, but as far as evolutionary game theory goes in general, you only need to know through calculus 3 to be able to solve a problem. Understanding how to test a specific solution to determine if it's an evolutionary stable strategy or not is a bit harder. The idea here is that it's a population that is essentially playing against itself, so some optimal strategies that would generally work in regular game theory don't make any sense in context. And if I remember correctly, there are other optimal strategies that simply aren't stable and are thrown out as well.

With all that said, if your game is bigger than 3x3 you're really going to want to use a computer. It get's tremendously complex.

I learned it from Owen's text: http://www.amazon.com/Game-Theory-Guillermo-Owen/dp/0125311516/ref=sr_1_1?ie=UTF8&qid=1349044502&sr=8-1&keywords=game+theory+owen

for most of the book you need to know up to real analysis but that section didn't require anything over calc III (unless you're trying to follow the proofs).

I had seen "The Art of Strategy" by Dixit and Nalebuff recommended here before, and thought it was a great place to start.

Thinking Strategically is by far the best game theory book for laypeople.

I'd recommend you check out Date-onomics: How Dating Became a Lopsided Numbers Game so that you keep it fresh!

Thinking Strategically by Avinash Dixit and Barry Nalebuff is a good one.

I guess it depends on how deep you want to study Game Theory. My university's Game Theory course (undergrad) uses Game Theory. An Introduction by Steven Tadelis.

Tadelis.

Google for game theory and Cold War or read: https://www.amazon.com/Prisoners-Dilemma-Neumann-Theory-Puzzle/dp/038541580X/ref=nodl_

This SHOCKING story of Trump's inauguration night is my standard response to off topic Trump spam.

https://www.amazon.com/Thump-Trump-Rump-Tea-Bagger-ebook/dp/B01K2E56N4/

Nah. I think I'll just compute it by hand... jk! But thanks! I had never heard of gambit before. I know there is the pivot method where you can use control sums and such, but I always find it to be a pain in the ass on paper.

Edit: And actually, I meant two different things. I watched the playlist, and read this.

http://www.amazon.com/The-Compleat-Strategyst-Strategy-Mathematics/dp/0486251012

Here is the book

http://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB113-1.pdf