Thinking Strategically is by far the best game theory book for laypeople.
Games, Strategies, and Decision Making
It's a really verbose textbook, and it sounds like the author is talking to you as a friend (if that's what you like).
You can find the section that I took a picture of in the Amazon "look inside."
Bargaining under asymmetric information. There is no single canonical model because there are many variations on this. Samuelson is one of the classics https://www.researchgate.net/profile/William_Samuelson/publication/4895364_Bargaining_Under_Asymmetric_Information/links/558d3f3308aee43bf6aefb74.pdf
But many new techniques dealing with continuous time have shown more tractable results.
Basically, there isn't a single framework that's used.
Predictably Irrational by Dan Ariely and A Beautiful Math by Tom Siegfried are both good and fun. The first is about behavioral/experimental economics which is rooted in game theory and the second is sort of a survey in a bunch of different ways in which game theory is used throughout economics as well as other subjects like biology. Both are what I would sort of call pop-nonfiction in the spirit of Malcolm Gladwell or Freakonomics, etc.
Thinking Fast and Slow by Daniel Kahneman and Nudge by Richard Thaler are both excellent but bit more psychology/behavioral in nature but certainly share a lot of the same themes as game theory.
How technical do you want to get? Thinking Strategically by Dixit and Nalebuff is a good introduction if you're looking for something that's applied and relatively nontechnical. Games and Decisions by Luce and Raiffa is fairly nontechnical as well (it's part of a collection of similar looking mathematical books that you might sometimes see in the math and statistics section of a bookstore), and I've actually found it to be very useful. Martin Osborne is very well known in this field, and he has a more comprehensive and more advanced book called A Course in Game Theory, though I know that some people aren't particularly fond of it's clarity and organization. Would link to Amazon but I'm on my phone. Hope that helps.
I think a heavy math approach is almost certainly the opposite of what you are looking for, likely something more general would apply best to the thinking from the article (which is a bit flimsy in its game theory understanding). My favorite text has been https://www.amazon.com/Game-Theory-Evolving-Problem-Centered-Introduction/dp/0691140510/ref=nodl_?dplnkId=58700dc0-416b-4248-9009-92e9341d2f63
There are lots of ways to approach game theory, so pick a reputable text that provides the types of examples you are looking for and dive in!
I actually took a course on this before since my degree is in economics. It's more geared to the behavior of firms and market structure rather than engineering democracy and governance of societies. But I found a book and a video series that look more geared to the type of knowledge I'm trying to acquire. Mechanism design seems to be the most relevant branch of knowledge so far. Probably some specific sections of quantitative political science as well.
Lecture series on mechanism design:
https://www.youtube.com/watch?v=BYjhJTXs65Y&list=PLcrc6i6xwaQQWi7prJYkI9SoRzDXEV01X
Book on political models:
https://www.amazon.com/gp/product/1108741916/ref=ewc\_pr\_img\_1?smid=ATVPDKIKX0DER&psc=1
This is sort of a tough question that I am not an expert on but it is a field of research I am trying to break into. I'll try to explain what I've learned so far. One of the issues with coordination games is equilibrium selection. If we take a look at the battle of the sexes game, there are two pure strategies and a symmetric mixed strategy. If people were actually playing this game, having three different predictions of play are not very useful when it comes to the ultimate goal of getting both people to show up at the same event.
There are a lot of techniques for trying to select equilibria (Harsanyi and Selten have a great book on this) but for a lot of games, they don't provide particularly good solutions. It turns out, one way of creating a unique equilibrium is by introducing private information. This is where the issue with common knowledge comes in. If players know the exact payoffs of every one else, they end up with multiple possible Nash outcomes. If they don't know what their fellow players' payoffs are (or receive a noisy signal about it), they base their actions on private info and deduced probability distributions. It turns out that given a sufficient amount of private information, the game can result a unique equilibrium.
The math for why this is true is quite complicated but I can direct you to a paper that answers your exact question (with regard to supermodular games although it likely extends to other classes). It is not an easy paper by any measure but Hellwig (2002) (link to science direct below) does explain it. If you are moderately comfortable with normal distributions, section 4, which provides the argument for why private info selects an equilibrium when common knowledge can't, is not too tough (although it is not as "simple" as he claims it is).
http://www.sciencedirect.com/science/article/pii/S0022053102929479
I listened to (only audio, but video format would be recommended as he sometimes would refer to graphs that I couldn't see!) the course "Games People Play: Game Theory in Life, Business, and Beyond" a few years ago. I found it highly enjoyable and there were certainly a lot of real-life examples. I remember that I liked the lecturer's general intellectual "style", if that makes any sense.
https://www.thegreatcourses.com/courses/games-people-play-game-theory-in-life-business-and-beyond
I wrote Game Theory 101 (and recorded its corresponding YouTube playlist) specifically for the non-mathematically inclined audience.
https://www.amazon.com/Game-Theory-101-Complete-Textbook/dp/1492728152
I'm like 95% confident that's correct.
I would check out this pdf of Fudenberg and Tirole's book and see if it meets your needs. It was basically my go-to text in Grad School. It would definitely suffice for a upper-division or grad level course.
https://homepage.univie.ac.at/Mariya.Teteryatnikova/WS2011/FT.pdf
Note that this link triggers a download of the following book: https://www.amazon.com/Game-Theory-Press-Drew-Fudenberg/dp/0262061414
A book focusing on game theory is The Mathematics of Poker. It uses simplified games to develop strategic principles, because game theory for full poker is really complicated.
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.
I wouldn't qualify the following as "case studies" but a lot of real-world situations are highlighted in the book "Thinking Strategically". I don't have my copy on hand, but it could be a good starting point? The book highlights situations utilizing game theory from the late 80s, so it's possible a few of the highlighted examples could be explored a bit more online. Hope that helps you a bit!
Binmore is a great writer. I learned GT from his textbook (different book, not good for starting out though).
I also like Thinking Strategically (there is a revised version with a new title) by Nalebuff and Dixit.
Any opinions on these two texts?
That book isn't bad. As a math major, you may like this more
http://www.amazon.com/Introduction-Game-Theory-Martin-Osborne/dp/0195128958
I like Binmore, but it's not the most straightforward, though it has more mathematical proofs than others. The most concise is Gibbons. It's graduate level but nothing in it would be hard for a math major.
This is a little too simplified for magic but gets at the idea certainly. You're right, this Magic would be classified as a sequential Bayesian game. Where your example is similar is a situation in magic in which you want to know whether your card can be countered or not. If you don't know what your opponent is holding then you can't know whether you need to play a bait card or you should go ahead and play the card you really want to play. But if you can look into your opponents hand and see that they do in fact have a counter card, do you play the bait card hoping they counter it or play the card you don't want countered for the sake of not losing tempo. Clearly it's not easy to model.
I've been looking into a book to get some ideas on modeling more complicated games and this book came to my attention. Do you know about this book at all? I am a senior undergrad math student, so I think it might be understandable enough. The sample pages were, but I'm sure it will get more complicated.