Reddit mentions: The best game theory books

You are in a very special position right now where many interesing fields of mathematics are suddenly accessible to you. There are many directions you could head. If your experience is limited to calculus, some of these may look very strange indeed, and perhaps that is enticing. That was certainly the case for me.

Here are a few subject areas in which you may be interested. I'll link you to Dover books on the topics, which are always cheap and generally good.

• The Nature and Power of Mathematics, Donald M. Davis. This book seems to be a survey of some history of mathematics and various modern topics. Check out the table of contents to get an idea. You'll notice a few of the subjects in the list below. It seems like this would be a good buy if you want to taste a few different subjects to see what pleases your palate.
  
  
• Introduction to Graph Theory, Richard J. Trudeau. Check out the Wikipedia entry on graph theory and the one defining graphs to get an idea what the field is about and some history. The reviews on Amazon for this book lead me to believe it would be a perfect match for an interested high school student.
  
  
• Game Theory: A Nontechnical Introduction, Morton D. Davis. Game theory is a very interesting field with broad applications--check out the wiki. This book seems to be written at a level where you would find it very accessible. The actual field uses some heavy math but this seems to give a good introduction.
  
  
• An Introduction to Information Theory, John R. Pierce. This is a light-on-the-maths introduction to a relatively young field of mathematics/computer science which concerns itself with the problems of storing and communicating data. Check out the wiki for some background.
  
  
• Lady Luck: The Theory of Probability, Warren Weaver. This book seems to be a good introduction to probability and covers a lot of important ideas, especially in the later chapters. Seems to be a good match to a high school level.
  
  
• Elementary Number Theory, Underwood Dudley. Number theory is a rich field concerned with properties of numbers. Check out its Wikipedia entry. I own this book and am reading through it like a novel--I love it! The exposition is so clear and thorough you'd think you were sitting in a lecture with a great professor, and the exercises are incredible. The author asks questions in such a way that, after answering them, you can't help but generalize your answers to larger problems. This book really teaches you to think mathematically.
  
  
• A Book of Abstract Algebra, Charles C. Pinter. Abstract algebra formalizes and generalizes the basic rules you know about algebra: commutativity, associativity, inverses of numbers, the distributive law, etc. It turns out that considering these concepts from an abstract standpoint leads to complex structures with very interesting properties. The field is HUGE and seems to bleed into every other field of mathematics in one way or another, revealing its power. I also own this book and it is similarly awesome. The exposition sets you up to expect the definitions before they are given, so the material really does proceed naturally.
  
  
• Introduction to Analysis, Maxwell Rosenlicht. Analysis is essentially the foundations and expansion of calculus. It is an amazing subject which no math student should ignore. Its study generally requires a great deal of time and effort; some students would benefit more from a guided class than from self-study.
  
  
• Principles of Statistics, M. G. Bulmer. In a few words, statistics is the marriage between probability and analysis (calculus). The wiki article explains the context and interpretation of the subject but doesn't seem to give much information on what the math involved is like. This book seems like it would be best read after you are familiar with probability, say from Weaver's book linked above.
  
  
• I have to second sellphone's recommendation of Naive Set Theory by Paul Halmos. It's one of my favorite math books and gives an amazing introduction to the field. It's short and to the point--almost a haiku on the subject.
  
  
• Continued Fractions, A. Ya. Khinchin. Take a look at the wiki for continued fractions. The book is definitely terse at times but it is rewarding; Khinchin is a master of the subject. One review states that, "although the book is rich with insight and information, Khinchin stays one nautical mile ahead of the reader at all times." Another review recommends Carl D. Olds' book on the subject as a better introduction.
  
  Basically, don't limit yourself to the track you see before you. Explore and enjoy.

You can't apply logic like that to determine left/right.
Left and right are just abstractions based on where parties sat in French parliament.

The book you need to read is Game Theory and Canadian Politics. It's more obvious in Canadian politics because of the multiple parties, but it applies to all countries.

There is no solid logical basis for either side. There are just various interest groups that form alliances in the hopes of winning power and getting their agenda through.

Each party is trying to form at 50%+1 coalition with as few opposing interests as possible.

Within each party different interest groups fight for more power. The party platforms reflect this. If you listen to primary speeches, you'll hear candidates try to appeal to each group.

Anyways the black block appeal to aging 60s activists who have romanticized their pasts and union people who wish they got to take part in strikes of the past that won major workers rights.

They are solidly in the left wing camp, even if it doesn't make any sense.

I don't think they have much influence.

But like social Darwinists on the right, it's the best fit for them even if none of their policies will ever be implemented.

I can think of a few

• Paul Kennedy's "The Rise and Fall of the Great Powers" - WHY and how whole empires fall
  
  
• Niall Ferguson's "The Ascent of Money" - How money rules the world - here's how.
  
  
• Jarred Diamond's "Guns, Germs and Steel" - his thesis might not be entirely correct - but it's a VERY fair look at how our history was influenced by these factors.
  
  
• Bruce Bueno De Mesquita's - "The Predictioneer's Game" - - How quantitative models are SCARILY accurate
  
  
• Emanuel Derman's "Models Behaving Badly" - And how sometimes quantitative models are totally wrong.
  
  
• Paul Roberts - "The End of Oil" - Probably the most serious and balanced read on what could be one of the most important economic problems facing our modern civilization in the next 20 years.
  
  
• Frank & Cook's "Winner Take All Society" - and why things are a problem.
  
  
• Richard Florida's "The Great Reset" - Florida is a pretty good author all around - far better than some others in the pitch.
  
  
• James Bamford's amazing "Body of Secrets" - Not all our enemies are external, and sometimes our allies turn out to actually be thuggish & deadly enemies.
  
  
• Iris Chang's "The Rape of Nanking" - Nobody here is exactly as they appear.
  
  
• Carl Sagan's "A Demon Haunted World"
  
  
• Robin Marantz Henig's "A Monk in the Garden" - Yeah - the priest that proved Darwin's theory, in 1865.....oh yeah and he invented statistics along the way.
  
  
• Brian Sykes' "The seven Daughters of Eve"
  
  
• Douglas Hofstadter's "Metamagical Themas" - Every page is practically amazing - a collection of amazing old articles from Dr. H's work
  
  
• Kristina Borjesson's edit of "Into the Buzzsaw" - the hard truth about a couple of things in the US media
  
  
• Richard Dawkins' "Climbing Mount Improbable" - a great work about such an amazing idea.
  
  
• Kim Sterelny's "Dawkins vs. Gould" - this is a REAL debate about evolution!
  

The recommended text for the networks section of my complexity theory course is Networks: An Introduction by M.E.J. Newman. I haven't read it yet but the instructor spoke highly of it.

For game theory I'd recommend the Yale Open Course on Game Theory. You should be able to find a bunch of readings linked on the site.

Martin Nowak's book Supercooperators is also pretty interesting. It's a nice bridge between game theory and networks. It's nice because it focuses on evolutionary and spatial game theory which maps rather neatly onto network theory.

Samuel Bowles would also be a good place to start especially since it's a bit more economics oriented. He's doing some of the most interesting work on applying game theory to the evolution of social institutions.

There are also a number of game theory courses that come up regularly on coursera. i'm not sure if they'll be back in session over the summer but you can probably check.

>You are not ruining the economy by shopping there.

Well, yes, you are. Shopping at Wal-Mart is the same as defecting in the Prisoner's Dilemma problem, except with a gazillion players instead of two. By shopping there, you get some small gain for yourself at the expense of a net larger loss to the world at large (including you). It is pretty classic game theory.

Free markets in general are known to fail at that kind of choice: people tend to pick the path that yields personal short-term gain over collective benefit, even if the choice yields long-term ruin. In the case of environmental destruction, the costs are external to the system as a whole, and there are whole branches of economics discussing how to tweak the market to account for external costs of actions.

In the case of economic plundering (like Walmart engages in) the costs are internal to the eeconomy but are deferred and homogenized so that the cost to each individual isn't directly visible at the time of purchase -- one might call them "artificially externalized" costs.

Edit: I seem to be attracting a fair number of downvotes. I'll charitably assume they're not knee-jerk responses. Here are some some nice references: The Bully of Bentonville; Fishman's nice book on the Wal-Mart Effect; a nice documentary DVD; and Davis's fun pop-level introduction to game theory.

I've got a couple of weeks off work coming up, so I ordered 6 books off Amazon last night to keep me out of trouble:

• Differential Games by Isaacs and the identically titled Differential Games by Friedman. Differential games involve the mathematical simulation of chase and evasion scenarios such as the Homicidal Chauffeur and the Princess and the Monster. These scenarios are fun to play with from a recreational perspective, but also have practical applications to e.g. warfare and optimal control theory. I'd love to do a PhD in this field.
  
  
• An Introduction to Celestial Mechanics by Moulton. Not really my field, but it's interesting enough.
  
  
• Yippee Ki-Yay Moviegoer : Writings on Bruce Willis, Badass Cinema and Other Important Topics by Vern. It's a book of movie criticism that will go nicely with my copy of Seagalogy: The Ass-Kicking Films of Steven Seagal by the same author.
  
  
• Remember I told you before that I was rereading some of the books I read as a child? Well, don't judge me but I've also ordered Dark Moon by David Gemmell and Dragonsdawn by Anne McCaffrey. It's all about the nostalgia, yo.

Your post has too little context/content for anyone to give you particularly relevant or specific advice. You should list what you know already and what you’re trying to learn. I find it’s easiest to research a new subject when I have a concrete problem I’m trying to solve.

But anyway, I’m going to assume you studied up through single variable calculus and are reasonably motivated to put some effort in with your reading. Here are some books which you might enjoy, depending on your interests. All should be reasonably accessible (to, say, a sharp and motivated undergraduate), but they’ll all take some work:

(in no particular order)
Gödel, Escher, Bach: An Eternal Golden Braid (wikipedia)
To Mock a Mockingbird (wikipedia)
Structure in Nature is a Strategy for Design
Geometry and the Imagination
Visual Group Theory (website)
The Little Schemer (website)
Visual Complex Analysis (website)
Nonlinear Dynamics and Chaos (website)
Music, a Mathematical Offering (website)
QED
Mathematics and its History
The Nature and Growth of Modern Mathematics
Proofs from THE BOOK (wikipedia)
Concrete Mathematics (website, wikipedia)
The Symmetries of Things
Quantum Computing Since Democritus (website)
Solid Shape
On Numbers and Games (wikipedia)
Street-Fighting Mathematics (website)

But also, you’ll probably get more useful response somewhere else, e.g. /r/learnmath. (On /r/math you’re likely to attract downvotes with a question like this.)

You might enjoy:
https://www.reddit.com/r/math/comments/2mkmk0/a_compilation_of_useful_free_online_math_resources/
https://www.reddit.com/r/mathbooks/top/?sort=top&t=all

Structure your free time. If you intend to study at a certain time, plan out what you want to do then. I find it helpful to plan it out in 30 minute intervals.

Study Math. Misteaks. . . and how to find them before the teacher does. . . provides great guidance on how to study it.

If you're already interested in game design, then books on game theory might interest you. I read this one in college, but I see that now it's gotten pretty expensive.

Check your local library for something good. Being more concerned with theory than the latest hawtness means that your library might actually have some applicable texts!

Look kid, I know that politics seems interesting to you. But mathematical game theory is how adults play politics.

http://en.wikipedia.org/wiki/Game_theory

http://www.amazon.com/Political-Game-Theory-Introduction-Analytical/dp/0521841070

http://www.amazon.com/Theory-Political-Scientists-James-Morrow/dp/0691034303

http://books.google.com/books?hl=en&lr=&id=UyMXon0JmBsC&oi=fnd&pg=PR7&dq=game+theory+politics&ots=A6enCFbut3&sig=Q1bZCn7AUDH3C2W7qczOXbo1X6M#v=onepage&q=game%20theory%20politics&f=false

http://journals.cambridge.org/action/displayAbstract;jsessionid=994ECBF78CFF765C0B302FDAA2A07BB9.journals?fromPage=online&aid=7631624

Now, I have a feeling you're the troll. Do you understand why you need partners in game theory and why you need to have cooperation? Cooperative action is more important than having a specific bill without the ability to pass it.

Politics is a give and take. You pander/trade/scheme/steal/lie/cheat/win. That's how you play. This is why you use Game Theory. If Obama would fucking tat back, the Republicans would have to be on their toes. Warren is tatting. That's a good strategy.

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.

Linear programming:

• Vanderbei, Linear Programming: Foundations and Extensions
  
  Combinatorial optimization:
  
  
• Papadimitriou and Steiglitz, Combinatorial Optimization: Algorithms and Complexity
  
• Cook, Cunningham, Pulleyblank, and Schrijver, Combinatorial Optimization
  
  Game theory:
  
  
• Fudenberg and Tirole, Game Theory
  
• Osborne and Rubinstein, A Course in Game Theory
  
  Combinatorial game theory:
  
  
• Berlekamp, Conway, and Guy, Winning Ways for Your Mathematical Plays (volume 1, volume 2, volume 3, volume 4)
  
• Berlekamp, The Dots and Boxes Game: Sophisticated Child's Play
  
• Albert, Nowakowski, and Wolfe, Lessons in Play: An Introduction to Combinatorial Game Theory
  
• Conway, On Numbers and Games

If you're studying Mathematics and Computer Science I think you're already pretty good set up for Game Theory. Do you have some specific concerns? Otherwise I would recommend to start learning Game Theory and learn mathematical/statistical prerequisites when needed.

For an Introduction to Game Theory I can recommend

• Game Theory 101: The Complete Textbook by /u/wspaniel (who will most likely respond to questions here if you ask nicely)
  
• or Game Theory: An Introduction by Steven Tadelis

Chaotic Elections by Donald Saari is pretty good. He loves the Borda Count procedure.

Cardinal subtraction:
> k1-k2=k3 iff k1+k3 =k2

In this case, k1=k2 so we need to find the value(s) of k3 that don't change k1 when added. Unfortunately this includes all the finite numbers and k1. It does however give you a family of answers that satisfy the equation, so in a sense any answer you take from that set is correct. Maro can basically give any ruling and it won't "break math".

Once we get to Omnific Integers we can start to give nice answers (You can do similar things with Ordinals, but the math is not as nice since you don't have negatives among other things). The first infinity is ω, and:

> ω-ω=0.

In fact, the omnific integers satisfy all the basic laws of arithmetic. ω+1 > ω > ω - 1> 0 in this setting.
You can divide and multiply as well, so if I have ω+18 life and cast a [[Dire Fleet Ravager]], I will have ω/3+6 life after the effect resolves. Knuth wrote a small book about Surreal numbers, which are used to construct to construct the omnific integers. On numbers and games is a more in depth look at this number system.

I'm not in my office right now (and I can't recall from memory since it's not my main area), but the following book is quite nice, in my opinion:

http://www.amazon.com/Axiom-Choice-Lecture-Notes-Mathematics/dp/3540309896/ref=sr_1_7?ie=UTF8&qid=1422306222&sr=8-7&keywords=axiom+of+choice

It does a good job of keeping track of different levels of "choice" and which results follow (or are equivalent) to which levels.

> Opening Theory Made Easy

LOL I said $10 not $100!

http://www.amazon.com/Opening-Theory-Made-Easy-Principles/dp/4871870367/ref=sr_1_1?ie=UTF8&qid=1405216740&sr=8-1&keywords=opening+theory+made+easy

This is the absolutely best intro book on linear algebra I've ever experienced, plus it's cheap: http://amazon.com/dp/0822053314

Probability is easier IMO, so just about any book will do. This is my favorite since it covers just about everything quickly: http://amazon.com/dp/0486450376

Umm, just read any game theory textbook. Here are a few that discuss daily rewards and the research that support their conclusions.

https://www.amazon.com/Games-Theory-Applications-Dover-Mathematics/dp/0486432378

https://www.amazon.com/gp/product/1470422107/ref=s9_acsd_newrz_hd_bw_b3cY_c_x_5_w

https://www.amazon.com/gp/product/0691090394/ref=s9_acsd_topr_hd_bw_b3cY_c_x_3_w

I think this is, by far, the best Game Theory book around. But, I'm not sure it is really "an introduction to game theory".

This book is decent: http://www.goodreads.com/book/show/79831.Games_and_Decisions
As is this (I think this is the one that I read): http://www.amazon.com/The-Mathematics-Games-Dover-Books/dp/0486449769

Game Theory: A Nontechnical Introduction

I'm a Statistics student, so naturally, I love the idea of applying numbers and statistics to decision making. I find the book fascinating.

I started with Anatol Rapoport's Two Person Game Theory. It's a bit out of date, and covers only the very basics, but it's very readable and motivates the crucial concepts very well.

game theory online course

non-poker non-technical game theory book

Obviously MoP and AoNLHE are better more relevant.

Game Theory: A Nontechnical Introduction might be a good place to get started.

You seem to have a similar taste in non-fiction to me. Here are a few more that I've either read or have been recommended to me.

The Undercover Economist

I.O.U Why Everyone Owes Everyone and No Once Can Pay


I heard this guy give a fascinating interview but his book is getting mixed reviews, I'm still tempted though...

Predictioneers-Game

This course was offered this semester.

For those curious, this course is about Combinatorial Game Theory, not Game Theory.

"Lessons in Play" was the textbook used this semester.

It doesn’t seem to be grounded in philosophy. I would argue Jon Conways writings on games and numbers are a clear influence.
https://www.amazon.com/Numbers-Games-John-H-Conway/dp/1568811276

Oh, and a cheap plug for my uncle:
Misteaks. . . and how to find them before the teacher does. . .

1. https://www.etsy.com/listing/169430515/pokemon-cufflinks-silver-plated-pokeball
   
   
2. https://www.etsy.com/listing/187751419/magic-the-gathering-wooden-deck-box
   
   3A. http://www.thinkgeek.com/product/1dbd/?srp=1
   
   3B. http://www.thinkgeek.com/product/f26d/?srp=15
   
   3C. http://www.thinkgeek.com/product/1f9e/
   
   4A. https://www.etsy.com/listing/124965957/modest-mouse-rock-band-hooded-sweatshirt
   
   
3. http://www.ebay.com/itm/CLUE-Game-The-Office-Discover-the-Secrets-of-Dunder-Mifflin-Scranton-NEW-/331378026590?pt=Games_US&hash=item4d27ab685e
   
   
4. https://www.etsy.com/listing/200194238/personalised-framed-classic-hipster?ref=related-3
   
   
5. http://www.thinkgeek.com/product/1134/
   
   
6. https://www.etsy.com/listing/189860997/vintage-disneyland-the-happiest-place-on
   
   
7. https://www.etsy.com/listing/206140919/lack-of-cheer-t-shirt-tee-top-shirt
   
   And... 9. http://www.thinkgeek.com/product/e97b/?srp=11
   
   Or... 9. https://www.etsy.com/listing/206651799/cookies-for-santa-santa-plate-christmas (with homebakes yummies!)
   
   
8. http://www.amazon.com/Game-Theory-101-Complete-Textbook/dp/1492728152/ref=sr_1_1?ie=UTF8&qid=1415938617&sr=8-1&keywords=game+theory
   

You might dig this book:
http://www.amazon.com/gp/aw/d/0486406822/

According to Horst Herrlich, "every vector space has a basis" is equivalent to AC.

I disagree; I think there is a need to be a dick about it, because you wrote this:
>I feel like there’s a thread of Democrats who just don’t understand the Prisoner’s Dillema at all.

Not only does this comment carry a superior tone, it's also wrong. r/politics is full of amateurs--many of whom are teenagers--who think they're experts in law, politics, and economics. They all congratulate each other for "getting it" when there are people who actually study these things. It is the acme of ignorance.

Game theory is math-intensive, and there is probably no way around that once you get past the oversimplified models. But this book seems to give a reasonable explanation without being too rigorous [1]. I haven't read that one. But Fudenberg and Tirole's text on game theory is often considered the standard.

https://www.amazon.com/Game-Theory-Nontechnical-Introduction-Mathematics/dp/0486296725

> Are there key ideas and considerations when working with particular game mechanics? Are there any critical questions I should be asking myself before the game starts? While its underway?

There is a whole field of study based around these questions. If you don't mind a little reading try looking into Game Theory.