
Game Theory: Open Access textbook - hocaoglv
https://arxiv.org/abs/1512.06808
======
lynal
There are many sources to develop an understanding of game theory. To build
mastery in game theory, check out Osborne and Rubinstein's text. The authors
offer it as a free download
([http://arielrubinstein.tau.ac.il/books.html](http://arielrubinstein.tau.ac.il/books.html)).

This is the text used by advanced graduate students, the material is explained
precisely.

~~~
TheGorramBatman
It's a pretty intro level book, but a great one.

I'd say its suitable for maybe junior level undergraduates.

------
jessriedel
It's a shame that he released it under a no-deriv's CC license. The actual
cost of textbooks is small compared to the penalty we all pay from not having
our textbooks iteratively refined. [http://blog.jessriedel.com/all-
posts/2015/04/16/beyond-paper...](http://blog.jessriedel.com/all-
posts/2015/04/16/beyond-papers-gitwikxiv/)

------
wenc
Has anyone here applied Game Theory to a real-world productionized problem?
I'm curious.

There are many hypothetical situations where game theory is said to be useful,
but I've never seen an application of it in real life.

~~~
ucaetano
Most corporate strategy/competitive strategy problems use game theory on a
daily basis. Market entry, retaliation, oligopoly, monopoly, etc. are good
examples.

Game theory-heavy industries are the ones in a competitive balance. Think
Coke/Pepsi, telecom, etc.

Another way game theory helps is in building the right mindset: you assume
that your opponent is just as rational and smart as you, and will be trying to
predict how you will react just as you're doing with him/her.

This helps to avoid the failures that result from underestimating your
competitors ("we're smarter than them" or "we're better than them").

Disclaimer: I work in strategy.

~~~
mud_dauber
Any chance of elaborating? I'm curious if GT is a 'real tool' (compared to,
for example, SWOT analysis), or a high-level mindset?

~~~
ucaetano
More of a high-level mindset, since GT is more of an academic topic.

A lot of the effects described in GT can be learned by practice and
observation of human competitive behavior, but studying it gives you a much
better understanding of why certain situations happen, or how competitors will
react.

The market entry game (retaliate/accommodate) is usually the best example:

[https://books.google.com/books?id=xhAACwAAQBAJ&pg=PA77&lpg=P...](https://books.google.com/books?id=xhAACwAAQBAJ&pg=PA77&lpg=PA77&dq=market+entry+retaliate+vs+accommodate&source=bl&ots=7Rnu5vHxkp&sig=FeuTp81X0iW3ScNk3jFKKIENx_4&hl=en&sa=X&ved=0ahUKEwiekJezoIjYAhUB1GMKHenRBFcQ6AEIPDAC#v=onepage&q=market%20entry%20retaliate%20vs%20accommodate&f=false)

Another example is signaling: when you publicly declare that you will match
prices aggressively and will never be undercut, that's not actually a threat
to your competitors, but a signal that if they keep prices high, you will as
well, avoiding a price war.

~~~
wenc
It sounds like in your examples, ideas and conclusions from GT were used to
inform practice (sort of like mental models), but GT models themselves were
not explicitly deployed.

Game Theory is first and foremost a quantitative, mathematical theory, and I
was wondering in what situations one would actually use the mathematics in
production systems or in a mathematical analysis. There are a few replies on
this thread that alluded to some applications.

~~~
ucaetano
> in what situations one would actually use the mathematics in production
> systems or in a mathematical analysis. There are a few replies on this
> thread that alluded to some applications.

I never worked directly with this, but auctions, resource allocation, etc. all
use the mathematical tools from Game Theory.

Corporate strategy is too complex and nuanced to build hard mathematical
models, so you need higher-level abstractions.

------
tramGG
I'm looking to learn Game Theory. Anyone with knowledge in this space have
good additional recommendations?

~~~
ianai
I had a professor once classify GT as a sub set of statistical decision
theory. Might be worth picking up a SDT text.

Does anyone ever read Theory of Games by von Neumann?

~~~
madhadron
This is backwards. Decision theory, which is the foundation of inference in
statistics today (Bayesian, minimax, etc. are all special cases of it) is
formulated as a one player game. Certain things mesh nicely when you realize
this. For example, we know that there is a Nash equilibrium for large classes
of games if we allow random strategies. Likewise, for decision theory with
nonconvex loss functions, optimal procedures are almost always random.

But: game theory of two or more players is qualitatively different. For a one
player game, we speak of optimal strategies. For multiplayer, noncooperative
games, Nash equilibria take what would seem to be the obvious generalization
of that and twist it in a whole new direction.

------
azdle
Looks like there are more format options here:
[https://archive.org/details/1512.06808v1](https://archive.org/details/1512.06808v1)

------
ivan_ah
Aside: I misinterpreted the title as saying "applying game theory to OER
textbooks" and imagined a paper discussing the incentives/payouts for creators
of educational content like textbooks.

Some possible moves:

    
    
         - Write for a mainstream publisher (payout: ~5% royalties, reach: medium)
         - Self publish commercially (payout: 45%+ royalties from createspace/lulu, reach: small)
         - Release for free as OER under public domain / CC0 (no payout, reach: broad)
    

I'm fascinated by the interplay between the for-money publishing business and
the idea of open source content, and would really love to see a paper studying
this subject. Some concrete questions: 1\. If an author is interested in
maximizing total payout, should she write for a mainstream publisher or self-
publish? 2\. If an author is interested in most educational impact (maximize
the number of readers), should she pursue a one of the commercial routes
(publish or self-publish) or release the book as public domain?

The answer to 2. is not obvious: some of the best textbooks I know are free
(GFDL, CC *, or public domain because old), but somehow they don't get the
respect they deserve because people have the perception of "free" as being
somehow inferior quality. People think, if the book really was any good,
surely you'd have to pay for it?

Even more interesting is to consider the game theoretic aspects of multiple
authors/contributors. Why are software projects on githun with hundreds of
collaborators the norm, but textbooks project limited to one or few main
authors?

------
zwaps
I use Game Theory in pretty much everything (academic) Here are some thoughts
on the literature.

There are several different strands and evolutions of Game Theory.

1\. Game Theory (non-cooperative):

The basis was Neumann/Morgenstern Theory of Games. It has been suggested in
this thread, however its focus is a bit obscure today. Still useful for
repeated games, for example. Both authors are also important for Decision
Theory, see below. Afterwards came Nash, defining the what the basic solution
concept would be up until maybe 1990. Simple Nash equilibria are used
primarily where rational agents choose in mathematically nice spaces where
uncertainty is not a major factor.

Following Nash, the Game Theory literature developed to produce equilibrium
refinements. These, usually subsets of Nash equilibria, were created because
Nash often predicts very little - the space of equilibria is often so large
that nothing can be learned, or uncertainty requires the incorporation of
different information sets of agents. The first developments came while
incorporating uncertainty and multi-stage games (where people move in
sequence). Harsanyi was able to show that most configurations of uncertainty
situations can be represented as a Bayesian Game (the issue was the recursion
of "he knows, that I know, that he knows that I know..."). The problem became,
that these often produced unintuitive and large sets of equilibria. So we have
refinements. Some target robustness, like Selten's Trembling Hand. Others
target "natural behavior", empty threats and so on. Almost all of those
refinements are a subset of a Nash concept. The development of refinements was
en vogue prior to the 90's, when it stopped for reasons I will detail below.
Basic Nash has survived, however, and is still the go-to tool to understand
multi-agent decision problems (at least initially).

1.a Cooperative Game Theory:

Largely in parallel, mathematicians like Shapely and later economists like
Roth also tried to think about cooperative games. Here, we don't look directly
at what individual people do in isolation, but rather what groups are stable
and plausible and what they can achieve. If for example a smaller group can
"break" a coalition, then such a large coalition can not be considered a
plausible solution. Matching theory comes from here, for example, so you will
find it in most problems of assignment (say, students). Much as non-
cooperative Game Theory, it is applied widely.

2\. Decision Theory:

Decision theory developed in parallel and is a wide field. It is, however,
critically important to Game Theory because it sets the stage for information,
constraints and decisions that agents take. Expected utility, by Neumann and
Morgenstern, was and is the basic instrument to understand how agents
incorporate their knowledge. This was based on objective probabilities, so in
parallel the Bayesian stream also developed. With a monumental and beautiful
proof, Savage then developed Bayesian Decision Theory (based on works by de
Finetti and others). This is critical to many, many fields in maths,
statistics and science in general, and was then the basis for Game Theory.
Aumann is associated with latter refinements of decision theory. Later on, the
idea of uncertainty (Knightean uncertainy) became important. This is when you
can not assign a probability to an outcome. Paradoxes by Elsberg and Allais
have shown that this is actually an important decision problem in real life.
Multiple approaches exist to generalize Decision Theory, such as Prospect
Theory, MinMax Preferences, integration by capacities as opposed to measures.
Schmeidler, Gilboa and Wakker are some names. Game Theory exists in this space
as well.

3\. Evolutionary Game Theory:

The idea came from Biology and is important because it is a way to justify
Game Theoretic outcomes without even requiring purposeful action by agents. It
had a huge impact on many problems, especially dynamic ones and "top down"
models, but did not surplant traditional Nash in general. Some scientists
believe it should. Other's think it's just one more tool. There are those who
believe the whole of social sciences should be based on it... Let's say it did
not achieve that yet.

4\. Economic applications:

Economics was historically the discipline to apply Game Theory most. Initial
concepts like Nash justified many early models of Markets. Earlier concepts of
non-perfect competition were formalized with Game Theory. Things really
started to take off when asymmetric information were introduced. Think Moral
Hazard, Signaling Games, Contract Theory and so forth. What we know about
economics, organizations, business, competition and many social phenomena
today has largely been developed by applying Game Theory. There are too many
great names to mention: Akerlof, Tirole, Spence, Hart, Homström, Myerson,
Stiglitz.

5\. Mechanism Design and Auction Theory

In the 70's and 80's, from the above applications, economists like Hurwitz,
Myerson and Maskin developed mechanism design. The idea is simple and genius:
If agents play games, what if we can choose the game they play? Which game do
we choose without them walking away, but with us getting the desireable
outcome? What is, in other words, the optimal mechanism inducing the agents to
play a game? Initial examples and todays shining example of econ in action is
Auction design. Which sort of auction mechanism is best to sell ads, be ebay
or assign broadband licences? Mechanism design leads to very complex problems,
which is why until the early 90's many simplified assumptions were used. While
mechanism design has been very useful, this also lead to two developments. In
econ, papers started to get more and more complex to accomodate real life
issues like non-monetary transfers, dynamics, complex type sets and so forth.
Computer scientists trying to implement mechanisms quickly discovered that
many were simply to complex, so they started Algorithmic MD.

6\. Experimental and behavioral games:

So earlier, I said that a whole cataloque of equilibrium refinement basically
died out. Why is that? Well, with behavioral econ we were introduced to more
realistic approaches to decisionmaking. Then questions arose, such as "what if
I can not count on rationality of my competitor". As it turns out, this may
actually break the inference of Nash equilibria pretty handily.

At the same time, economists and psychologists put people in experiments to
play games. In some situations, Nash worked well. In other situations, one
could accomodate much by using more complex Decision Theory. But in many
instances, people would just not play Nash. In other words, they couldn't even
figure out the most basic solution concept. Indeed one can do all sorts of
experiments in a Game Theory 101 class showing that people often choose much
too heuristically. Equilibrium refinements make Nash more complex, it was
clear they had to be abandoned. Currently, research joint in decision theory
and game theory works on finding better ways to model behavior when Nash is
not reached.

Books:

Osborne/Rubinstein has been mentioned. Contrary to what was said, this is an
undergrad book and a solid intro. There are two classic works. The major one
is by Tirole and Fudenberg, the other is by Myerson. The former is more
standard, the latter is better. Now there is a new book by Maschler, Solan and
Zamir with like 900 pages. It's really good, and I would definitly get it as a
second book after an intro.

For Mechanism Design, the best book is by Tilman Boergers. It's also free to
download. Auction Theory specifically has a standard volume by Krishna. Both
of those are math heavy. This is true in general, but Game Theory concepts can
often be explained by intuition. For Mechanism Design, I fear that a solid
math background would be required, because the space of "choosing a game" is
mathematically not so nice. However solid means you should have a good
grounding in analysis and optimization, perhaps dynamic systems. Basically, a
math heavy undergrad education will be fine.

hope this helps

------
nurettin
Explanation of Part V in the introduction is interesting and might be a
property which sets this book apart from the fold.

------
nurettin
Anyone know of any sources for game theory applications to ethics?

