
Iterated prisoner's dilemma contains evolutionary opponent dominating strategies - ryanmolden
http://www.pnas.org/content/early/2012/05/16/1206569109.full.pdf+html
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saurik
So, I understand the argument that having more memory than your opponent is
marginalized, and I then understand why, if you have a good memory-one
strategy, you may as well just play oblivious (directly marginalizing the
opponent's memory).

Appendix A: """The importance of this result is that the player with the
shortest memory in effect sets the rules of the game. A player with a good
memory-one strategy can force the game to be played, effectively, as memory-
one. She cannot be undone by another player’s longer-memory strategy."""

However, I'm having a hard time understanding how a memory-one strategy
actually can be good, given that if your opponent has a theory of mind you
apparently want to be paying enough attention to notice and dial down your
extortion factor.

Discussion: """However, if she imputes to Y a theory of mind about herself,
then she should remain engaged and watch for evidence of Y’s refusing the
ultimatum (e.g., lack of evolution favorable to both)."""

How does one actually "remain engaged and watch for evidence" without having
access to at least as much memory as their opponent's theory? It would seem
that the "should" in this paragraph undermines the "can" in the previous one
due to a conflict over "good".

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tveita
Yes, they would appear to contradict each other.

What's happening here, I believe, is that neither of the players are actually
playing a memory-one game. They extract a result for memory-one games and try
to apply it to reason about a memory-N game, which I believe might be an
error.

The "evolutionary" strategy used by Y is in fact a way for Y to base their
decision on the outcome of many previous games. X is similarly using a long-
term strategy. In the end, the players end up in a meta-game that is similar
to the original one.

Note how this meta-game only works if both players agree to it -- if X is "out
to lunch", as they put it, or if Y was simply playing a memory-one strategy
without evolutionary adaption, the meta-game does not exist.

The title holds - they show how to use a local optimum to exploit a hill-
climbing evolutionary player. However this can not be used to beat a true
memory-one player, and I think the assumption that Y would require a "theory
of mind" to counter this strategy is unfounded.

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neilk
Could we say that this famous episode of _Golden Balls_ demonstrates a simple
application the idea?

Quote: "You're about to walk away with my money because you're an idiot."

<http://www.youtube.com/watch?v=S0qjK3TWZE8>

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super_mario
That's well known if you ever took evolutionary biology course, or game theory
course.

Even popular books like Richard Dawkins' "The Selfish Gene" talk in some
detail about it, and this 25 hour video course is also a must see for pretty
much everyone:

<http://youtu.be/NNnIGh9g6fA>

~~~
tomrod
This is really what I signed on to add. This paper really adds nothing to what
is already known in various other fields. Perhaps its new to the authors'
field however? I'm not a Computer Scientist so I'm not sure.

(Full Disclosure: {Applied Games in Economics} \in {What I do})

~~~
hythloday
I'm really interested in this, but I have an extremely shallow knowledge of
applied game theory. Can you point out some papers or textbooks you'd
recommend on this subject? Particularly about the design of strategies that
will dominate evolutionary strategies.

~~~
tomrod
In all reality, one of the best places to start is Wikipedia. The sources
quoted in the game theory articles are fantastic.

Also, "Game Theory" by Fudenberg and Tirole of you're mathy, or Gibbons if
you're wanting a fairly awesome introduction: [http://www.amazon.com/Game-
Theory-Applied-Economists-ebook/d...](http://www.amazon.com/Game-Theory-
Applied-Economists-
ebook/dp/B004EYT91Y/ref=sr_1_2?ie=UTF8&qid=1338129525&sr=8-2)

There are also a lot of blogs on algorithmic (computational) game theory if
that is of interest to you.

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ajtulloch
Pretty amazing for a gentleman of 88 (Freeman Dyson). What an amazing life he
has led.

<http://en.wikipedia.org/wiki/Freeman_Dyson>

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_pferreir_
Really, do people still embed PDFs in HTML frames? :)

~~~
tar
Direct Link:
[http://www.pnas.org/content/early/2012/05/16/1206569109.full...](http://www.pnas.org/content/early/2012/05/16/1206569109.full.pdf)

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yxhuvud
"This fact is important. We derive strategies for X assuming that both players
have memory of only a single previous move, and the above theorem shows that
this involves no loss of generality. Longer memory will not give Y any
advantage."

Makes me think of parsers and lookahead-tokens.

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tylerneylon
I arrived at some related results in game theory in 2005. If I understand this
new paper correctly, section 1.4 in this pdf is similar but less formal:

<http://www.math.nyu.edu/~neylon/files/game_thy1.pdf>

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adelphoi
The best strategy appears to be the most sane. A great metaphor for life as
well:

[http://www.gmilburn.ca/2010/02/24/triumph-of-the-golden-
rule...](http://www.gmilburn.ca/2010/02/24/triumph-of-the-golden-rule/)

~~~
zenogais
I'm actually working on a research paper at the moment which shows how this
case is overstated. The IPD merely shows that given a situation in which
neither party has any advantage over the other the best choice for maximizing
outcomes is cooperation. In this sense the prisoner's dilemma "begs the
question" or assumes the answer it then provides. There is no "moral symmetry"
in this game, merely a set of preconditions (poorly representative of the
"real world") which make this cooperative outcome inevitable.

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dsirijus
I always love to enrage board game geeks by purposedly going out of Nash
equilibrium after first giving them impression that I won't.

Good strategy for infrequent players that one is.

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CurtMonash
My quick reaction is to be confused about why X being unaffected by Y's longer
memory would that Y is unaffected as well. In the zero-sum case, this would be
obvious, but the whole point is that we're not in a zero-sum game.

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raverbashing
I don't understand why so many people like the prisoner's dilemma.

Sure, it's a standart problem in game theory, but it's "uninteresting" to say
the least

For example, it has a limited Nash Equilibrium
<http://en.wikipedia.org/wiki/Nash_Equilibrium>

It also is rarely applicable to "real situations" like Economy, populations,
etc.

Sure, the wikipedia page has various examples, but in real situations it's
usually something else, as there are more details

~~~
hythloday
What game would you recommend instead?

~~~
raverbashing
Depends on the situation

There is:

Stag Hunt <http://en.wikipedia.org/wiki/Stag_hunt>

<http://en.wikipedia.org/wiki/Volunteer%27s_dilemma> is also interesting

<http://en.wikipedia.org/wiki/Nash_bargaining_game>

~~~
cliffbean
Volunteer's Dilemma and the Nash Bargaining Game have more complex equilbiria,
so they're not quite as good if you're looking for an introduction to game
theory. Stag Hunt is basically a game about whether the players know they are
in such a game and can communicate about it, so it's not the best for learning
about games themselves. Prisoner's Dilemma really stands out among the basic
games.

But really, Prisoner's Dilemma is uniquely fascinating in iterated form [0].
Iterated Stag Hunt would be boring, and Iterated Volunteer's Dilemma would be
crazy, but Iterated Prisoner's Dilemma is a very deep game which seems to have
things to say about Biology, Politics, and Computer Science all together.

[0] <http://en.wikipedia.org/wiki/Repeated_game>

~~~
raverbashing
True

I don't deny the learning importance of the PD. But it would be more
interesting if other types of games were explained as well.

Otherwise it's just PD and it gets boring.

About the Iterated PD yes, it's very interesting! Especially evolving
competing strategies in it.

