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".
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.
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:
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})
:) I was more worried about my inability to fully understand this paper (which is worth re-reading many times), than complaining about it being embedded in an HTML frame.
"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."
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:
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.
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.
The prisoner's dilemma is very useful as a beginner/layman introduction to the game theory mindset. It has a similar role arithmetic has in preparing you to calculus/differential eqs.
[+] [-] saurik|14 years ago|reply
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".
[+] [-] tveita|14 years ago|reply
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.
[+] [-] neilk|14 years ago|reply
Quote: "You're about to walk away with my money because you're an idiot."
http://www.youtube.com/watch?v=S0qjK3TWZE8
[+] [-] super_mario|14 years ago|reply
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|14 years ago|reply
(Full Disclosure: {Applied Games in Economics} \in {What I do})
[+] [-] ajtulloch|14 years ago|reply
http://en.wikipedia.org/wiki/Freeman_Dyson
[+] [-] _pferreir_|14 years ago|reply
[+] [-] tar|14 years ago|reply
[+] [-] rayanm|14 years ago|reply
[+] [-] TeMPOraL|14 years ago|reply
[+] [-] require|14 years ago|reply
[deleted]
[+] [-] yxhuvud|14 years ago|reply
Makes me think of parsers and lookahead-tokens.
[+] [-] tylerneylon|14 years ago|reply
http://www.math.nyu.edu/~neylon/files/game_thy1.pdf
[+] [-] adelphoi|14 years ago|reply
http://www.gmilburn.ca/2010/02/24/triumph-of-the-golden-rule...
[+] [-] zenogais|14 years ago|reply
[+] [-] jethroalias97|14 years ago|reply
[+] [-] dsirijus|14 years ago|reply
Good strategy for infrequent players that one is.
[+] [-] CurtMonash|14 years ago|reply
[+] [-] raverbashing|14 years ago|reply
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
[+] [-] gosub|14 years ago|reply
[+] [-] chrismealy|14 years ago|reply
[+] [-] hythloday|14 years ago|reply
[+] [-] Jauny|14 years ago|reply
[deleted]