I've been fascinated with Game Theory ever since I was introduced to the concept by the movie "A Beautiful Mind"(see, watching movies can be useful). To be honest the movie didn't say much about game theory itself and whatever little was used in the story line was mostly wrong. (the solution given by the movie to the bar pick up problem is not a true Nash equilibrium for this type of game, see here[pdf] for the true equilibrium point for this game)
Still it made me look up John Nash and his work and I was hooked.
The nice thing about game theory is that the problems it tries to solve will sound very familiar to you and hence it is more likely to have a readily applicable value to you. To illustrate here's an example of a problem.
Now one of the first games you'll read about if you poke around looking for stuff about game theory is prisoner's dilemma, and I'm sure many of you will have heard of it. And that's exactly why it will *not* be my example.
Instead, why don't you think of the following:
In the June 1983 issue of Scientific American, Douglas Hofstadter announced a largest-number game open to anyone who sent in postcards before midnight, June 30, 1983. The prize was $1 million divided by the total number of entries. To enter the contest the rules say that all you have to do is send in a single 3 by 5-inch card with your name and address and a number indicating how many entries you wish to submit. Everyone is allowed unlimited entries, or rather limited only by one's ability to write a number on the 3x5 card.
Now think about how would you play this game... or rather how it should be played...
Don't look here, you should still be thinking :P
When you're done thinking, you can check for solution, rationale, and what actually happened in this contest here[wikipedia], and here[heretical.com].
Fun ha?
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3 comments:
Game Theory is always a very interesting topic :), it actually got in me the first time I studied it in college as a part of OR (Operations Research) and it is really proves “cogito, ergo sum” if you know what i mean! “I am thinking, therefore I exist”.
It is also simple topic if you think about it as a basic programming model (LP/NLP/Dynamic or even Probalistic and time series model) associated with some decision analysis (based on some objectives and constraints).
It surprised me knowing that your first exposure to this topic was through the movie, institutions should re-organize CS curriculum sooner :)
You'd be surprised how bad our curriculums were :)
I had to study Quantum Physics, Game Theory, and believe it or not most Data Structures on my own.
I forgot to mention that I'm impressed by your use of the more accurate translation for "cogito, ergo sum" instead of the more traditional "I think, therefore I am". Definitely a statement :)
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