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I was never good at card games, mainly because I never played them (rough childhood, another time another place). So you can imagine the fun time I spent in probability counting the likelihood in drawing 4 heart of spades (is that even a hand?). Bridges? Never heard of them. Chess? Not the European kind with knights, queens and stewards that's for sure. Never been to Las Vegas either.

Oh I never did any sports either because that is a waste of time.


I recently developed an interest in game theory, in conjunction with an economics class I am taking. But I am not sure what this subject is all about.

Does the intuition in game theory come from realistic games? I recall watching a beautiful mind and John Nash was studying some game play.

To all the game theorists out there, how much real life games I need to know how study this subject?

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    $\begingroup$ None, it's math after all... I doesn't have anything per se to do with "actual games" anyway. $\endgroup$ – Stefan Perko Feb 28 '15 at 23:38
  • $\begingroup$ Oh I see...too bad people don't distinguish problems associated with drawing an algorithm from "real games" versus the problems studied in game theories. For example, if I need to develop an algorithm from a theoretical game of chess (some chess variant), do I need to know game theory? $\endgroup$ – Olórin Feb 28 '15 at 23:41
  • $\begingroup$ Nash's game theory has (I think) very little to say about chess, where the difficulty is mainly that the possible number of states the game can pass through is so vast. It has applications to some "real life games" but it also potentially applies to "real life" such as contract negotiations. $\endgroup$ – David K Feb 28 '15 at 23:46
  • $\begingroup$ Any well written problem or example in any textbook will give enough context in order to allow the student to arrive at an answer even if they had never heard of the game in question before, be it a question on game theory or probability or otherwise. If it is a question you are personally pursuing outside of a standard course for personal research, then you would be expected to do enough research on the subject to be familiar with the problem before starting. $\endgroup$ – JMoravitz Mar 1 '15 at 1:47
  • $\begingroup$ @MathNewb You'd want to accept an answer, if you don't plan on giving a bounty (Even if answers aren't necessarily satisfactory). $\endgroup$ – Kugelblitz Mar 15 '15 at 1:16
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Math (and by proxy economics) distinguishes really two real classes of decision-making. 'Decision theory' generally concerns a rational agent trying to make the best choice against some exogenous uncertainty (against 'nature'). A decision theoretic problem you might run into in life:

"You are moving away from your old town, sometime in the next year. You are presently sitting down to order at your favorite local restaurant. Do you get your favorite dish now? Or do you experiment and see if there's something you like more."

The answer all hinges on the natural uncertainty the decision-maker is facing. Game theory on the other hand, deals with when your 'opponent' isn't nature, your opponent is a rational, clever being who takes into account the same thoughts you do. An example of a game theoretic problem might be:

"What is the best way to bid in an Ebay auction, knowing that everyone else is asking the same question"

The phrase 'games' here doesn't have the usual layperson meaning of sport, or board/card games, or video games etc. It simply refers to any strategic interaction with intelligent, rational counterparts. So no background in those card games needed. (Source: I do game theory for a living and still don't know how to play poker).

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Few things to say about this...

  1. Game theory is the scientific study of strategically interdependent decision making.
  2. Applications of Game Theory in real life situations, and real life games subsequently, are many.
  3. A prerequisite for learning this is not real games, fortunately!
  4. You will be exposed to many new games through this subject of study.
  5. Whenever common games which you might have come across might be the focus of a problem, usually all relevant details will also be given, thereby making 'not knowing many games' not so much of a disadvantage.

Note:

Check out this website to learn the basics very well... : http://gametheory101.com/Home.html

Check out the e-books as well...seriously cheap, yet very, very useful (By the same website owner/author): http://gametheory101.com/Textbook.html

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Game theory is the theory of interactive decision situations where groups of agents make decisions that lead to outcomes, and where each agent has preferences over the outcomes.

One collection of such decision situations are the so-called "parlor games" that include poker, chess and so on. These are classicly discussed due to their simplicity and the fun fact that much of the same analysis is useful for a game like poker and a game like a nuclear standoff between rival nations.

Mathematical Game Theory is applied mathematics and makes use of results from Linear algebra, analysis (such as fixed-point theorems), and many other mathematical fields. Applied Game Theory then applies these results and modeling techniques to social situations, from economic systems to these simple (strategically active) parlor games.

The intuition comes from simple games and complex games everywhere (see Dads and Cads for another example) and the similarities bewteen the two. I recommend going to the source and reading parts of Von Neumann and Moregnstern's Theory of Games and Economic Behavior to supply the background you want. For a mathematical treatment consider Gonzalez-Diaz et. all and An Introductory Course on Mathematical Game Theory (from which my first paragraph above was adapted). There are also two AMS Student Mathematical Library books worth reviewing.

So, let the theory you find lead you to whatever understanding parlor games you require. Modeling poker is actually quite difficult if you're interested, start with "simplfied poker" and see where it leads you.

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