What is game theory?

Question

I am interested in the Nash Equilibrium and other ideas of game theory, but I don't know much about it and I don't know where to find out more. I am NOT looking for a layman's introduction to the field. I am pretty good at mathematics, so I just want to dive right in and get dirty with the theory itself. Any suggestions on where to start would be great.

Answer 1

There aren't, as far as I know, good review articles about Game Theory as a whole; the reason is simple: the field has witnessed an explosive growth in the past 20 years, and any attempt at a review article will become a textbook and, in fact, almost all textbooks are highly selective in their choice of topics.

So the choice must be textbooks and/or lecture notes; there are very good former ones, while the latter have the advantage of being freely available (but with less quality, on average).

My personal choices are:

(1) Start with Ken Binmore's "Fun and Games": despite the name, this is NOT an introductory textbook.

(2) To see games from a different perspective, study also Roger Myerson's "Game Theory: analysis of conflict" (Myerson is Nobel Prize winning economist). This is more advanced than Binmore's text.

(3) The famous F&T; this the dreaded Fudenberg and Tyrole's "Game Theory"; it is THE reference advanced textbook, but it's highly demanding.

As for internet resources, the most complete is the GameTheory.net (link below); there you'll find lecture notes, book reviews, etc.

You should also see the Game Theory entry in the Stanford Encyclopedia of Philosophy (yes, Philosophy). It's not mathematical, but it's also not introductory; it's greatest value is its annotated bibliography, but it DOES offer some good insights that more mathematical oriented works pass by.          

Answer 2

In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his or her own strategy (i.e., by changing unilaterally). If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium. In other words, to be a Nash equilibrium, each player must answer negatively to the question: "Knowing the strategies of the other players, and treating the strategies of the other players as set in stone, can I benefit by changing my strategy?"

Stated simply, Amy and Bill are in Nash equilibrium if Amy is making the best decision she can, taking into account Bill's decision, and Bill is making the best decision he can, taking into account Amy's decision. Likewise, many players are in Nash equilibrium if each one is making the best decision that they can, taking into account the decisions of the others. However, Nash equilibrium does not necessarily mean the best cumulative payoff for all the players involved; in many cases all the players might improve their payoffs if they could somehow agree on strategies different from the Nash equilibrium (eg. competing businessmen forming a cartel in order to increase their profits).

http://en.wikipedia.org/wiki/Nash_equili...

Answer 3

Personally, I started with Saul Stahl's book: _A Gentle Introduction to Game Theory_.

There are more rigorous treatments of the topic, if you really need it, but you can just go to a college library and look up "linear programming" or "game theory".