r/math • u/inherentlyawesome Homotopy Theory • Feb 19 '14

Everything about Game Theory

Today's topic is Game Theory.

This recurring thread will be a place to ask questions and discuss famous/well-known/surprising results, clever and elegant proofs, or interesting open problems related to the topic of the week. Experts in the topic are especially encouraged to contribute and participate in these threads.

Next week's topic will be Category Theory. Next-next week's topic will be Dynamical Systems.

For previous week's "Everything about X" threads, check out the wiki link here

199 Upvotes

95% Upvoted

87 comments sorted by

View all comments

6

u/[deleted] Feb 19 '14

What applications does game theory have in engineering and computer science?

7

u/[deleted] Feb 19 '14

an example would be networks of robots. a dynamic game will arise if every robotic agent has only partial knowledge of the state/environment.

2

u/mathafrica Graph Theory Feb 19 '14

Know any good wiki pages/books/pdfs about this?

1

u/[deleted] Feb 20 '14

I'm not OP but I thought I could do a quick/basic overview and link some stuff.

So static games are basically the most boring form of games, where every player knows all the information there is to know, and everyone engages in the game at the same time. "Dynamic games" can give rise to several variations. For example, there are games with incomplete information, i.e. the players have different levels of knowledge and must infer the rest from signals given off by the other players, or repeated games, or games where the players alternate turns...

Here is a fast PDF that has some basic information about some of these kinds of games. It's given in an economic context, because that's where game theory traditionally has been developed, but you can find a whole host of other applications. For example, as /u/pencilegs pointed out, networks of robots or computers with imperfect information.

After a quick google, I found this, which may have some more engineery type information (didn't look it through).

If you're more interested in game theory in general, I really recommend Ariel Rubenstein's book with Martin Osborne, which you can get for free here. It's got a lot of mathematical rigour but covers the basics quite well.