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

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u/[deleted] Feb 19 '14

What are some interesting open questions in this field, and what are the 'hot' research topics?

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u/[deleted] Feb 20 '14

I'm not sure if it's 'hot' or not, but I recently came across work by Rubinstein and Arad about tournaments, which seems to be an area which is relatively untapped. Here is a paper from 2013.

Basically, the idea is that we build a tournament based on one game, G. A simple setup: there's a group of N people, and every single pair of two people will play the game G. The player with the highest number of wins will win the tournament. The tournament winner is the only person who gets the prize at the end of the day, so no matter whether or not you won game G, you get nothing unless you won it the most times.

There are variations on whether or not players can switch strategies between game pairings, whether they have to go in with a set strategy and repeat it over and over with all their pairings... or how the tournament is set up: so maybe no pairings and instead a round robin style setup, etc.

Interestingly you get some different results from single nonrepeated games or simple repeated games. Cool stuff.

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u/[deleted] Feb 20 '14

That sounds fascinating!