Computing equilibria in games and the complexity thereof is imho still quite a young field in which a lot of work still is to be done (especially the former).
GAMUT (2004) is a very nice "suite of game generators designated for testing game-theoretic algorithms".
An example (2005) of a complexity result is that in normal form games, deciding if there exists a pure Nash equilibrium is a NP-complete problem. There are other types of equilibria each with their complexity results in different types of games.
An example (2014) of an (exact) method that solves said decision problem is a mixed 0-1 linear program.
So we have:
- Problem(s) that are considered hard.
- Instance generators (GAMUT)
- Algorithms to solve said problems.
By hard I mean (most likely) not solveable in polynomial time.
Yet, to the best of my knowledge, no benchmarks have been created for any problem in Game Theory. I think, however, benchmarks could prove very interesting to compare algorithm results in future research.
How would one go about creating benchmarks? What is a good benchmark and what are good problem instances to benchmark? If someone decides to create a benchmark for some problem in some field, how is this process approached?
Examples of benchmarks: Graph coloring, Steiner Trees, equilibria in games (coming soon?), ...
