Article structure about qe_libraries_article HOT 7 CLOSED

Thanks @Smit-create. If you can put a rough draft together I will step in and do the next pass.

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Thanks @Smit-create! Just a few random "highlights":

• The main aim of the game_theory submodule is to provide efficient implementation of state-of-the-art algorithms for computing Nash equilibria of normal form games, relying only on "standard" libraries (i.e., those that are available in the default Anaconda distribution) such as NumPy and SciPy, while leveraging Numba's JIT compilation technology wherever possible.

• Currently, game_theory contains, among some others, implementations of:

  • support and vertex enumeration algorithms, support_enumeration and vertex_enumeration, for computing all Nash equilibria of a (non-degenerate) normal form game with two players;
  • the Lemke-Howson algorithm, lemke_howson, for computing one Nash equilibrium of a normal form game with two players; and
  • the McLennan-Tourky algorithm, mclennan_tourky, for computing one Nash equilibrium of a normal form game with N players.

  In particular, lemke_howson scales up to games with several hundreds actions.

• It also contains several learning/evolutionary dynamics algorithms, such as fictitious play (and its stochastic version), best response dynamics (and its stochastic version), local interaction dynamics, and logit response dynamics.

• Possible future projects include adding more equilibrium computation algorithms for N-player games and supporting extensive form games.

• (If we also talk about Julia versions, GameTheory.jl has a few more interesting implementations, thanks to a larger variety of available packages in Julia (where there is an official collection of packages which we can freely depend on).)

• It is to apply not only to this submodule, but to the whole QuantEcon.py package, that we strictly restrict ourselves to depend only on libraries available in Anaconda for installation and maintenance ease, while we try our best not to sacrifice the efficiency (speed) of the code by using Numba. I think this point should be emphasized in the paper.

These are just random sentences, not meant to be included as is. Please elaborate and edit them...

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I have opened a sample PR #6 which tries to include markov. For now, I have added the MarkovChain details and if that looks good, I can start working in a similar fashion to complete the markov sub-package. Please have a look and let me know if you have any suggestions like adding more details, adding more code, etc.

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@oyamad Can you please highlight the 2-3 functions from game_theory that you would like to have in the article? I can add that using the documentation.

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I'll try to wrap up points 4 and 5 soon together and I think we will be close to the finish line of a very rough first draft.

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Many thanks, @oyamad. I'll try to frame some sentences around this to include in the article.

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@jstac I have added some sections so we can see a rough idea of the article. It still needs some information from your end like Abstract, Introduction, Future work, and if you are interested in adding something like: https://www.nature.com/articles/s41592-019-0686-2#Sec28. Thanks! Please let me know if you want to add anything else.

Also, we need to decide whether to keep it limited to QuantEcon.py or also add something about QuantEcon.jl.

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