Problems reproducing Axelrod, 1980

[jamesking]

I am new to this library, and as a Hello World-style exercise, I am trying to reproduce the results in Axelrod, 1980 where Tit-For-Tat famously wins Axelrod's first IPD tournament.

>>> import axelrod as axl
>>> players = [s() for s in axl.axelrod_first_strategies]
>>> tournament = axl.Tournament(players, turns=200, repetitions=5)
>>> results = tournament.play()

This I hope matches the tournament setup in the original paper. (200 steps and 5 repetitions).

The problem I have is that Tit-For-Tat doesn't win as expected. Instead it ranks 3rd or 4th on successive tournaments. In each tournament First by Stein and Rapoport ranks first. Here's a sample output.

>>> results.ranked_names
['First by Stein and Rapoport: 0.05: (D, D)', 'First by Grofman', 'First by Shubik', 'Tit For Tat', 'First by Nydegger', 'First by Tideman and Chieruzzi: (D, D)', 'First by Davis: 10', 'Grudger', 'First by Graaskamp: 0.05', 'First by Downing', 'First by Feld: 1.0, 0.5, 200', 'First by Joss: 0.9', 'First by Tullock', 'First by Anonymous', 'Random: 0.5']

So… what am I doing wrong?

[meatballs]

Probably nothing!!

Here's a talk I gave on our attempts to reproduce the second tournament a few years ago (apologies for the lighting):

https://pyvideo.org/pycon-uk-2017/god-is-real-unless-declared-an-integer.html

[drvinceknight]

And here is a post I wrote a little while ago about your exact exercise @jamesking: https://vknight.org/blog/posts/reproducing-axelrods-first-tournament/

And the docs cover some of this as well: https://axelrod.readthedocs.io/en/stable/tutorials/running_axelrods_first_tournament/index.html

:)

[jamesking]

🤯 🤯 🤯

@meatballs and @drvinceknight - thank you for your quick answers and for the excellent work on this library. @meatballs - I enjoyed your talk.

From what I understand…

1. The first tournament was not possible to replicate and Tit-For-Tat does not consistently rank first amongst the original strategies.
2. If the original FORTRAN functions are called with a Python wrapper, then the second tournament does replicate, more-or-less, and Tit-For-Tat does rank 1st.
3. However, the overall rankings in these round-robin tournaments are very sensitive to factors like the mixture of strategies, choice of random seed and are not particularly robust.

Would that be fair?

[jamesking]

This is also confusing me.

There were 15 strategies in the original tournament. 200 moves per game and the tournament was repeated 5 times.

15 * 15 matches * 200 moves * 5 tournaments = 225,000 and not 120,000

[jamesking]

I wrote something up about this here: https://jamesking.io/2025/09/02/failing-to-reproduce-axelrod

[drvinceknight]

From what I understand…

1. The first tournament was not possible to replicate and Tit-For-Tat does not consistently rank first amongst the original strategies.
2. If the original FORTRAN functions are called with a Python wrapper, then the second tournament does replicate, more-or-less, and Tit-For-Tat does rank 1st.
3. However, the overall rankings in these round-robin tournaments are very sensitive to factors like the mixture of strategies, choice of random seed and are not particularly robust.

Would that be fair?

I think that's a good summary. 👍

[drvinceknight]

I wrote something up about this as a draft here: https://jamesking.io/drafts/failing-to-reproduce-axelrod

Nice write up!

[drvinceknight]

@jamesking we have just put up a preprint we have been working on for a long time looking at reproducing Axelrod's second tournament: https://arxiv.org/abs/2510.15438

[jamesking]

@drvinceknight Thank you for sharing this.