Spatial tournaments

A spatial tournament is defined on a graph where the nodes correspond to players and edges define whether or not a given player pair will have a match.

The initial work on spatial tournaments was done by Nowak and May in a 1992 paper: [Nowak1992].

Additionally, Szabó and Fáth in their 2007 paper [Szabo2007] consider a variety of graphs, such as lattices, small world, scale-free graphs and evolving networks.

Let’s create a tournament where Cooperator and Defector do not play each other and neither do TitForTat and Grudger :

../../_images/spatial.png

Note that the edges have to be given as a list of tuples of player indices:

>>> import axelrod as axl
>>> players = [axl.Cooperator(), axl.Defector(),
...            axl.TitForTat(), axl.Grudger()]
>>> edges = [(0, 2), (0, 3), (1, 2), (1, 3)]

To create a spatial tournament you pass the edges to the Tournament class:

>>> spatial_tournament = axl.Tournament(players, edges=edges)
>>> results = spatial_tournament.play()

We can plot the results:

>>> plot = axl.Plot(results)
>>> p = plot.boxplot()
>>> p.show()
../../_images/spatial_results.png

We can, like any other tournament, obtain the ranks for our players:

>>> results.ranked_names
['Cooperator', 'Tit For Tat', 'Grudger', 'Defector']

Let’s run a small tournament of 2 turns and 2 repetitions and obtain the interactions:

>>> spatial_tournament = axl.Tournament(players ,turns=2, repetitions=2, edges=edges)
>>> results = spatial_tournament.play()
>>> results.payoffs
[[[], [], [3.0, 3.0], [3.0, 3.0]], [[], [], [3.0, 3.0], [3.0, 3.0]], [[3.0, 3.0], [0.5, 0.5], [], []], [[3.0, 3.0], [0.5, 0.5], [], []]]

As anticipated not all players interact with each other.

It is also possible to create a probabilistic ending spatial tournament:

>>> prob_end_spatial_tournament = axl.Tournament(players, edges=edges, prob_end=.1, repetitions=1, seed=10)
>>> prob_end_results = prob_end_spatial_tournament.play()

We see that the match lengths are no longer all equal:

>>> prob_end_results.match_lengths
[[[0, 0, 20.0, 1.0], [0, 0, 46.0, 13.0], [20.0, 46.0, 0, 0], [1.0, 13.0, 0, 0]]]