@Stuart, you have misunderstood.
There may be a maximal element among the convex combinations of cyclic preferences, when the VM axioms fail to hold. SSB utility axioms have to hold in this case.
This maximal is a good candidate for choice from the cyclic preferences. So the claim that a violation of VM axioms leads to a money pump is false, even in the presence of cyclic preferences.
Read Fishburn’s Nonlinear Preference and Utility Theory (1988) or the very recent Essays in Honor of Fishburn, edited by S. Brams et al.
You should probably start your discussion from Merrill Flood’s 1952 article on preference cycles, available from Rand. http://www.rand.org/pubs/authors/f/flood_merrill_m.html
I read the article, also. The description of the game was a bit short and somewhat ambiguous.
The game is designed to show people who participate why it is hard to maintain collusion or price fixing amongst oligopolies, secret agreements are not enough. It was a good demonstration of the difficulties in maintaining a secret deal. Far better than simply reading about it.
A number of theorists think that price fixing is mystery because the economics of it should make any agreements disappear.
However, there are price fixings in the real world which are regularly prosecuted. So, how are the Ashley’s dealt with by those groups?