Very interesting. So considering a journey like Ipswich to Ramsgate: the reasonable route involves Greater Anglia and Southeastern, each comprising about half the journey. So one way of looking at it is that these two TOCs comprise a joint monopoly for journeys by rail between Ipswich and Ramsgate - therefore they are not permitted to collude in setting the price. Well that's what I always thought, but something never quite added up there, and I'm wondering now if I've misunderstood?
All the fares for that journey are set by Greater Anglia. The walkup fares are routed ✠ANY PERMITTED, but more interestingly the advance fares have two separate routeings: ✠AP GRTANG&CONCTS and ✠AP GA PLUS HS1, the latter being more expensive for each tier.
So unless Greater Anglia are being incredibly considerate of Southeastern's need to put a premium price on travel via HS1, this does indeed look like there has been co-operation between the two TOCs. Are they also permitted to co-operate when setting the walkup fares? If so, this explains a lot - particularly something else I have been wondering about how so many fares not set by GWR have intricate evening peak restrictions out of Paddington, corresponding to the departure times of long-distance trains.
A final thought: when two TOCs have a joint monopoly like this, must a TOC notify the other affected TOC of its intention to introduce cheap advance fares, or (for example) to change its yield management strategy so that many more cheap advance fares become available for sale? If not, then I'm guessing it defaults to ORCATS allocation of the revenue, but the connecting TOC might have to wait until the next fares round to implement a new agreed allocation, if it is not happy with the "cheapness" of the advance fares that have been introduced? Which seems a bit unfair?