Doncaster has 66 daily weekday up services, of which four are Grand Central, seven are Hull Trains and 55 are the franchise operator. There's undoubtedly some competitive pressure on pricing, but if you look at the actual fares being charged, it would appear that other factors are at play.
For example, GC and HT services fares are likely to be fairly reflective of the Doncaster to London point-to-point demand at specific times of day, whereas the franchise operator's fares look to be a lot more 'managed'.
The latter generally offers its lower Advance fares on the slower York stoppers, but seems to restrict the lower fare tiers on the fasts, even at the limits of the booking horizons. Having said that, it also often makes lower tiers available on component sectors of its route, presenting split ticket opportunities for those in the know.
York, to a lesser extent in terms of effect from Grand Central, sees a similar thing with fares on the franchisee apparently being restricted. The fast 17:58 to King's Cross tomorrow can't be had for less than £149.50 in First. The slow 18:02, even only 24 hours out, is £64. We can't know how many £149.50 tickets are being sold, of course, but I have on many occasions seen the 17:58 go out very, very lightly loaded, while the 18:02 boards in swarms in the bay across the platform.
Of course, all this from the franchise operator may be reflective of its financial woes; and these methods of revenue management have not delivered the results that they were aiming for.