Right at the low end of the range, economies of scale can be pretty fierce.
Consider a land journey from A to B, and compare the costs of road and rail travel.
For example, let the cost of the journey be 100.
When one person travels, there is no cost advantage to the car. But if there are two
people in the car, then the cost per person is 50; on the train, this would be 100. For four people, the comparison is starker; 25 per passenger compared to 100, therefor the train becomes four times more expensive.
Carpooling is economically very cost effective.
However, there are some advantages to train travel. It is often more comfortable and less stressful; it is frequently faster, and it is possible to work on a train. It's also often environmentally better, and where the journey is to a city centre, avoids congestion and delays.
How can the playing field be levelled ?
Now, an empty seat on a train is a perishable commodity. It is better to have a seat occupied, even at a reduced price, than have it empty; and the occupant may purchase food or beverages or other on-board services, ofsetting margins.
For this to work, there must be a way of marketing unoccpied seats on the train that would not otherwise be taken up by full fare passengers. This precludes many forms of pre-booking; it's more like the "standby" system operated by some airlines. And since many full-fare passengers don't pre-book, the resolution of ticket availability needs to happen very fast, just as the train is arriving in the station.
On arriving at the station, participants register for "pool" or "group" travel and proceed to the departure platform. They wait in a special area with an indicator board displaying their "queue numbers".
When the train arrives, it reports how many unoccupied seats it has to the local systems, which calculate a reasonable ratio between "pool" tickets and keeping some seats free for passengers waiting at subsequent stations.
As the normal passengers board, the "pool" passengers are notified of the "accepted" pool numbers. These groups can board the train and pay fares (on board) according to numbers; two passengers pay 1.5 times the single fare (75% each), three pay 1.66 times and so on. Thus economies fo scale are preserved and the route operator receives revenue on what might be otherwise empty seats.
Those who are not sucessful in being allocated "pool" seats have the option of paying full fare, or travelling by car.
This would work best on long distance services with few stops.