Design pattern for object containing sets of other objects

I have a complex structure of classes Hero, Castle, Artefact and Position. They are in the following relationships:

• A Position can contain several or none Heroes, while a Hero can be only on one Position.
• A Castle belongs to one Hero and can be built on one Position. A Hero can have 0-1 Castles. A Position can have 0-1 Castes as well.
• An Artefact can either be buried in a Position or can be equipped by a Hero. Thus, Artefact has reference to 0-1 Heroes and 0-1 Positions. A Hero can have 0-1 Artefacts and a Position can contain 0-1 Artefacts as well.

Now, to implement those both-way relationships, it is difficult to always change the references in all affected objects (e.g. when a Hero equips an Artefact, I have to change Hero.Artefact, Artefact.Hero, Artefact.Position and Position.Artefact). Therefore, I am using a Game class, that serves as a container for all of them (in other words, the Game class has 4 lists, one for each class).

Then, I add the reference just to the containing Game and with the help of IDs I am able to change the individual references much more elegantly (equipping the Artefact again):

Artefact.HeroID = newHeroID;
Artefact.PositionID = null;

All the accessors in the respective classes then allow me to get the right object(s):

Hero.Artefact
{
    get
    {
        return this.Game.Artefacts.FirstOrDefault(a => a.HeroID == this.ID);
    }
}

Artefact.Hero
{
    get
    {
        return this.Game.Heroes.FirstOrDefault(h => h.ID == this.HeroID);
    }
}

etc.

Is there a name for this design pattern (is it a design pattern)? It is really hard to find the right answer, when you know the implementation, but don't know the name :D (the other way around is quite simple).