To summarise, Plato fills his cave with the following things (moving from back to front):
- a back wall on which shadows pass
- chained prisoners watching the shadows
- a small wall
- people walking past carrying objects
- a fire
- the cave entrance.
Cave vs Cave doesn’t have room tiles that exactly correspond to these spaces. Nevertheless, it is possible to furnish your cave in a way that mimics them.
The space occupied by the chained prisoners in the allegory can be represented in game by the Dungeon tile. This must be placed at the back of the cave if it is to correspond most closely with Plato’s scenario. Alternatively, you could use the Secret Chamber tile as it ostensibly operates in the same way and requires the same wall configurations. However, the Dungeon tile is the preferred option. Once built, the front wall of the dungeon will then need to be razed so that the shadows cast by the light further out in the cave can be cast onto the dungeon’s back wall.
There's no equivalent to Agricola’s Hearth or Fireplace cards in Cave vs Cave so it's not possible to directly replicate Plato’s fire on your player board. (In the full version of Caverna there is a Cooking Cave tile.) The nearest equivalent is the Bakehouse room. I think it's safe to assume that there’s a fire in the bread oven. This will create the light that is required to cast the shadows back into the dungeon.
Between the Bakehouse (standing for Plato’s fire) and the Dungeon containing the chained prisoners it is necessary to have a wall. This is the easiest part of the allegory’s geography to recreate in game. This is because the Bakehouse room has a very specific wall requirement. In order to furnish your cave with this room you need to have three walls in place, one of which can simply be positioned on the side that faces the dungeon. For our purposes, we can simply assume that this wall is a little lower than the others, so that the light from the oven can cast the shadows of the dwarves working in the Bakehouse onto the wall at the back of the Dungeon. For added flavour, we could even build the Shelf in the space between the two other rooms, although given the requirement that this be built on a single wall it would require a more complicated sequence of player actions.
Is recreating Plato’s cave in Cave vs Cave a viable game strategy? Not really. Whilst it’s possible to achieve it does depend upon you taking a very specific chain of actions, which in turn depends upon your opponent not doing them. It's also reliant upon the right room tiles being available and you having the materials to pay their cost. The Dungeon alone costs three stone and four gold to build and requires four walls to be in place, which means building a minimum of one but more likely two.
For all its difficulty, Plato’s cave would at least score reasonably well. The Dungeon is worth 11 victory points and generates gold when building a wall on future turns (which will come into play when, in this strategy, you go on to build the Bakehouse). Furthermore, the Dungeon is the second highest scoring tile in the game and so is good in the event of a tie (it can only be beaten by the State Room). Similarly, the Bakehouse is worth a further six points and again provides a way of getting gold.