[saurik]

I am reasonably certain (but would love to learn more) that a complete description of the strategy used by players in that game is as follows:

1) when squeezed, the middle player will move to just "outside" of the opponent further from a wall 2) otherwise, the player in the middle prefers to be in the middle of the middle (to hedge against new players or take advantage of stupid existing players) 3) an outside player in a good position will move to be directly next to the middle player 4) an outside player in a bad position will temporarily choose to be the middle player, and then /immediately/ choose between strategy #1 and #2

The only rule in this situation that causes player to not be directly next to another player is #2. The two outside players will then either a) invoke rule #3 to put all three players next to each other or b) invoke rule #4 to move all the players closer together. The middle player, when squeezed, just uses rule #1 to move next to another player.

In essence, it is my belief that there will be no stable configuration of the players for this game (unlike the two player case, where "next to each other in the center" is stable), but that at all times the players will be clustered together while they shuffle themselves.

[philbo]

I think the strategy would depend on the cost of moving. If moving has no cost associated with it, then I see the game playing out as you describe. But if the cost of moving repeatedly becomes prohibitive, players would be more likely to adopt a strategy of equidistant equilibrium.