In Game Theory usage, multi-player generally means "The more complicated case". So, two-player games are relatively easy to figure out because of the lack of any cooperation. As soon as you add a third player, collusion is possible and things get more complicated. This is obvious in games such as Risk or Diplomacy where alliances are a possibility, but it can also come about in Dominion. For instance, on a board without +actions, if player 1 and 2 both play Torturers, player 3 got hit by two Torturers which wouldn't be possible in a 2-player game on the same board. Also, Council Room can compound more easily.
Basically, in two-player games, your actions are directly influenced by your opponents' actions, but with more players, your actions are influenced not only by what each player did but on the interactions between the actions they took.
Also, in two-player, the only order that can change is who went first, which usually doesn't have a very big impact on Dominion. But in a three-player game, there are more possible orders and where you are relative to a player can make a big difference. In Dominion, some of the cards which affect this are Possession, Masquerade, Tribute, Envoy and Contraband. If you have a kingdom with Masquerade, Contraband and Envoy you want the player who makes some decisions for you to be inexperienced with the card. For example, the player who discards the possession you picked up with Envoy without realizing that you don't have another action. With Tribute and Possession, you want the player whose deck you're using to not know how to counter the card you're using. For example, the player who opens Governor-Chapel with Possession on the board. Or the player who loads up on Harem and Nobles with Tribute on the board.
