Here's a Random Thought [TM]. Just to get it out of my system. Feel free to add your own thought and comments on the subject.
Some two-player games feel very interactive and confrontational, whereas some multiplayer games can feel as if you are playing a solitary game. Indeed, sometimes when you play the same game with more players it may feel less confrontational. With more players it becomes more important to focus on your own plans, and it become less importnat to focus on hindering your opponents' plans. More players -> less confrontational. Isn't that a strange paradox?
Not if you understand what my playing group calls the "delta". The delta is the total relative difference (in victory points, or resources, or what have you) between one player and the other players. This is easiest to explain with an example. Suppose it's your turn in a game and you can choose between taking either action A or taking action B. Action A gives you 2 victory points. Action B gives you 3 victory points, and another player 2 victory points. Which action should you take?
The answer is: it depends on the number of players. If there are only two players in the game (you and your opponent) you should take action A, because that creates a relative difference of 2 victory points. Action B would only create a relative difference of 1 victory point.
Now, suppose there are four players in the game. Taking action A would now give you a relative difference of 2 victory points per opponent, for a total delta of (3 opponents x 2 VP =) 6. However, taking action B would give you a difference of 1 victory point when compared to one player (the one who received the 2 victory points), and 3 victory points relative to the other two opponents. This creates a total delta of (1+3+3=) 7, which makes taking action B the better move.
What about three players? Then action A would give you a delta of (2+2=) 4. Action B would yield a delta of (1+3=) 4.
Five players? Action A yields a delta of (4x2=) 8. Action B yields a delta of (1+3x3=) 10.
As you can see, in a two player game you would choose the action that helps your opponent the least (action A), whereas it is the better plan to take the action that also helps someone else in a multiplayer game (action B), and the latter action becomes even more lucrative when you add more players to the game.
Let's do another example. Action A gives you 2 VP. Action B now gives you 3 VP, and another player also 3 VP. How many players does the game need to make action B better than action A? The answer: five players.
Four players. Delta action A (3x2) = 6. Delta action B (0 + 2x3) = 6.
Five players. Delta action A (4x2) = 8. Delta action B (0 + 3x3) = 9.
Now, I know that games aren't always that simple. Often actions don't just yield bare VPs to players, but it is a complex thing of shifting different kinds of resources and possible ways for scoring VPs. Diplomacy and psychology come in as well, making actual analysis during a game a lot harder than my simple calculations above. Also, players will need to factor in a player's current standing. It's a much better idea to help the player in last place a little than giving free VPs to the player who's leading, for example. However, I do think it is important for a designer to understand how the delta works, and how it can alter changes in a game with a varying number of players.
The player has to choose between A or B, there's no other option.
The examples I gave are purely theoretical. Think of it as your first turn in a game, with many more turns yet to come, and where your decisions do not affect what other players can do.
Of course, in a real game you won't make decisions in such a vacuum, they will be based on your current standing in the game, the standing of other players in the game and how your choices affect the choices of other players, etc. I haven't taken a decision tree into account here, that would be food for another Random Thought[TM] ;)