This morning I saw a wonderful webcomic about a game played by Neitzsche, Schopenhauer, Epictetus and Buddha. One of Epictetus' lines summed up something that I've seen several players do over the years: "The only thing you can control is your own virtue, and the most virtuous thing to do is fulfil your civic responsibilities, which is why I select the moves which best help all players."
On the one hand this is a very pleasant attitude for a player to adopt, why not make moves which make everyone else happy? After all, everyone's playing the game to have fun so if everyone is happier then the game is serving its purpose to a much greater extent than it would if you didn't pick moves based on what suits the other players.
That being said, I often hark back to players having different reasons to play games and considering this behaviour in those contexts can make it less desirable. If a player is using a game as a form of socialising it could reasonably add something. If a player is using a game as a form of expression it would very definitely help to have another player trying to feed you the parts to finally manoeuvre your pieces to spell out a message (or whatever else you're trying to do). On the other hand if you're there for the competition having an opponent drop out harms the experience and if your purpose is in seeking challenge then suddenly finding that there is none undermines everything that you were playing for in the first place.
That being said a perceptive player following such a philosophy would presumably modify their behaviour. The nature of moves "which help all players" change depending on the players, in some cases the move which helps them the most is the one which provides them with the greatest challenge.
So what does this mean for designers?
Well, to a very large extent the choices that are available to a player in a game and the consequences of them will influence how they play. On a basic level this means understanding things like giving players the option to harm specific other players as an alternative to advancing their own position means that some players do just that. On a more subtle level the consequences of these actions will impact which philosophies of play that players subscribe to.
For instance, the 'average' player that I know will play to win and make moves to advance their own position to the best of their ability. They play for fun, but value challenge and competition, so will play to win as part of how they play for fun. If playing to win contradicts their overall goal they tend to relax or abandon it. For instance plenty of players I know won't run big money in Dominion in sets where it's strictly the best alternative, instead preferring to cobble together an engine out of dodgy parts because they enjoy doing it more. Ultimately they switch their objective from competition to expression - but continue trying to win within the limits of that expression.
This can also occur with respect to how other players react. In a deeply antithematic move I know players that won't knock another player below two(ish) cities in Game of Thrones unless they're going to win swiftly afterwards. Being eliminated when there's not another game to go to is rubbish and being nearly eliminated with just a few units - enough that you can't leave the game but not enough to ever again have an impact on it - is just plain miserable. I know plenty of players who'll play for competitive reasons, but will switch to a socialising outlook if the alternative is making someone else have a rubbish game. No matter how anti-thematic it is not to kill all of the Starks while you can.
These choices, while ultimately down to the individual personalities and beliefs of the player, are steeped in the choices made by the designers of those games. That same group of players will follow their personal objectives to the bitter end in a game of Dead of Winter because the game doesn't have as many miserable game states. Doing badly might bring no joy in one game, but being ejected from the colony and having an exile objective is something that people can have fun with.
Pulling this together, we can recognise that players adopt different philosophies with respect to how the play games, that players switch between them and that the design of the game can influence when and how players make these switches. Furthermore a game should be designed with particular goals in mind, often relating to the manner in which players will get the most out of those games.
So our goal, as designers, should be to recognise how our design choices impact players gameplay philosophies and to try to steer them towards mindsets that mean that they'll get the most out of our games. That won't be a particular mind set because there is no one right way to play games in general (no matter how vehemently people may argue it on the forums). However there will be a way to play that best suits your game and that helps people get the most out of it - so look for ways to signal it and mechanics that naturally encourage players towards the ideal mode of thought for your game.
Whatever that may be.