What In The Heck Is A "Game", Anyway?

Can "games" be serious? Can "games" be art?  Or put it another way, if it's serious and art, is it still a "game"?

Knowledge is socially constructed and expressed individually.  That said, there are many definitions of "game" and many more connotations.  Roger Caillois has his famous four types: the Agon, Alea, Ilinx, and Mimicry.  Modern videogames usually blend all four types into a single experience.  +4 two-handed entertainment of smiting? Apparently there are quite a few people out there who want to see gaming recognized as more than just child's play.  

First, it already is - even by those who decry it as a social drain or the pasttime of slackers (paradoxically it need not be either and yet can be both).  I've discussed this briefly in my only other blog post ("Immersion and Designer Intent" - which apparently was neither interesting nor crappy enough for anyone to comment either + or - style, but i digress); but to restate it even more briefly - games (as traditionally understood, i.e. ways of having fun that have rules) play a vitally important role in the creation and sustenance of society.  Scholars from Schiller to Whitehead to Huizinga to Baudrillard and so on have recognized this and written on it. Even those who claim that videogames are a great evil do so because they recognize the basic power of games.

Second, the further something gets from play, i.e. the less fun is the focus, the more it becomes something else: politics, religion or philosophy.  These *can* be fun, but fun is not their focus: social change, theological reflection, or comprehension of the abstract is the now the focus. 

So, what's the point? Games are fun.  They can be more than that: frightening and enfuriating and tense and exhilarating and uplifting (true of sports games, videogames, and card games alike). But at their core, they are fun - if there's nothing fun about it it's not a game: it might be a contest, or a competition, but it's not a game.  

If something (say, studying for the GRE) isn't fun to anybody else, but you make it fun for yourself, have you transformed that thing into a game?

(i don't have THE answer, but my instinct says that the focus here still isn't fun, fun has simply been introduced as a new element)

I've done little to actually define "game" - how do you define it?