Games are formal structures

A student recently asked, "How is a game a formal structure?"   Great question.

First of all, let's look at the definition of a system:

sys·tem, n.

1. A group of interacting, interrelated, or interdependent elements forming a complex whole. 

2. A functionally related group of elements, especially:

a. The human body regarded as a functional physiological unit.

b. An organism as a whole, especially with regard to its vital processes or functions.

c. A group of physiologically or anatomically complementary organs or parts: the nervous system; the skeletal system.

d. A group of interacting mechanical or electrical components.

e. A network of structures and channels, as for communication, travel, or distribution.

f. A network of related computer software, hardware, and data transmission devices.

3. An organized set of interrelated ideas or principles.

4. A social, economic, or political organizational form.

5. A naturally occurring group of objects or phenomena: the solar system.

6. A set of objects or phenomena grouped together for classification or analysis.

7. A condition of harmonious, orderly interaction.
8. An organized and coordinated method; a procedure. 
9. The prevailing social order; the establishment.

All of the definitions in red are directly applicable to games. Now, let's examine what makes a formal system.

According to M. Alan Kazlev [1], a formal system is [a construct] in which statements can be constructed and manipulated with logical rules. So at the core, a game is basically a logical construct. Everything else is superficial, that is to say, the narrative, characters, music and art is all window dressing placed on top of the construct for aesthetic reasons.

Here's an example from Raph Koster of how a story tacked onto a formal game structure can have profound ethical implications:

The bare mechanics of the game do not determine its semantic freight. Let’s try a thought experiment. Let’s picture a mass murder game wherein there is a gas chamber shaped like a well. You the player are dropping innocent victims down into the gas chamber, and they come in all shapes and sizes. There are old ones and young ones, fat ones and tall ones. As they fall to the bottom, they grab onto each other and try to form human pyramids to get to the top of the well. Should they manage to get out, the game is over and you lose. But if you pack them in tightly enough, the ones on the bottom succumb to the gas and die.

I do not want to play this game. Do you? Yet it is Tetris. You could have well-proven, stellar game design mechanics applied toward a repugnant premise. To those who say the art of the game is purely that of the mechanics, I say that film is not solely the art of cinematography or scriptwriting or directing or acting. The art of the game is the whole….

 …All artistic media have influence, and free will also has a say in what people say and do. Games right now seem to have a very narrow palette of expression. But let them grow….It is not surprising that we wonder whether games or TV or movies have a social responsibility–once upon a time we asked the same thing about poetry. Nobody really ever agreed on an answer.

    The constructive thing to do is to push the boundary gently so that it doesn’t backfire. That’s how we got Lolita and Catcher in the Rye and how we got Apocalypse Now. As a medium, we have to earn the right to be taken seriously. [2]

[1] http://www.orionsarm.com/eg-topic/45b2b9be57dea
[2] "A Theory of Fun for Game Design" Raph Koster, 2004  http://www.theoryoffun.com/