Puzzles and Games

I'm working myself up to a large-scale assault on Greg Costikyan's definition of a game, but that'll take some time. He makes a distinction between a puzzle and a game, and while I agree with his conclusion, I'm left a little frustrated by the lack of a rigorous definition of "puzzle."

So batter up, here's a swing at it. I'll define a "choice activity" as a sort of activity in which a) a person can choose a series of actions or symbols, arranged in a temporal or spatial order, in such a way that those actions/symbols satisfy a set of constraints. A puzzle is a choice activity in which there is only a single person participating, or a group of people acting with a shared goal. In simple puzzles, the constraints are fixed; in most puzzles, the selection of various actions changes the constraints. For example, writing down a word in a crossword puzzle adds the constraints that those letters must be used by the crosswise words.

A game, then, is just a choice activity in which there are two or more participants, and there is some utility function that defines whether, at any time, if a player is winning.

What's interesting about these definitions is their parallelism to Turing Machines and hypercomputation. Puzzles, with their "arrangement of symbols according to constrains" is almost a classic Turing Machine definition. And games, with their interactivity between competing forces, reflect Robin Milner and others' proposals for augmenting Turing Machines.