From PhilPapers forum Philosophy of Language:

2009-12-06
Games and Family Resemblances
Reply to Jim Stone
Hi Jim,

Perhaps this is off-topic, but isn't your point about games being defined as "rule-defined activities" countered by what Wittgenstein goes on to say in the Investigations about rule-following? Namely: "This was our paradox: no course of action could be determined by a rule, because every course of action can be made out to accord with the rule. The answer was: if everything can be made out to accord with the rule, then it can also be made out to conflict with it. And so there would be neither accord nor conflict." (PI 201)

Although I'm no expert, my understanding of W's later work is partly an attempt to uproot the foundationalism of meaning, such as that which he attempted to establish in the Tractatus, while at the same time shifting the derivation of meaning "back to the rough ground" of its actual use in the community. If we accept that games and language-use are both rule-based activities, then I don't see that it makes a lot of difference to W's attack on foundationalism. To reverse the analogy, the rules of our games aren't derived from a Platonic world of perfect rules, but rather, the rules of our games are based on convention.

If W's point on this topic is to try and illuminate the conventionalism of the rules of language-use and meaning, then how does your claim that a game must be a conventional "rule-defined activity" affect this?

You may be right, the analogy of family resemblances, by way of a comparison of a word's meaning, to games, may be imperfect. Then again, the word "game" itself might be aptly applied to situations that fall outside of your proposed - dare I say "absolute" - definition.

Also, if others accept 'catch' or the 'pretend play' of children as "games" then isn't that the counterexample you were asking for? If, to you, the only acceptable definition of a game is one which is a "rule-defined activity involving a state which counts as performing the activity successfully because it is so defined by an arbitrary rule," then what sort of counterexample is possible?

(I've just noticed that I've repeated some of what Roger Harris recently posted - only with a lot less eloquence. Ah well.)