Universality of Games

Had a student in my logic class mude with some friends about the universality of games. It turns out that kids in the US, Burma, and Nepal all play both hide and seek and freeze tag. Their question was whether that was an indication that these games were universal.

It seems like there are three options here:

(1) The commonality is the result of intercultural interaction. Colonization likely communicated a number of cultural artifacts in both directions and the game could have had one invention and been carried to other places.

(2) The games are simple enough that they arose independently in the same form. They are basic games requiring no equipment and with rules that are not complex, so it could be coincidence that disparate cultures would invent the same sort of games.

(3) The most interesting was their idea which was a sort of playtime Chomskian move, that the human mind is hardwired with a "game grammar" such that at certain times, human children everywhere will not only be led to play, but to play in certain well prescribed ways.

The additional bit of evidence they supplied was that terminology was not translation or transliteration. For example, in Burma, freeze tag is called statue tag and the person doing the tagging is not called it, but the tiger. If the game had been carried over, the rules likely would have brought with them the terminology, but here are terms that make more sense culturally.

So, while we would all, I think, want to say that play itself is a natural part of human life, especially childhood, are the particular games also universal and if so, in what way?