The space-continuous version of Go is cool, but I was still hoping for some game that used continuous time. An extremely simple time-continuous game would be some sort of pursuit; pursuit curves are well-studied. Various forms of car (track) racing would qualify; it is possible to pass, but only on various sections of the track, and you have to be well-positioned to do it. Having 2 identical cars (white & black?) that start one behind the other wouldn't guarantee a win for white, so long as air resistance is a part of the game -- the black car behind can "draft" & then slingshot past the leader at an appropriate moment. But I was hoping to undiscretize some simple, common discrete games. In chess, one might define a unit of energy as a usual chess move. One could move several pawns in one "move", so long as the sum total of the energy is =1. I suppose a pxp capture would require a whole unit of energy. How would "en passant" work? At 02:11 AM 2/9/2012, Gareth McCaughan wrote:
It turns out, unsurprisingly, that this has been considered before; see, e.g., http://www.di.fc.ul.pt/~jpn/gv/boards.htm .