- FIT 2009 -
June 14-27, 2009, Novi Sad
Using coalgebraic methods, we show how to
extend Conway's original theory of games to include infinite games (hypergames).
We take the view that a play which goes on forever is a draw, and hence
rather than focussing on winning strategies, we focus on non-losing
strategies. Infinite games are a fruitful metaphor for non-terminating
processes, Conway's sum of games being similar to shuffling.
Hypergames have a rather interesting theory, already in the case of
generalized Nim. The theory of hypergames generalizes Conway's theory rather
smoothly, but significantly. We will indicate a number of intriguing
directions for future work, and we will briefly compare infinite games
with other notions of games used in computer science.