Using coalgebraic methods, we extend Conway's theory of games to possibly
non-terminating, i.e. non-wellfounded 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. Hypergames are a
fruitful metaphor for non-terminating processes, Conway's sum being similar to
shuffling. We develop a theory of hypergames, which extends in a non-trivial
way Conway's theory; in particular, we generalize Conway's results on game
determinacy and characterization of strategies. Hypergames have a rather
interesting theory, already in the case of impartial hypergames, for which we
give a compositional semantics, in terms of a generalized Grundy-Sprague
function and a system of generalized Nim games. Equivalences and congruences on
games and hypergames are discussed. We indicate a number of intriguing
directions for future work. We briefly compare hypergames with other notions of
games used in computer science.Comment: 30 page