Conway Games, coalgebraically

Using coalgebraic methods, we 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 indicate a number of intriguing directions for future work. We briefly compare infinite games with other notions of games used in computer science.