This study introduces the concept of “compound games” and investigates whether the decomposition of a game – when implemented – influences behaviour. For example, we investigate whether separating battle of the sexes games into a pure coordination component and the remaining battle of the sexes component changes coordination success. The literature attributes high coordination rates in pure coordination games with focal points to team reasoning and low coordination rates in related battle of the sexes games to level-k reasoning. We find that coordination
success in compound games depends on the decomposition and order of component games.