Most octopuses are regarded as solitary and distinctly asocial. Although there are many published studies of signaling behaviour among schooling cuttlefish and squids, there are very few of similar behaviour among the octopuses. The exceptions are related to display behaviours and morphology of octopuses in pre-copulatory periods. However, in this study we show that Octopus tetricus produce displays that predict the subsequent outcome of pair-wise interactions. That is, they signal their intent to escalate or retreat from agonistic interaction. O. tetricus is a medium-sized common shallow-water octopus of southeastern Australian and New Zealand water.  We examined 193 pair-wise interactions during 60 h of video recordings of octopus behaviour at an extended midden where this species occurs in high density. Body color was measured as pixel intensity difference of the octopus head and mantle from an adjacent region of the substrate. The relative body darkness of the approaching and responding octopuses predicted interaction outcomes. Interactions in which dark body color by the approaching octopus was matched by dark body color by the reacting octopus typically led to escalated displays or fighting behavior. Dark or intermediate body color by the approaching octopus that was met by pale color in the reacting octopus was followed by retreat of the paler octopus. Particularly dark approaching octopuses gave chase to paler retreating octopuses. Other potential signals included postures and behaviors occurring in specific contexts such as between mated male-female pairs (reaching behavior) or by presumed male octopuses to intruders into their proximity (body posture displays). This study is the first to document signaling of intention during agonistic interactions among octopuses.