Zhen Li¹, Tao Gao²; ¹Zhejiang University, ²UCLA

Vision plays a crucial role in non-visual processes by offering structured, universal representations that other cognitive systems can leverage without maintaining their own visual systems. This capability allows vision to influence downstream cognition, as seen in phenomena like the minimal group effect, where arbitrary color labels shape group identification, and focal point effect, where visual salience aids coordination among identical options. This study explores how latent hierarchical visual structures influence strategies of conflict and coalition formation in adversarial contexts. We developed a three-player territory expansion game where competition and cooperation coexist. Players competed for fixed territories while avoiding costly battles. Alliances, though beneficial, were challenging due to the absence of communication and mechanisms for enforcing alliances. Players navigated ambiguous relationships, where any individual could be an ally or adversary at any moment. In Experiment 1, participants played on one of two game boards: a uniformly colored Non-Structured board or a Structured board inspired by Mondrian art, featuring hierarchically organized colored blocks generated by a latent parse tree. Although irrelevant to gameplay rules, the visual structure significantly reduced battle frequency and intensity. On the Non-Structured board, players engaged in "a war of every man against every man," as described by Hobbes. Conversely, on the Structured board, players residing in sibling groups within the perceptual hierarchy were more likely to ally against the non-sibling group, which ended with the smallest territory. Crucially, these effects emerged only through gameplay. In Experiment 2, when participants were asked about their strategy after observing the structured board without gameplay, they showed no recognition of non-sibling group disadvantages or preference for allying with sibling groups. These results underscore that humans take advantage of structured visual representations in conflict resolution by transforming a structure of perception into a structure of bargaining, provided they share the same visual scene.