In international conflicts, a land power may be motivated to wage wars for territorial expansion, but engaging in a prolonged war is costly. Therefore, the decision between war and peace is of critical importance and has been extensively studied in game theory by analyzing the payoffs associated with different actions. In various fully cooperative games, participants have been shown to converge on visually salient choices. However, in pure zero-sum competitions, focal points are of little use because rational decisions are completely determined by the payoff matrix. It remains unclear how focal points function in mixed-motive competitions such as ground wars, where intense competition coexists with opportunities for reciprocal settlement. In existing studies of mixed-motive games, researchers have mainly focused on manipulating information directly related to the rules and rewards of the games. Therefore, it remains unknown whether perceptual grouping, which is irrelevant to the rules and rewards, can influence the progress of conflict.

Addressing this question, the present research demonstrates that perceptual grouping, although completely irrelevant to the payoffs, can nevertheless provide salient visual common ground as a mutually recognized focal point. As a result, it significantly reduces conflicts between powers and facilitates peaceful settlements along the borders of perceptual groups. To test this idea, we designed a two-player game that highlights three fundamental principles of land-power competition. Players' wealth increases with territorial expansion. However, war is expensive even for the winner, and troops consume more supplies as they move farther from the capital. The players' goal is not to annihilate the opponent but to acquire the maximum wealth. We employed a between-group design in which participants were divided into two conditions. In the grouping condition, players competed on a battlefield divided into two perceptual groups marked by colors, whereas in the non-grouping condition the battlefield was homochromatic and contained no perceptual grouping. Importantly, the colors were completely irrelevant to the rules of the game.

In Experiment 1 (a six-grid battlefield) and Experiment 2 (a seven-grid battlefield), human participants in the grouping condition initiated fewer wars, accumulated more wealth, and achieved more peaceful settlements than those in the non-grouping condition. Moreover, the perceptual boundary was respected by the players: they were less likely to cross a line when it was marked by perceptual grouping. We propose that this facilitation of peace arises from perceptual grouping serving as a shared visual common ground among humans. To test this mechanism, in Experiment 3 we presented the two participants with different battlefields: the color of the middle grid was reversed. One player saw three red grids and four blue grids, whereas the other saw four red grids and three blue grids. Under this condition, the effect of perceptual grouping disappeared. When perceptual grouping was mismatched between players, it failed to constrain conflict. In addition, the effect of perceptual grouping appeared to be largely implicit, as almost all participants failed to report any influence of the color groups on their decisions.

Our findings provide strong evidence that perceptual grouping, as a purely visual phenomenon, can facilitate tacit cooperation between participants in repeated mixed-motive game situations. This discovery supports the hypothesis that even in intense competition, humans tend to seek reciprocal settlements by aligning their expectations with salient visual cues that serve as perceptual focal points. The results also offer insights for the design of AI systems: in human-AI interaction, rational decision-making alone is insufficient; AI systems must also learn human psychological and perceptual representations in order to collaborate effectively with humans. More broadly, this study suggests that the balance of power in the world may be implicitly and subtly influenced by humans' perceptual grouping of territory.