Fig. 1: Schematic representation of the Space Dilemma.

a Participants first positioned themselves in the space, hidden from the other player. They were then presented with a bar moving across the space (representing their location) and were required to commit to a certain location by pressing a button while the bar was moving through it. The bar would take 4 s to reach the end of the space. Once they responded, the bar stopped at the chosen location and was shown for the remainder of the 4 s. After both counterparts positioned themselves, their respective positions were shown to each other for 1–1.5 s before the target appeared (left panel). The player closer to the target won the trial (three examples in right panel) as identified by the colour of the target. The reward obtained is inversely proportional to the distance to the target, and reflected by the size of the target square. b The average reward for each player depends on the position in the territory. In each panel, the colour intensity represent the average reward obtained playing that position over many trials. In individual settings (top panel), the best strategy—to minimize distance to the target and maximize rewards - is to target the middle of the space. However, in the two-player space dilemma, as deployed here, multiple configurations exist. Fully cooperative behaviour involves both players positioning themselves in the midpoint of each hemifield, which minimizes the average proximity to any possible location of the target, thus maximising gains (second panel from the top). As this strategy is not a Nash equilibrium, players may have the incentive to deviate from their half side and thus cover more territory (third panel from the top). As such, any positioning closer to the midpoint can be defined as more competitive behaviour. When both players are highly competitive they both target the midpoint, winning less on average (bottom panel).