The court performs its rope-dancing (tightrope-walking) and secret thread-jumping/thread-limboing for Gulliver, who explains that these games are very dangerous and are used to determine which members of court should fill vacant offices. Those skilled at the games are conferred great status and respect.
Curiously, the Lilliputian state uses tests of physical power and agility (rather than tests of moral power and reason) to determine who will hold its governmental offices.
Later Gulliver builds a platform with his handkerchief and has the Lilliputians joust on it to everyone’s delight, though he stops when someone falls through the cloth.
The fact that his handkerchief can be used as a stage emphasizes Gulliver’s very different size (and perspective). He is a gentle, moral friend, stopping the game to protect physical safety.
Gulliver realizes that the “great black substance” Lilliputians report having found on the beach is his hat. He’s still chained and not allowed to get it himself. The Lilliputians retrieve and return it to him, though, by dragging it the whole way, they’ve damaged it.
The Lilliputian perspective doesn’t recognize a human hat as a hat and therefore doesn’t know how to treat it as a human would.
For amusement, the Lilliputian emperor has Gulliver stand upright and has his whole army march through Gulliver’s legs, ordering the soldiers to treat Gulliver decently “upon pain of death.”
A juxtaposition of perspective: the king protects Gulliver’s physical safety and announces his physical power over soldier’s bodies (he can kill them). However, Gulliver is so much larger than everyone that he faces little risk and could easily stamp everyone to death, which is perhaps why he can afford to resort to moral power rather than physical power—because he is in fact so physically powerful that he is essentially invulnerable.
Gulliver has all along been begging the Lilliputian emperor for liberty and the emperor and his council (all except for Skyresh Bolgolam, a sour minister who dislikes Gulliver) agree on the condition that Gulliver sign an agreement. The articles of the agreement state that: Gulliver will not leave the kingdom or enter the metropolis without permission, that he will not trample the fields or the Lilliputians, that he will carry Lilliputian messengers on urgent errands, that he will be an ally against the Blefuscians in warfare, that he will help maintain the kingdom and will survey its circumference, and that he will for his compliance be provided with a specific amount of food and drink. Gulliver notes that the specific amount was ingeniously calculated according to his body measurements. He signs and is freed.
The treaty functions to restrain Gulliver’s physical power (by restricting his movements, making him promise to put his large size to Lilliput’s use, and denying him sustenance if he should choose to disobey these conditions). Only after Gulliver has submitted to these restraints on his own physical power will the Lilliputian state agree to withdraw its own physical hold on him (the chain imprisoning him in the temple).