In what ways does Hamlet’s “antic disposition” affect the actions of other characters in Act 2 of Hamlet.

Certainly the chief impact of the "antic disposition" or
feigned madness that Hamlet adopts on other characters in the play is to greatly concern
them as to what is ailing Hamlet. Note that it is Ophelia's terrified reaction to Hamlet
appearing in her chamber that convinces Polonius that Hamlet is mad because of his
thwarted love for Ophelia. Note what he concludes:

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This is the very ecstasy of
love,

Whose violent property fordoes
itself,

And leads the will to desperate
undertakings,

As oft any passion under
Heaven

That does afflict our
natures.

Polonius is thus led
to believe that Hamlet is "mad" because of the way he had commanded Ophelia to not
receive his attentions any more. Ophelia is clearly greatly concerned and shocked by
Hamlet's madness. Act II scene 2 indicates how Claudius has enlisted two of Hamlet's old
friends, Rosencrantz and Guildenstern, to help him ascertain the cause of Hamlet's
madness:

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...so by your
companies

To draw him on to pleasures, and to
gather

So much as from occasions you may
glean,

Whether aught to us unknown afflicts him
thus

That open'd lies within our
remedy.

Claudius and Gertrude
therefore are concerned by Hamlet's "transformation" and hope to use his old friends to
find out the cause and therefore, as Claudius says, cure
him.

It is hard not to relate Hamlet's madness to a kind of
detective story. Having introduced this new element into the plot of the play, the other
characters desperately try to work out what the reason for this madness is and how they
can cure it.