AGADAH: The Gemara gives several reasons why invited Haman to join her and
the king at the first dinner she made in the king's honor, as part of her
plan to have him rescind the decree against the Jews. The Gemara questions
why Esther invited Haman to come to the first meal along with the king, when
she was not going to reveal herself until the second meal.
The VILNA GA'ON (Kol Eliyahu 142) cites a statement of the Gemara in Pesachim
(111a) in order to explain Esther's motivation.
The Vilna Ga'on said that "had I been there, I would have added another
reason why she invited him." The Gemara (Megilah 15a) says that when Esther
heard the news of Haman's plot against the Jews, it shocked her so much that
she became a Nidah. Three days later, she made the first banquet for
Achashverosh and Haman. Her motivation was to invite the two of them and, as
a Nidah, to situate herself between them.
The Gemara in Pesachim says that if a woman walks between two men while she
is a Nidah, then if it is the beginning of her state of Nidah, one of the men
will be killed, and if it is the end of her state of Nidah, a quarrel will
arise between the men.
Based on this, Esther reasoned that if she was at the beginning of her state
of menstrual bleeding, then one of them would die, leading to the annulment
of the decree against the Jews. If she was at the end of her state of Nidah,
then a quarrel would arise between Achashverosh and Haman, and again
Achashverosh would rescind the decree. Either way, the decree would be
rescinded as a result of Esther's strategy! (In the end, both outcomes proved
true; a quarrel erupted between Haman and Achasverosh, and Haman was killed.)
(The Gemara in Ta'anis (29a) says that when the senate made a Gezeirah, if
one person in the senate would die, then it would be taken as an omen that
the Gezeirah must be annulled, see the "Nusach Acher" in Rashi here DH
she'Yehareg. However, it is not entirely clear that this rule actually
applied in the case of Haman, since it is evident from the Megilah that his
death did *not* cause the decree to be rescinded. Since the decree was signed
with the *king's* signet, it didn't seem to matter what happened to Haman.)
The Gemara cites ten reasons why Esther invited Haman to the banquet that she
had arranged for the king. Raban Gamliel states that the reason suggested by
Rebbi Eliezer ha'Moda'i is the most befitting of all. Rebbi Eliezer ha'Moda'i
said that Esther's intention was to make the king and all of the other
officers jealous of Haman, which indeed is what ultimately happened. During
the second banquet which Esther arranged, when the king stepped out into the
palace garden, Haman pleaded for his life from Esther, and when Achashverosh
returned he found that Haman had fallen on the couch with Esther. Achasverosh
exclaimed, "Ha'gam li'Chbosh Es ha'Malkah Imi ba'Bayis!" -- "Does he even
want to overtake the queen with me in the house!" (Esther 7:8). Charvona, one
of the officers present, gave the king the idea to hang Haman on his own
gallows.
There is a remarkable allusion in the Megilah that this was Esther's
motivation in inviting Haman to her banquet, in the very verse cited above.
The only place in all of Tanach in which we find the word "Mishteh" (banquet)
as an acronym (either as Roshei Teivos, the first letters of four consecutive
words, or as Sofei Teivos, the last letters of four consecutive words) is in
this verse, that expresses how jealous Achashverosh became of Haman --
"Ha'ga*m* li'Chbo*sh* E*t* ha'Malka*h* Imi ba'Bayis!" (RAV MORDECHAI ARAN in
NIFLA'OS MI'TORASECHA)