Desperately needs help with nested looping

[B. Fongo]

I'm quit confused with what I have below.

I have 2 database tables; Games and groups.

Name     Group
#############
John ,    GroupA
Miler,   GroupA
Peter, GroupB
Mathew, GroupB
Mark, GroupB
Luke, GroupA

I'm trying to select the members based on their groups and insert them
into a different table.
I've written my script to receive the names of the group from param()
and do the job for me, but something is wrong somewhere that makes the
script fail. It inserts members of only one group even if param contains
two group. I've modified the script several times, but still not getting
the desired result.
Assuming the using selected 3 groups and sends them to the script, it
should insert members of all the 3 groups into the games table.
################################################
#!/usr/bin/perl -w

use CGI;
my $obj = new CGI;

use vars qw(@groups $group);


@groups = $obj->param('groups');

do_db();

############ Subroutine##############
sub do_db {

  
  foreach (@groups){
        
    $sth = $dbh->prepare(qq{SELECT Name FROM Groups WHERE Group =
"$_"});
    $sth->execute();
  }
  while (my @value = $sth->fetchrow_array){
        foreach $member (@value){
          $dbh->do(qq{INSERT DELAYED INTO Games(Name) 
          VALUES("$member") ||  print_error("$DBI::err","$DBI::errstr)
&& die;
       }
  }

}

Your help will be appreciated.