One of my bridesmaids was the first to RSVP which happens to be one of game winning criteria. Is it ok for a member of the bridal party to win a gift or are they out of the running?
Who is hosting your bridal shower? As the bride, you really shouldn't have anything to do with planning or giving out prizes. This is the responsibility of the host. If your bridesmaid is not hosting, then I would think she is eligible to win a prize.
Although, typically the shower games are played at the shower, where all can participate and enjoy. Top Wedding Questions Forum Moderator - "Write your sorrows in the sand, your blessings in stone".