Transgender people in sports

Saw a story on Caitlyn Jenner playing in her first golf tournament and it made me wonder about how the issue should be handled in sports.  It's no question that men have, for the large majority, more physical strength than women.  So is it fair, for someone who was born a man, to play as a woman?  It goes both ways too, a person who is born as a woman but identifies as male could be atmuch greater risk in certain sports, like MMA for example, if they decided to play the sport under the gender they identify with instead of the gender they were born due to inherent physical differences between male and female.