How should you react after your ex girlfriend gives you the silent treatment and dates other guys after you sincerely attempt to make peace with her after a misunderstanding?

You should accept that others play games as relates to relationships and choose not to play the games yourself.

If she is your ex-girlfriend, she is no longer in a relationship with you. You should convince yourself that what she does is not important to you. You made the attempt to fix whatever problems you had. It did not work. Be mature and move on with your life. It may hurt, but life goes on. Time doesn't heal all wounds, but it does give you distance and may help you with perspective.