He authorized her to get divorced and she got divorced herself
Question

                My wife insisted on divorce a lot so I just said to her: “ I am not going to divorce you, if you want to get yourself divorced, then it is up to you” and I authorized her to divorce herself. She said openly after this: “I get myself divorced”. She tried a lot to make me take her back at that night. She thinks that what happened does not count as divorce, because she did not mean it. She does not believe that there is no joking when it comes to the matter of divorce. I did not authorize her again after this when I saw how rush and irresponsible she behaved. While I thought that it would stop her to ask for divorce again. What is the ruling on what happened?.
Praise be to Allah.If the husband says to his 
    wife: Divorce yourself, or It’s up to you, or You choose, or I authorize you 
    to get divorced, and she says, I divorce myself, then it counts as a 
    divorce. 
The fuqaha’ discussed in 
    detail a number of divorces that the wife may do, depending on the phrase 
    used by the husband, but as the wife only issued one divorce to herself, 
    there is no need to go into those details here. 
Based on that, one divorce 
    takes place if the wife says “I divorce myself from you” and it cannot be 
    accepted from her that she did not intend a divorce, because if divorce is 
    mentioned clearly, then the one who issued it is not to be asked about his 
    intention, and the divorce counts as such even if he says I did not intend 
    it. 
If this was a first or 
    second divorce, then you may take her back so long as the ‘iddah has not yet 
    ended. 
The wife has to understand 
    that divorce is a serious issue, and that there is no room for joking or 
    playing about in this matter. It counts as a divorce whether it is issued in 
    earnest or in jest, as the Messenger of Allaah  (peace and blessings of 
    Allaah be upon him) said: “There are three matters in which seriousness is 
    serious and joking is serious: marriage, divorce and taking back (one’s 
    wife).” Narrated by Abu Dawood (2194), al-Tirmidhi (1184) and Ibn Majaah 
    (2039); classed as hasan by al-Haafiz Ibn Hajar in al-Talkhees al-Habeer 
    (3/424) and by al-Albaani in Saheeh Sunan al-Tirmidhi (944). 
It is not permissible for a 
    woman to ask her husband for a divorce unless there is a reason which makes 
    it permissible for her to do so, such as bad treatment. See the answer to 
    question no. 117185. 
See also the issue of 
    Tafweed al-Talaaq (delegating divorce) in al-Mawsoo’ah al-Fiqhiyyah 
    (13/113) and al-Sharh al-Mumti’ (13/84). 
And Allaah knows best.