God does not allow polygamy. Although during the times of the old and even presently it was within the power as a king, that's why we hear of cases of Solomon and other Kings as at that time. Having multiple wives was a thing that was rampant as at then.
But it was not allowed by God to David or to Solomon. Some of the sad experiences they had could be attributed to their disobedience to God. In the case of David his child died at a very tender age. While in Solomon's case, God turned His back on him in the latter part of his life because he abused his power as a king. He had 700 wives and 300 concubines. God wasn't pleased with Solomon because of those acts that he had done.
Polygamy is not allowed but men can choose for themselves because we are given the power to choose either to obey or to disobey God. It depends on our decision. God prescribes, but it is up to us to decide. And whatever our decisions may be, we will be answerable to God. Whatever things we have done; be it good or evil, we will all be answerable on the day of judgment.
