Question

polygamy is gradually decling in our societies

Answer 1

In most areas of Europe proper polygamy (multiple wives) died out with the advance of Christianity. But some areas - chiefly Scandinavia and the Celtic world - held on to its cultural importance, and allowed a high-ranking man to have an official wife under canon law as well as several 'in the Danish custom.' The church regarded more Danico wives as mistresses, and their children as illegitimate. But cultures which accepted them saw them as lesser or even full-status wives, and children born to them as legit.

These cultures often had other odd marriage practices, such as the Gaelic 'left-handed' marriage and kings legally marrying their tribal land. And they were regarded as 'incestuous' by outsiders, as the church had harsh bounds on consanguinity. People could not marry if they were closer by blood than six generations (later changed to four). These cultures went 'screw that.' But they never married any closer than cousins. They weren't actually incestuous, by our standards.

As to when it declined, I'm not so sure about Scandinavia. But in the Celtic world (especially Ireland and Gaelic Scotland) it outlasted the high medieval. It was common and culturally-acceptable for important leaders to have high-status mistresses as late as the late 1400s, and a few continued the practice after that. It ended because societies which didn't tolerate it came to control the church regionally, so it faced increased religious opposition whereas once churchmen would nod along.
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