"The Lady or the Tiger?" does suggest the possibility of polygamy due to the bizarre practice of the king's arena. In the arena, the person on trial must choose between two doors, one featuring a lovely lady and the other a terrible tiger. The narrator points out that:
"It mattered not that he might already possess a wife and family, or that his affections might be engaged upon an object of his own selection; the king allowed no such subordinate arrangements to interfere with his great scheme of retribution and reward."
So if the accused person did have a wife, the natural conclusion would be that he would gain an additional wife if he chose the door with the lady. The semi-barbaric king who uses the arena as his preferred system of justice probably would have no qualms about the practice of polygamy in his kingdom. This detail really reveals that the king is purely interested in the spectacle for his own entertainment and benefit, not really caring about the lives of the people affected.