In Frank Stockton's short story "The Lady or the Tiger", I think the author's purpose is to present a familiar fairy tale with an ending which will provoke enthusiastic discussion about which choice the princess made. We all make decisions and with decisions come consequences. In this case, the decision and the consequence are life or death. Readers are to use the information in the story such as the semi-barbaric king or the princess's jealousy of the woman chosen for her lover to marry if he lives as guides to their own belief about the ending. I think that Stockton believed that whatever choice the reader made, it would reveal more about the reader and his beliefs about people than it would about the story.
The purpose of this short story is to provoke a discussion about human nature: are people primarily motivated by good or by evil impulses? It is also meant to provoke a discussion about love: is love dominated by possessiveness, self-interest and envy or by an altruism that leads to self sacrifice for the beloved?
In this story, a fable set in a fairytale kingdom, a monarch determines the guilt or innocence of someone accused of a crime in the following way: the accused party must, before a stadium filled with people, choose one of two doors. Out of one door comes a beautiful maiden (the story assumes heterosexuality and an accused male) that the accused can then marry (this means he is innocent) and out of the other comes a hungry tiger that will devour the man (this means he is guilty).
In this story, the monarch's daughter falls in love with a commoner. The enraged king has the commoner put on trial for daring to woo a princess. The princess knows which door holds the tiger and which her beautiful rival. She indicates to her beloved to open one of the doors. But the story ends before the reader knows which one.
The characters in the story are generic--they are types rather than developed characters--which makes this story a parable about human nature rather than about the particularities of certain personalities.
Which door the reader suspects the princess chose says something about how that reader understands both human nature and human love.