The game of life and death March 19, 2011Posted by Ezra Resnick in Game theory.
You and your sweetheart have been captured and brought before a semi-barbaric (yet game-theory-savvy) tyrant. He informs you that your fate will be decided by the outcome of a little game he invented, which he calls “The Game of Life and Death.” The tyrant produces two identical gold coins, and hands one to you. One side of the coin is engraved with a tree (i.e., Life), while the other side is engraved with a skull (i.e., Death). All you need to do is choose which side of the coin to play. The tyrant will do likewise, and your choices will be revealed simultaneously. You and your sweetheart’s fate will then be determined as follows:
|Tyrant plays Life||Tyrant plays Death|
|You play Life||Only your sweetheart dies||You both live|
|You play Death||Only you die||You both die|
You have until the next morning to make your decision. Before you are taken away, though, you see the tyrant whispering something into your sweetheart’s ear. Later, in your cell, you ask her what he said. Your sweetheart looks into your eyes, and tells you that the tyrant promised he would play Death. If the tyrant is to be believed (and he is known for being an honest tyrant), this is good news, because then you can save both yourself and your sweetheart by playing Life. Your sweetheart encourages you to do so.
But suddenly a thought occurs to you: what if the tyrant actually told your sweetheart that he intended to play Life? In that case, she might be lying in order to get you to play Life as well, and so sacrifice her life for yours! If this is the case, you must certainly play Death, so that she will live. On the other hand, if you play Death, and it turns out that both the tyrant and your sweetheart were truthful (meaning that the tyrant plays Death as well), then both of you will be killed — even though you would both have gone free if only you had followed your sweetheart’s advice…
So what would you do? Life or Death?