Today's episode of Doctor Who featured an interesting dilemma, centered around an object called the "Osgood Box". I'm not well-versed enough in game theory to recognize it as an existing problem, but it seems to me that principles of game theory could potentially be applied to it.
The Setup: There are two factions, currently at cease-fire (Humans and Zygons). One rebel of one faction (Zygon) is attempting to break the cease-fire and ignite a worldwide war. Zygons are shapeshifters, and there are twenty million of them hidden among the Human population of Earth. Most Zygons just want to live in peace pretending to be Humans, and most Humans don't know Zygons exist at all.
The Zygon rebel commander and U.N.I.T.'s Chief Scientific Officer face off with two boxes between them. Each box has two buttons, labeled "Truth" and "Consequences".
The Doctor informs them that one of the two buttons in front of the U.N.I.T. CSO will release a gas that will create a chain reaction in Earth's atmosphere and kill every Zygon on the planet, and the other will detonate a nuke directly underneath them, annihilating London in the process (as well as all of the characters in the room). One of the buttons in front of the Zygon rebel commander will cause all Zygons on the planet to revert to their natural form for an hour (revealing them to Humanity at large and kickstarting the war), while the other will prevent any Zygon on Earth from shifting out of their current human form ever again.
The Question: Given this information about what the four buttons will do,
- Should the U.N.I.T. CSO press either button in front of her, and if so is there enough information to get a better than 50% chance at stopping the war by pressing a button?
- Should the Zygon rebel commander press either button in front of her, and if so is there enough information to get a better than 50% chance at starting the war by pressing a button?
- If either representative of her species chooses to press a button, should her opponent change her decision about pressing a button and/or which button to press?
Resolution in the Show: (Spoilers for DW fans who have not watched the episode)
The Doctor has setup the situation to try and keep the peace, explaining that the two boxes are a microcosm of every single war ever waged. The U.N.I.T. CSO opts to press neither button, and the Doctor monologues at the Zygon rebel commander for a bit, before she comes to the conclusion that neither box does anything at all. None of the four buttons are pressed.
The U.N.I.T. CSO expresses incredulity at the situation, and the Doctor tells her "that's what you said the last 15 times," before wiping her memory of the events.