Game Theory

Game Theory Parables for Game Designers

How to Build a Doomsday Device

How many times have you been in an area control game and received a threat, like “if you attack me here, I’ll attack you back, and then we’ll both lose” ?  How many times has it worked?

It shouldn’t work, because it’s a non-credible threat.  Let’s suppose you receive this threat, and you decide to attack anyway.  Presumably, you’ll get the benefits of that first attack, putting you ahead in the game.  But then your opponent has to decide whether or not to follow through with their threat.  If they do, everyone is worse off, including them.  If they don’t, they stay where they are at.  Why would a rational player choose an action that sets them behind?

(note: there are some factors that could answer this, like spite, or reputation, or other meta-game effects - let’s set those aside for now and focus just on the game state and maximizing points/chances of winning).

This sort of situation appeared in the Cold War between the USA and the USSR.  Both sides rapidly built up their nuclear stockpiles, but figured the peace would hold under the threat of mutually assured destruction.  That is, if the Americans ever attacked the Soviets, the Soviets would retaliate, and both sides (including us caught in the middle!) would be obliterated.  This outcome was thought to be enough to ensure a stalemate.

But put yourself in the Soviet war room during an American attack on one of your satellite countries.  If the attack is happening, then that poor country is already doomed.  You would then have the choice to retaliate, and doom everyone, or not retaliate and maintain the status quo.  The seemingly rational option would be to not retaliate, but if so, then the threat is worthless.

Any threat that commits you to taking an action that you wouldn’t choose to take is non-credible.

So how do you make these sorts of threats credible?  Let’s turn to Dr. Strangelove for inspiration.  In this classic scene, the Americans are deciding how to handle what looks like a rogue American strike on the USSR.  The Soviet ambassador describes the inevitable Soviet response (their “Doomsday Device”), and in doing so he outlines the principles of making a threat credible.

First, note that when the American president (Peter Sellers) asks if the Soviets are threatening to carry out this retaliatory attack.  The Soviet response?

“No sir.  It is not a thing a sane man would do”

This points out that the retaliation is insane, irrational, and would not be chosen by the Soviets if they had a choice (as described above).

The Soviet Doomsday Device is designed to trigger automatically, to take away the decision making agency of the Soviet Premier.  This is important because, if the choice is offered, a rational player wouldn’t retaliate, so the choice must be taken away.  It is also an automatic commitment to a non-rational response — if the response was rational, the Premier wouldn’t need a device to force it.

Could the device be disarmed?  No, that would defeat the purpose of it, restoring agency to the Premier who would not then choose to retaliate. 

Is such a machine possible?  Dr. Strangelove (Peter Sellers) points out that such a device, with its automatic commitment to the insane response, is essential to its design.  “Deterrence is the art of producing in the mind of the enemy the fear to attack.  So because of the automated and irrevocable decision making process which rules out human meddling, the Doomsday machine is terrifying, simple to understand, completely credible, and convincing”

This is how to make a credible commitment.  Well, almost.  Despite the existence of the Doomsday Device, the Americans attacked anyways.  Why?  Simple — they didn’t know about it!

“The whole point of the Doomsday machine is lost if you keep it a secret!  Why didn’t you tell the world?

The existence of a Doomsday Device needs to be common knowledge for all parties: the Americans need to know about it, the Soviets need to know that the Americans know about it, etc.  A grand, public spectacle to reveal the Device to the world would have prevented this whole situation.

Alas, the Premier loves surprises.

What can you, as a Game Designer, take away from this?  If your game is the sort of thing where threats (or promises!) are common, then you may want to include some mechanisms to enable players to make their commitments credible. 

First, provide a way to “lock-in” the threat, so that it cannot be undone later on.  Commit a card face down, program an action, impose a stiff penalty, anything like this would work.  You need to remove player agency, and force them to follow through on their threat if it comes to it (though if the threat is credible, they won’t have to).

Second, let players make it public.  A response card cannot be held in hand, or hidden in the mind of the player.  It must be seen by all that if the action is taken, the response will be automatic.  Note that it really does have to be seen by everyone, not just the player being threatened.  If one player has a (semi-secret) Doomsday Device aimed at another player, a third player may inadvertently instigate a war because they won’t know that the second player is operating under the fear of a Doomsday Device.  Making the Device public for everyone gives everyone the proper knowledge needed to act in the way that the Device-builder intends.

This holds for promises as well as threats.  In The Maltese Falcon, Sam Spade returns the titular Falcon to Mr. Gutman, after the promise of a substantial award.  The actual award was less than substantial.  Spade mentions “we were talking about more money than this.”  Gutman replies “Yes sir we were, but we were talking then.  This is actual money, genuine coin of the realm.  With a dollar of this, you can buy more than with ten dollars of talk.”

Talk is cheap.  Once he gets his hands on the Falcon, why would Gutman follow through on the substantial reward promised to Spade?  His promise is revocable, and nothing holds him to it. Spade should have known.

For another real-life example of a Credible Commitement, recall Cortés’ conquest of the Aztecs as described in The Emergence of Modern Game Theory.  Burning his fleet is a public, irrevocable commitment to an irrational action.

Let players burn their fleets.

Sam Hillier