Would a rational actor ever build a weapon that would destroy both himself and his opponent?

If we take it at face value, it would seem that it’s never a good idea to make something that would harm you and your opponent. Afterall, despite man’s impeccable’s record for finding new ways of killing, he still values self preservation fairly highly. Even in scenarios such as suicide bombing, the bomber is usually convinced that he’s dying for a good cause or that there is an afterlife which is worth blowing himself up for.

So here’s a basic sequential game. The actor, row, goes first and the actor, column, goes second. Row’s nuclear weapon does not harm himself while column’s nuclear weapon is self destructive. A utility of 1 means survival. A utility of 0 means destruction.

The Nash Equilibrium for this game is 1, 1. If row decides to Nuke, column can punish row by nuking as well. To column, it makes no difference. Once row has launched his missiles, he is as good as dead. Because row knows that if he nukes, column will punish, his best strategy is to not nuke. Column’s best decision is then to not nuke.

So the above scenario is still fairly abstract. There are a few things to note. The game does not predict what will happen in the future. It may well be that both parties will decide to develop even more destructive and effective weapons, or it could be that both parties will try to┬ánegotiate┬ádisarmament. I cannot forecast how the game will change, but I can say that under the circumstances in the above game, it is entirely rational to have a weapon that’s self destructive.

The key is that column does not build the self destructive weapon because he wants everybody to die. In fact, everybody dying is equally as bad as having row nuke for column. He builds the weapon because row will react differently if he knows that he cannot nuke with impunity. Having the weapon is better than having no weapon. Having no weapon is effectively declaring to row that you will always play a no nuke strategy in which case column’s fate depends on whether or not row feels like destroying column. If we modify row’s utility value from deciding to nuke to be 1.1 so that it’s higher than 1, row still does not have an incentive deviate if it knows that column will nuke if it does so. We can interpret the 1.1 utility as row’s increased utility from not having an opponent. Now if column is forced to play a not nuke strategy because it does not have the weapon available, then row’s best decision would be to nuke. Column has a clear incentive to have the weapon.