What economic lessons can we learn from House of the Dragon? That is the goal of this series, as each week during House of the Dragon Season 2 we are dropping a new video examining economic concepts from Game of Thrones or House of the Dragon. Check out the video below.
Warning - serious spoilers ahead!
The Game
The situation at the end of episode 1 of season 2 is pretty crazy.
The Queen is in a game vs. two assassins and the stakes are high. What are they? They are playing for the life of the prince, the heir to the throne. The assassins want to kill the prince - and only the prince. But there are two kids who look the same to them. Queen Helaena knows which one is the prince and which isn’t. The assassins decide to ask Queen Helaena to point to the prince. At this point, we’ve got a game that can be represented by a 2*2 payoff matrix.
The Queen can be truthful in her response and point to the prince or lie and point to the prince’s sibling. The assassins can either believe the queen or not when they choose who to kill. There are four possible outcomes in this game:
The Queen is truthful and the assassins believe her (and kill who she points to)
The Queen is truthful and the assassins do not believe her (and kill the child she does not point to)
The Queen lies and the assassins believe her (and kill the child she points to)
The Queen lies and the assassins do not believe her (and kill the child she does not point to)
At each of these outcomes there are payoffs. The result is either the prince or his sibling dies. The Queen wins if the prince survives. (Yes, one of her children is still murdered, so it’s not really winning. But the goal is to have the heir to the throne survive.) The Assassins win if they kill the prince.
What makes this game interesting is there is no pure strategy Nash Equilibrium. A Nash Equilibrium is a stable point in a game, where neither player is willing to change their choice given the other players actions.
Here, however, that will never be the case. At each of the four possible outcomes, someone loses the game and would want to switch their choice. For example, if the Queen lied but the assassins believed her, the Queen wins. And therefore, the assassins would rather choose the strategy of not believing her, because they would win.
The Mixed Strategy Nash Equilibrium
In a game like this, there is no pure strategy Nash Equilibrium. There is, however, a Mixed Strategy Nash Equilibrium. A Mixed Strategy Nash Equilibrium occurs when players randomize their strategies and given these randomized strategies, no player has an incentive to change their choices. For example, in rock paper scissors, if each player randomly played rock, paper, and scissors 1/3 of the time, nobody has an incentive to move away from that randomized strategy and that is the Mixed Strategy Nash Equilibrium of the game.
In the scene, Queen Helaena would want to randomly choose the prince 50% of the time and the assassins would want to believe her 50% of the time. We won’t go through the analytics here, but if you want more on how to solve, check out this previous post I made during my game theory class.
For more, watch the video
There are some extra considerations we haven’t yet discussed - to learn about those, watch the video below.