Question

1. Below is an example of a classic prisoners’ dilemma game.

In Westeros (see Game of Thrones) the dead are coming with winter. Which outcome has the best overall consequences and the best chance of surviving for Cersei and Daenerys?

	Cersei fights (cooperates)	Cersei runs (defects)
Daenerys fights (cooperates)	Each has 70% chance of surviving and 30% chance of being slaughtered	Cersei has 10% chance of being slaughtered, 90% chance of escaping Daenerys is completely screwed and has 95% chance of being slaughtered, only 5% chance of surviving
Daenerys runs (defects)	Daenerys has 10% chance of being slaughtered, 90% chance of escaping Cersei is completely screwed (and deserves it because she is evil) and has 95% chance of being slaughtered, only 5% chance of surviving	Each has 20% chance of surviving and 80% chance of being slaughtered

What is the best option for each queen thinking only of themselves?

What is the outcome for all participants if each queen pursues her best option?

Answer 1

Let's make the matrix again with payoffs in terms of chance of survival (in%).

	Cersei fights	Cersei runs
Daenerys fights	70,70	5,90
Daenerys runs	90,5	20,20

If Daenerys chooses to fight, Cersei will choose to run (90>70).

If Daenerys chooses to run, Cersei will choose to run.(20>5)

If Cersei chooses to fight, Daenerys will choose to run.(90>70)

If Cersei chooses to run, Daenerys will choose to fight.(20>5)

So, the Nash equilibrium is for both queens to run (Defects, defects).

Q. Which outcome has the best overall consequences and the best chance of surviving for Cersei and Daenerys?

Answer. We can see that if both queens decide to fight there chance of survival is 70% each instead of the Nash equilibrium at 20% survival chance.

So overall best consequence is for both queens to fight (cooperates, cooperates)

Q.What is the best option for each queen thinking only of themselves?

Answer. When each queen thinks of themselves they decide to run (defects). As the (payoff) chance of survival is highest when they run (90%).

Q.What is the outcome for all participants if each queen pursues her best option?

Answer. If each queen pursues her best option i.e to run (defects).

The outcome will be for both queen to run with 20% survival chances.

Since both Queens think of their own individual gain and choose to run, they fail to realize that there is an even better payoff if only they cooperate and choose to fight.

If it helps, kindly upvote.

For doubts comment below.