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### Course: AP®︎/College Microeconomics>Unit 4

Lesson 5: Oligopoly and game theory

# More on Nash equilibrium

In this video we expand our analysis of the prisoners' dilemma to better understand the concept and definition of a Nash Equilibrium. Created by Sal Khan.

## Want to join the conversation?

• Can someone give me examples of the Nash Equilibrium in other games, such as Monopoly, Risk, Stratego, etc?
• The Nash Equilibria in Monopoly, Risk, Chess and Go are all fairly boring - it would just consist of whatever the optimal strategy is at each turn in the game.

Poker and Stratego however are much more complicated, because you don't know what your opponent has done. (In poker their cards are hidden from you, and in Stratego their board of pieces is turned around so that you know locations but not abilities.) In those games determining Nash Equilibria would be incredibly complicated. The NE would involve randomness - ie, in poker you should bluff some but not always, and you need to do so randomly to keep your opponent from predicting you.
• A Nash equilibrium is dependent on knowing that others will not change their positions. What kind of assumption is that? I don't see that as even remotely possible in the real world. If it is just a theoretical, or academic exercise that is fine, but it means a Nash equilibrium has no real world application. If that is the case what value is it?
• Fletch, in your original post you said "A Nash equilibrium is dependent on knowing that others will not change their positions", and in your response you said "It would be a reasonable assumption that every player would be constantly be trying to improve their position." These are both true, and you have basically answered your own question. Keep in mind we are working with the assumptions that

1. both players are rational
2. both players know all available moves and the corresponding payoffs

Given those assumptions, it is inevitable that rational players will end up in a NE. Once there, it doesn't matter whether the players "know" they are in a NE or not, player A simply knows that given B's choice, there is no advantage to be gained from switching positions, and vice versa. (Unless of course they collude and decide to switch together, which we already mentioned)

I agree with your sentiment that NE may not seem all that realistic in the real world, but I think it is because both assumptions are unlikely to always be true, not because it is dependent on knowing others won't change their positions.
• What is the difference between Nash equilibrium and dominant strategy equilibrium??
• That explains why socialism is the preferred choice (Nash equilibrium) over capitalism.
(1 vote)
• Could there be a situation in which there is NO Nash equilibrium?
• According to Nash's mathematical proof in his famous thesis entitled, "Non-Cooperative Games" (Princeton, 1950), the answer is no. In it he proved that, ". . . a finite cooperative game always has at least one equilibrium point." The equation proof is pretty hairy but not impossible to follow.
• Is there a real life situation where this can apply to?
• Yes, When dealing with chess it is used it programs that try to predict moves of the other player, also there is more complex theory behind this and can be used in any kind of negotiations between people. when it is important for one side to try and be like the saying goes one step ahead of the other person.
• would the situation (confess, confess) be a nash equilibrium so long as the nr. of years are less than the 10 received in the situation (confession, denial) ?
Meaning, would the situation (confess, confess) be a nash equilibrium even if the duration of incarceration was 9.9 years for both prisoners?
Just testing out the extreme cases so as to understand better the logic behind it.
• Yes, if the duration of incarceration for both confessing were 9.9 years each, both confessing would still be a Nash equilibrium. It would remain so as long as it is less than the 10 years.
• Is there a way to mathematically calculate or prove that confessing is the Nash equilibrium?
(1 vote)
• It's more logic based than math based.

Look at it from person A's perspective. He can either confess or not confess. If person B does not confess, it is best for person A to confess. If person B confesses, it is still better for person A to confess. So regardless of what person B does, it is best for him to confess, so therefore he will confess.

It works the same the opposite way. No matter what person A does, it is best for person B to confess, so therefore he will confess.

If they could both coordinate and make sure the other does not confess, neither would confess. But that's not the situation. Each knows that no matter what the other does, it is best for them to confess, so they do. They aren't looking for the best overall situation, they are looking to make their situation the best.
• How would you go about testing a possible Nash Equilibrium for more than one possibility or no possibility?