Intro to Game Theory and the Dominant Strategy Equilibrium

Game theory is the study of human behaviour in strategic settings. It is used to solve some of the harder problems in economics.

So what is a game? To have a game, you need at least two players, sometimes called agents, or, if you want to be really crazy, people. And you need payoffs for the players, you need to define the outcomes they can potentially get depending on how the game unfolds. And finally, you need rules for the game.

Now, it's not always obvious how people will behave, even with players, payoffs, and rules clearly defined. That's why game theorists have a number of solution concepts for games, including the dominant strategy equilibrium, the Nash equilibrium, the subgame perfect Nash equilibrium, the Bayesian equilibrium, and the weak perfect Bayesian equilibrium.

The most basic solution concept is the dominant strategy equilibrium. In a game, each player can have any number of possible strategies. One strategy strictly dominates another strategy if the player is always better off under that strategy no matter what other players do. If one strategy strictly dominates every other possible strategy a player could take, that strategy is a strictly dominant strategy. We have a dominant strategy equilibrium when all players play a strictly dominant strategy.

Now let's look at the most famous game in game theory, the Prisoner's Dilemma. There are two prisoners, prisoner 1 and prisoner 2, and they each have a choice. They can testify against the other, or they can keep quiet.

If they both keep quiet, they both get off with a light sentence, which I'll represent with a payoff of 2. Prisoner 1's payoff is on the left, prisoner 2's is on the right. If they both testify, they both get a moderate sentence. I'll represent the moderate sentence by a payoff of 0. Right about now, keeping quiet is looking like the best option, but there's more to this game. If one testifies and the other keeps quiet, the one who testified will get off scot free, and the one who kept quiet will get an extremely harsh sentence; they'll throw the book at him.

Think about this game for a moment. Keeping quiet looks like a pretty good option if both prisoners could promise not to testify. But these prisoners only care about their own self-interest. So, both prisoners may tell the other they pinky swear not to testify, but they won't keep that promise. If prisoner 2 keeps quiet, prisoner 1 is better off testifying. If prisoner 2 testifies, prisoner 1 is better off testifying. Testifying is a dominant strategy for both players, so both testifying is the dominant strategy equilibrium.

The prisoner's dilemma comes up in all sorts of situations. For instance, instead of prisoners our players could be, say, oil companies. If both set a high price they can sell for a high price, but each one has an incentive to undercut, in which case he will capture the entire market. The equilibrium outcome is for each company to charge a low price.

The prisoner's dilemma isn't the only game with a dominant strategy equilibrium. Here's a more complicated one. Can you tell which strategy is dominant? It's A for player 1, and E for player 2. So the dominant strategy equilibrium is A, E.

[lindakovler]

I just watched all 4 of your videos and they are great! I have a Game Theory exam tomorrow and had missed the original class on subgame perfect NE and nobody until now from my class had been able to explain clearly to me. Thank you so much - you have real talent!

[rosemaryb]

I am a doctoral education student in a decision making class- I read an article by Raiffa and he referenced game theory. I really appreciate this basic but essential lesson. thanks

[ninmachine]

This subject is an ADD nightmare, thanks for uploading!

[czure]

This was used in my Poli sci class to help illustrate the cause of World War 1. Thank you lol

[karyngeorgilis]

I'm a design major in the middle of an econ class, this was extremely helpful!

[MrBish]

Okay let me summarise:
1. Everyone in the game will do what is best for themselves.
2. You have to anticipate what the other player will do for you to make a counteractive move.
3. Each player's actions will be influenced by how the other player moves or acts.
eg. If I'm in the oil business:

1. My competitors will always try to maximise or increase their profit either by increase volume when prices are high or cut prices when there's an oversupply.
2. If I decide to keep my price of oil high and sell at that high price. The competitor will undercut my price to steal away profits.
3. So, in response to my competitor, I will match their oil price. If I do match the price cut of oil "I'll be in equilibrium" if I lower my price more than my competitor I will lose more money than if I had just matched the price cut.

[GCowner]

i have a real life example of this. I was contemplating taking someone to HR at work, and I knew that the other person had been talking about taking me to HR. I was too busy and scared so I didn't take her to HR, and she took me to HR.

I got absolutely screwed, even though I did not do anything remotely wrong as she had done (sexual harassment, telling me I need to get laid, bullying, etc.).

So I should have, according to game theory dominant strategy, taken her to HR. That way it would have cancelled out.

I got the book thrown at me. Damn it...wish I saw this video last year :(

[sreetamaray_]

The explanation is lucid and precise.Thank you for making this video :)

[pnesap]

@3:46 would be insightful to point out that despite player 2 "beating" player 1, both players benefit most (ie. just defeating opponent isn't always the optimal goal, just as losing is not always a bad thing). In other words, producing the highest outcome for _both_ players is optimal. And the bongos sound like annoying kitchen drawers shutting.

[marioarvayo]

Why is there no explanation on the more complex equilibrium?

Do you take the highest ratio? How is that determined when there are more options?

[SuperCoupe]

do i cut the light grey, medium grey or dark grey wire?

[DaWranglerGuy]

Thanks for the video! I am about to start off the new school year with a Game Theory course and this gave me a great introduction.

[stevo]

In the oil price example, the Low Price and High Price could be switched around since the aim is to make the biggest profit not the most sales.

[briannajenkins]

I liked the video but I really wish there was a great explanation to the last game as those are the ones I see more frequently.

[jl]

Poorly constructed video. Not sure why you wouldn’t explain the answer at 3:39.

[Silverstorm]

Exept that in real life, oil companies are doing illegal price fixing. I guess that'd be the dominant strategy ?

[gokcenyuksel]

Your videos are excellent. Keep going. We are waiting more videos. Thanks.

[kopanomoss]

i dont get the complicated example, what is the objective?

[dhakshirajan]

why cant the dominant strategy for player one in the final slide be B? he seems to be better off in more situations using B than A ie. situation in which player 2 uses E, F, G

[AshtonKutch]

A mixed nash equilibrium is like watching cars trying to maneuver past each other eventually its going to turn into a game but as you would expect people would be trying to find ways to get past but at the most complex level of the game people will need to make maneuvers that wont risk getting hit but getting by.