Intro to Game Theory and the Dominant Strategy Equilibrium

June 28, 2020

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.


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  • I came here after looking up how to communicate with MatPat…

    Abdelrahman Hamdy June 28, 2020 9:36 pm Reply
  • What a bullshit…it has nothing to do with math. More with human behavior and the way we humans are.
    But lets make it more dificult than it is and make theorethical models.
    like the the stupid Einstein.
    Come on people , use your brain.
    Einstein was wrong, and this is wrong to.
    Just because you are told this shit in school and that some have a PHD in this shit does not make is real.
    You wil learn more by reading some books about philosofie or phsicology than these stupid theory's.

    Hans Vos June 28, 2020 9:36 pm Reply
  • Well that's just a video, A YOUTUBE VIDEO, thanks for watching

    Natalie June 28, 2020 9:36 pm Reply
  • actually, the definition is wrong. game theory can be used to study the behavior of all beings, even plants. it is the mathematical study of strategy, to find the best outcome given the fact that there are other players in the game.

    Angela June 28, 2020 9:36 pm Reply
  • i believe this is wrong the way you explained it. I think you might have confused your numbers since you included zeros and negatives. the dominate strategy equilibrium should be for both players to keep quiet. For instance, if player one decides to keep quiet and is aware that player 2 will testify of course player one will keep quiet because he receive no jail time (-1). which dominates his strategy of testifying. Same goes for if player 1 knows that player 2 will keep quiet player one dominant strategy is still to keep quiet because he will receive 2 years rather than 3. thus we get players 1 strict dominance strategy is to keep quiet. Same can be said for player 2. For example, if player 2 knows that player one will testify than player 2 will want to keep quiet and go free (-1) is the pay out and if player 2 knows that player 1 will keep quiet player 2 will still keep quiet and receive a payout of only 2 years in jail. rather than 3 if player 2 testifies thus we have a dominant strat equil and that is for both players to keep quiet. which will get both players (2,2) however, it is rational for both players to testify and receive a payout of (0,0) so that is why they say we should never choose a dominant strategy

    william joyner June 28, 2020 9:36 pm Reply
  • This was used in my Poli sci class to help illustrate the cause of World War 1. Thank you lol

    czure94 June 28, 2020 9:36 pm Reply
  • What??? O_O

    Angel Manev June 28, 2020 9:36 pm Reply
  • "You can view, create and share your free QRPlaza School Cards for your students going to Join to QRPlaza platform and request your free coupon to generate your free digital and multimedia School Cards that you can share to your students in digital or paper format."

    Nihsreyasa Ramchandra June 28, 2020 9:36 pm Reply
  • BUT HEY!
    That’s just a theory!

    opaf June 28, 2020 9:36 pm Reply
  • The explanation is lucid and precise.Thank you for making this video 🙂

    Sreetama Ray June 28, 2020 9:36 pm Reply
  • Interesting to consider this applied to the Fed once you understand their true motivation

    GoneBamboo June 28, 2020 9:36 pm Reply
  • I'm a dominant

    Silverback 21 June 28, 2020 9:36 pm Reply
  • We can only predict short term economical climates presently due to how dog eat dog, corrupt, unscrupulous, childish, wretched and wicked those at the top of the food chain have become. LONG TERM requires organization and trust. Now we just have disorganization and mistrust. Corporate Responsibility and Business Ethics forrTrump 2020

    Andievo4U2 June 28, 2020 9:36 pm Reply
  • Dominant strategy. Yeah, that's it in a nutshell. Some people have to be in control, on top, in front. Some people are cool with giving and taking criticism and the back burner to make sure everyone in radius of your pie gets a slice. THE LATTER OF THE TWO ARE THE LEADERS OF TOMORROW. John Nash urged competition and growth sharing because not only does the economy rise you will always be better received by your competitors during "an unexpected company slump or travesty requiring support" Be nice to the people you deal with on your way up because they are the same ones you'll see on the way down.

    Andievo4U2 June 28, 2020 9:36 pm Reply
  • How do you know its A and E ???

    USF ALG11 June 28, 2020 9:36 pm Reply
  • Ya didn't help

    gamerxx gril June 28, 2020 9:36 pm Reply
  • Should be B, F for the complicated one, no? Without context for what the numbers represent we should assume 0, 0 is best like it was in the other games.

    S. P. Spatafore June 28, 2020 9:36 pm Reply
  • people

    nicholas valcke June 28, 2020 9:36 pm Reply
  • but hey, that’s just a theory!
    the game theory!

    mr. lowcase June 28, 2020 9:36 pm Reply
  • One person gets left hook to the face other person gets overhand right to the eye for trying to intervene, and the person kicking everybody's ass has the winning strategy

    vegasvillianCSWK June 28, 2020 9:36 pm Reply
  • Your videos are excellent. Keep going. We are waiting more videos. Thanks.

    Gokcen Yuksel June 28, 2020 9:36 pm Reply
  • Thank you

    Lil Dune Buggy June 28, 2020 9:36 pm Reply
  • Basically snitches get stitches.

    xfghkhjfsejid June 28, 2020 9:36 pm Reply
  • this example would’ve been better if you explained that 3 means you get off free and -1 means a harsh sentence. took me more than the video length to figure that out

    loltyriek June 28, 2020 9:36 pm Reply
  • i never comment on youtube videos, but the fact that you haven't just used prison sentences as the numbers is painfully annoying

    Modebayo Johnson June 28, 2020 9:36 pm Reply
  • you couldn't have used worse numbers if you tried.

    Trey Hughes June 28, 2020 9:36 pm Reply
  • Thanks

    Nick M. June 28, 2020 9:36 pm Reply
  • I finally understand! Thanks!

    Rob sywy June 28, 2020 9:36 pm Reply
  • Great video! Thank you for making it short and clear!

    Commentator 2 June 28, 2020 9:36 pm Reply

    Anime Freak2025 June 28, 2020 9:36 pm Reply
  • The best turn-based strategy – play cool!

    Пайзанат Гаджимагомедова June 28, 2020 9:36 pm Reply
  • Isn't the first one nash theory?

    Elijah Hua June 28, 2020 9:36 pm Reply
  • two dudes in a tight elevator and each one is holding a monstrous fart; could you please ANALyse this situation to see what is their dominant strategy?!

    Lee Amra June 28, 2020 9:36 pm Reply
  • This reminds me of that Tv show golden ball, its called something like that

    TheoMC14 June 28, 2020 9:36 pm Reply
  • Great video thanks. Subbed

    JR JR June 28, 2020 9:36 pm Reply
  • Stop complicating things by using minus 1, just use 1, 2 and 3

    Mathias Sammer June 28, 2020 9:36 pm Reply
  • 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.

    Brianna Jenkins June 28, 2020 9:36 pm Reply

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