Intro to Game Theory and the Dominant Strategy Equilibrium

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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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44 COMMENTS

  1. 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.

  2. 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.

  3. 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

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  6. 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.

  7. 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.

  8. 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

  9. 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

  10. i never comment on youtube videos, but the fact that you haven't just used prison sentences as the numbers is painfully annoying

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  12. 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?!

  13. 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.

  14. But both the robber and the victim have dominant strategies… its in te victims interest to lose 10 than potentially loose 1million, his optimal expected outcome is -20 versus -1mil, so his dominant strategy is to give the money, with respect to the robber its in his interest not to kill to have an expected outcome of +10… this gives a dominant equilibrium strategy of (-10,10) so there are no two nash equilibriums… as when there is a dominant strategy equilibrium the nash equilibrium also becomes (-10,10)

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