How to find DOMINATING STRATEGIES with Game Theory

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Check out Episodes 1 & 2 of the Game Theory Playlist ► • Game Theory
In Game Theory, a strategy is a dominating strategy if it always gives us the best payoff regardless of how our opponent plays, and similarly a dominated strategy gives us the least payoff, regardless of how our opponent plays. For example, Rock-Paper-Scissors has no dominating strategies as all three options are equally good against someone playing randomly. If we have a normal form game, written down with a payoff matrix, then we can search for dominating or dominated strategies for each player to help decide how people will play. In more complicated games, iterated elimination of dominated strategies can collapse to a single choice for both players. We first saw this idea back in Episode 1 on the Prisoner's Dilemma, but we now focus more fully on exploring the idea.
0:00 Dominating Strategies
2:23 Economics Example
8:30 Iterated Elimination of Dominated Strategies
12:15 Check out Brilliant.org
A note on the formal definition of a dominating strategy: a strategy a1 is a dominating strategy for player 1 if the payoff function u(a1,a2,...,an) is bigger than u(a1', a2,...,an) for all choices of a1' and al choices of a2,...,an.
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[@Salien1999]

The economics example touches on something I realized in college when trying to use decision matrices. The way you evaluate each possible decision drastically affects which decision is "best." For example, in the video you suppose that each firm is trying to maximize the money they get, leading to Firm 1 choosing not to advertise and then to Firm 2 choosing to advertise. Suppose that the two firms are each others' only competitors and that they're trying to knock each other out, though. In that case, they might try to maximize the *difference* between their own profits and the other firm's profits. If this is how they evaluate each option, then each firm should choose to advertise, which ironically minimizes the profits of each firm. And that isn't even getting into the different strategies of minimizing the worst case scenario vs maximizing the best case scenario vs maximizing the average scenario. This is why I find game theory and decision-making theory so fascinating.

[@airsquid8532]

I love the math side of seemingly simple games

[@DrTrefor]

It can be so cool!

[@MrFriday999]

Game theory seems like when psychology meets maths!

[@DrTrefor]

There definitely is lot of overlap!

[@crimfan]

@@DrTrefor Game theory has ebbed and flowed in psychology. It was pretty big for a while but I think at the moment it's not, but I suspect it'll be back sometime. Obviously it's a big topic in economics. Political science was very heavily into game theory for a while but I think it's not so dominant anymore, with a lot of the research having been taken over by things like field experiments. Biologists doing genetics also use it a lot.

[@crimfan]

@Geoffry Gifari That's true, though stable equilibria tend to "reassert" themselves in repeated play with randomness. For example in the Prisoner's dilemma (confess, confess) is the stable equilibrium while (deny, deny) is an unstable equilibrium. There are some connections to classification of attractors in differential equations. A whole class of games known as coordination games have multiple equilibria. The sushi vs. Thai game is an example of one of those. These can get really counterintuitive and have been used to model things like industry lock in.

[@Niglnws]

Yeah it is when humans meet each other. Either trust each others for better mutual benefits or dont trust each other and each care about their self interests and assume that the other do the same and assume that that is dangerous to them and conflicts begin. Thinking in this way help in preventing nuclear wars as each one do not want to be attacked so they declare that they will not attack as attack leads to being attacked.

[@nicomagrini7087]

Thanks, I have been waiting patiently. Great video 🙌

[@DrTrefor]

Glad you enjoyed!

[@SK_1337]

Great work!

[@abdullahfaisal4389]

Finally!! After half a month of tantalizing....

[@DrTrefor]

haha they come slowly but hopefully deliver:D

[@aashsyed1277]

this is an awesome video, awesome work!

[@DrTrefor]

Thank you!

[@xxxx015]

U got my Brian to work again after a lot of cringe KZbin shorts thank you

[@DrTrefor]

hahaha:D

[@jishnup1205]

Thank you 💖

[@bokaadoxo3481]

I paid money for a Coursera course on Game Theory and here I am learning more for free on youtube.

[@ariftans4593]

Quality content

[@yogeshkumarkc2204]

Enjoying the videos! Love from India Q : What book do you recommend to read that will go along with these videos??

[@MarZandvliet]

Firm 1 could easily get tired of (7,13) and start advertising to force a mutually undesirable (6,6) until firm 2 stops advertising. They could be like: "We'll stop this madness as soon as you stop this madness". The question becomes: which firm will go bust first at a revenue of 6. This assumes many turns played with the same payoff matrix, of course. This was fun! :)

[@crimfan]

Repeated games can really change the way things go with players choosing to punish. There was a big repeated Prisoner's dilemma tournament in the '70s published in Omni magazine about this very issue. en.wikipedia.org/wiki/Prisoner's_dilemma#The_iterated_prisoner's_dilemma Firms could also collude with the one that would have gotten 16 choosing to pay off the other firm. There's a whole area of game theory that deals with bargaining, as you might expect.

[@meunomejaestavaemuso]

Firm 1 should not advertise which would make firm 2 advertising, but them firm 1 could advertise and thus hurting firm 2 and forcing it to stop advertising (it would get 7 instead of the 6). Then firm 1 could stop advertising thus getting 16. Which would make firm 2 want to advertise. So in the long run they would be cycling clockwise in the diagram.

[@StaticBlaster]

Firm 1 should not advertise even though you might not know what firm 2 is going to do. If you do advertise, and if firm 2 decides to advertise that will be the worst case scenario. So not advertising is the dominating strategy.

[@wjrasmussen666]

Rock flies straight through paper

[@OBGynKenobi]

I wonder, do you apply these theories when you're out, let's say, buying a car, or negotiating something?

[@DrTrefor]

Yup. To a degree, at least. For instance, it guides the intuition that you should be walking away from a deal a percentage of the time in line with mixed mash equilibrium.

[@stefenleung]

except in reality it's always the bigger phone companies put more on the advertisement. i'm not saying the math is wrong, it's the assumption, the payoff are wrong. money isn't all of the payoff. building a brand name, hurting the competitors, etc are also part of the payoff.

[@danicarovo8818]

looking at this thumbnail i thought this was going to be another one of those alpha male videos lol

[@DrTrefor]

Lol I really am NOT that type of channel:D

[@danicarovo8818]

@@DrTrefor haha i figured, got here studying game theory:D