Game Theory Part 1: Dominant Strategy

this is our introduction to game theory game theory is all about interdependencies basically when you play any game soccer basketball football the outcomes from that game the results from that game is not just dependent upon you it's also interdependent interdependent upon what the other person does the strategies how they play also affects your own outcome and so that's what game theory is all about is understanding situations where you have interdependencies between different actors there's three things that all games Theory scenarios have to have they've got to first have players well our players today today are going to be Fred and Jack Fred and Jack were involved in a crime or actually we can think of maybe a series of crimes some major some minor the police have a lot of evidence on the minor crimes they have very little evidence on the major crimes they both been arrested they've been put into two different interrogation room groups they face strategies that's the next thing you have tasks you have to have players and you have to have strategies the strategies are very simple for this particular game Fred you can confess or he cannot confess same with Jack he's facing the same exact strategies he can also confess or not confess the third thing you have to have for a game is you have to have payoffs what are the outcome win or lose that's you know that's what we usually think about with the game but in this situation two different strategies and there's more than just [Music] payoff winning or losing in this particular game that we're going to look at today if Fred confesses and Jack confesses if they both end up confessing we're going to put the payoff to both of them right here Fred's payoff we're going to put here Jack's we're gonna put right there if they both end up confessing well the police you know still have a lot of evidence on them now they have even more evidence on them they're not going to throw the book at him because they did confess but they're still going to be putting put away for a pretty good amount of time eight years and eight years next we can think of a situation where Fred confesses and Jack does not confess in that particular situation Fred confessing he turned state evidence Jack he does not comply with the police he doesn't go along the police and so this is really going to be bad for Jack Jack's gonna end up in 20 years and for his participation with the police compliance with the police he's only going to get one year in this particular Square right here we're not the exact opposite Fred doesn't confess Jack confesses not good for Fred Fred it's going to serve 20 years and Jack for confessing turning state's evidence they're only going to put them away for one year finally we have a situation that Fred and Jack they both don't confess well that's the best situation for Fred and Jack they're gonna get the best result which is three years because the police still has some evidence for those minor crimes in three years now when you look at this board you would think well what's the best square for both of them right here three years three years problem is we've got a situation that their self-interest is not necessarily going to take us there so once again they're in these two separate rooms they have these two strategies that they can follow what we want to find out is what is the strategy they would likely follow if they follow their self-interest well what we're gonna look for is what we call the dominant strategy because either one of a dominant Shred a dominant strategy is a strategy that's best regardless of what the other player does dominant strategies strategy that's best regardless of what the other player does so Fred is that or that it's either one of those the dominant strategy well we're gonna evaluate both of these in regards to Jack confessing you're not confessing simply put Fred what should he do if Jack confesses should Fred confess or not confess well Fred confesses when Jack confesses eight years if Fred does not confess when Jack confesses Fred's going in 20 years so this is definitely the better strategy in that particular situation when Jack confesses we don't know if it's the dominant strategy what we're saying right now as Fred should confess if Jack confesses but is it a dominant strategy for it to be a dominant strategy it's got to be best regardless of what Jack does Jack could also not confess what should Fred do confess or not confessed well Fred confesses when Jack does not confess that's the best situation one year in jail if Fred does not confess when Jack doesn't confesses three years so put a little check mark right there for Fred it definitely looks like or idiots then and just look like Fred's definitely got a dominant strategy Fred should confess regardless of what Jack does so if we're gonna put an asterisk right there okay and we're also going to put one next to the strategy that is the dominant strategy ds4 damaged red jack does he have a dominant strategy does he have a strategy that's best regardless of what Fred does let's take a look if Fred confesses should Jack confess or not confess well if Jack confesses eight years when Fred confesses if Jack does not confess 20 years well that's not hard to see Jack should definitely confess we don't know for sure it's his dominant strategy confessing sits down to strategy we have to evaluate in terms of the other strategy that Fred could play Fred does not confess Jack confesses one year Fred does not confess Jack does not confess three years confessing is definitely a dominant strategy for Jack so in this particular situation we see that Fred has a dominant strategy Jack has a dominant strategy so where will they tend to gravitate if they play this game based on their self-interest they will tend to gravitate right to this box right there which on our next module we'll also find out is the Nash equilibrium

Channel: Econbusters

Views: 393,593

Rating: 4.8822355 out of 5

Keywords: Game Theory, Dominant Strategy, Prisoners' Dilemma

Id: x8gOi7D6QeQ

Length: 6min 54sec (414 seconds)

Published: Tue May 28 2013