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Repeated Games

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Alright. So now let's talk about a different kind of game. The repeated game. So a repeated game is more realistic, right? When we were talking up to now we were talking about one time games, right? Where you got to play one time and that was your best shot. You give it your best shot that one time and do what you can write. But a repeated game. It it's gonna be a situation where we play the same game over and over again. Right? This makes more sense in real life. Jack and Jill's output decisions. They're not just gonna produce water one time for their town. And that's it. They'll probably have to keep making these decisions week after week, month after month, right? They're gonna have to keep making these decisions and this interdependence between them makes a bigger deal when we have to keep making these decisions over and over. Right? So when we have to make this decision over and over, it's gonna cause them to want to collude even more. Right? So what we're gonna see is that this repeated game, right? It's that one time game that we're playing over and over again. So our strategies are gonna be different cause we're not just playing one time. Okay, so we've got a couple strategies here. Uh The first one is called tip for tat Okay. A tip for tat strategy. I put it in kind of common terms here. That's the idea of I'm gonna do whatever you did last time. Okay, I cooperate this period. All right. So the first period you're gonna cooperate And then if you didn't cooperate, next period, I'm gonna cheat. Right? So, I'm always gonna do what you did last period. If you cheated last period this period I will cheat. If you cooperated last period this period, I will cooperate. Right? So you're just retaliating based on what they did last period. The other strategy is the trigger strategy. So the trigger strategy is someone who's gonna cooperate forever until you cheat. Once if you cheat, once that's it, they're done with you. They're gonna cheat forever going on right there triggered. And they're just gonna keep cheating from that point on. All right. So, you can imagine when we have our Jack and Jill decision Um their their decisions in the long run, right? When they're having to make this decision week after week, they're gonna probably try and aim for a collaborative agreement right? Somewhere where they can both be earning 1800 instead of the 1600 they would earn when they both cheat. Right? So, let's go ahead and try some practice problems with these new strategies that we learned

Jack employs a tit-for-tat strategy. If Jill cooperates this period, how many gallons will Jack produce?


Jack employs a tit-for-tat strategy. If Jill cheated last period, what will Jack’s total profit equal this period?