May 6th, 2010 | 
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Tommy and Angelica have to divide a dozen cookies between themselves. Tommy’s parents have given Angelica the responsibility of choosing how to split them. The catch: if Tommy doesn’t like the offer, he can reject it and leave both children with nothing. How do they rationally work through their situation? This video also serves as a soft introduction to forward introduction–note that we must guess what sort of offers the first player will make and then check to see how the second player will respond.
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Never watched Rugrats, did you?
i hear what you’re saying and agree, but rather see an example that uses 2 random people, rather than siblings. and instead of cookies, maybe something with higher value like Millions of dollars. =D
I was wondering if it was an assumption of game theory that actors are rational, or if at least some branches of it considers these problems with irrational actors. In reality, this situation sounds a lot like division of plusvalue into profit/wages, and we find that when a certain threshold of ‘unfairness’ occurs, people are willing to go on strike and gain 0 in order to cost a comparatively much higher value to their employer, as a strategy of negotiation.
My homework set for this covers when two get taken away each time and when they both get to go back and forth for a certain number of offers. I will be covering these in future videos. But first we need backwards induction, which is something we haven’t covered yet.
Interestingly, though, when you cut in half or take away two each time, you get Rubinstein bargaining, which I alluded to in the video.
Insightful thinking on your part.
What about a game where the girl gets to offer a deal. If the boy accepts the cookies are distributed as such. If he declines the amount f cookies are cut in half rounded up and he gets to propose a deal. Repeat this process until a deal is accepted or no cookies are left. What about if two cookies are subtracted each time a deal is rejected? What if there is a limit to how times deals can be proposed, then after the limit is reached, nobody gets any? What about a mix of these scenarios?