I am trying to formalize what I think should be solvable by some game theory, but I don't know enough about decision theory to come up with a solution.
Let's say there are twins who live together. For some reason they can only eat when they both are hungry. This would work as long as they are both actually hungry at the same time, but let's say that one twin wants to gain weight since that twin wants to be a body builder, or one twin wants to lose weight since that twin wants to look better in a tuxedo.
At this point it seems like they have conflicting goals, so this seems like an iterated prisoner's dilemma. And it seems like if this is an iterated prisoner's dilemma, then the best strategy over the long run would be to cooperate. Is that correct, or am I wrong about something in this hypothetical?
I agree with Nancy that this doesn't look like a prisoner's dilemma.
You could think about this as a dynamic game, but it seems simplest to model it as a static game with two strategies: eat heavily and eat lightly. Both have to choose eat heavily to actually eat enough to gain weight, since it sounds like both have to agree every time they eat. The payoffs then look something like:
..... Heavily | Lightly
Heavily | 1,0 | 0,1 |
Lightly | 0,1 | 0,1 |
with the bodybuilder as the row player and the model as th...
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