If we pretend “resource games” always have utility logarithmic in resources, then we can save almost everything, since that’s just a transform. We might lose some results about iterated games, since normally iterated games are assumed to be worth a discounted sum (just like rewards in reinforcement learning).
One major case where game theory is applied to a resource is evolutionary game theory, where the payoffs are assumed to be reproductive success. I don’t think they do anything logarithmic, and I’m confused about whether they should or not. (I think they should? Reproductive strategies should be evaluated like Kelly betting? But I could be missing something.)
Another case is mechanism design, where payoffs are often thought of as monetary. I think there, too, they often assume (erroneously) than utility is linear in money, when a logarithmic assumption is more appropriate. However, I’m not sure where this makes a real difference vs a cosmetic difference.
It’s a good question.
If we pretend “resource games” always have utility logarithmic in resources, then we can save almost everything, since that’s just a transform. We might lose some results about iterated games, since normally iterated games are assumed to be worth a discounted sum (just like rewards in reinforcement learning).
One major case where game theory is applied to a resource is evolutionary game theory, where the payoffs are assumed to be reproductive success. I don’t think they do anything logarithmic, and I’m confused about whether they should or not. (I think they should? Reproductive strategies should be evaluated like Kelly betting? But I could be missing something.)
Another case is mechanism design, where payoffs are often thought of as monetary. I think there, too, they often assume (erroneously) than utility is linear in money, when a logarithmic assumption is more appropriate. However, I’m not sure where this makes a real difference vs a cosmetic difference.