If that were not the case, then the maximising agent would transform itself into a satisficing agent, but, (unless there are other agents out there penalising you for your internal processes), there is no better way of maximising the expected U than by attempting to maximise the expected U.
Is that really true? This seems to be the main and non-trivial question here, presented without proof. It seems to me that there ought to be plenty of strategies that a satisficer would prefer over a maximizer, just like risk-averse strategies differ from optimal risk-neutral strategies. eg. buying +EV lottery tickets might be a maximizer’s strategy but not a satisficer.
How come this is true (apart from the special case when other agents penalise you specifically for being a maximiser)? Well, agent A will have to make decisions, and if it is a maximiser, will always make the decision that maximises expected utility. If it is a satisficer, it will sometimes not make the same decision, leading to lower expected utility in that case.
Yes, the satisficer can be more risk averse than the maximiser—but it’s precisely that that makes a worse expected utility maximiser.
Unlike a maximiser, that will attempt to squeeze the universe to every drop of utility that it can, a satisficer will be content when it reaches a certain level expected utility (a satisficer that is content with a certain level of utility is simply a maximiser with a bounded utility function).
Does it make sense to to claim that a satisficer will be content when it reaches a certain level of expected utility though? Some satisficers may work that way, but they don’t all need to work that way. Expected utility is somewhat arbitrary.
Instead, you could have a satisficer which tries to maximize the probability that the utility is above a certain value. This leads to different dynamics than maximizing expected utility. What do you think?
Instead, you could have a satisficer which tries to maximize the probability that the utility is above a certain value. This leads to different dynamics than maximizing expected utility. What do you think?
If U is the utility and u is the value that it needs to be above, define a new utility V, which is 1 if and only if U>u and is 0 otherwise. This is a well-defined utility function, and the design you described is exactly equivalent with being an expected V-maximiser.
Is that really true? This seems to be the main and non-trivial question here, presented without proof. It seems to me that there ought to be plenty of strategies that a satisficer would prefer over a maximizer, just like risk-averse strategies differ from optimal risk-neutral strategies. eg. buying +EV lottery tickets might be a maximizer’s strategy but not a satisficer.
I reworded the passage to be:
Yes, the satisficer can be more risk averse than the maximiser—but it’s precisely that that makes a worse expected utility maximiser.
OK, that makes more sense to me.
Does it make sense to to claim that a satisficer will be content when it reaches a certain level of expected utility though? Some satisficers may work that way, but they don’t all need to work that way. Expected utility is somewhat arbitrary.
Instead, you could have a satisficer which tries to maximize the probability that the utility is above a certain value. This leads to different dynamics than maximizing expected utility. What do you think?
Related post on utility functions here: https://colekillian.com/posts/sbf-and-pascals-mugging/
If U is the utility and u is the value that it needs to be above, define a new utility V, which is 1 if and only if U>u and is 0 otherwise. This is a well-defined utility function, and the design you described is exactly equivalent with being an expected V-maximiser.