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.
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.
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.
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.