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.
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.