Satisficing is to accept the first-seen option that met certain thresholds, known as *aspirations*. Assume options are presented as vectors , and the aspiration level as . There is an indicator function for accept,

and a payoff function of the option, . The option is assumed to be stochastic with density function .

The probability of an option is acceptable is

the expected payoff of *any* option is

and the expected payoff of an *acceptable* option is

Consider options presented in tandem, the decision maker must take one of them. Thus the last one must be accepted if presented. The policy would be on setting the aspiration to maximize the expected payoff. Let the value of a policy at state to be . Then we have

and

for .

The goal of optimal satisficing is to find . As for positive function , the optimal usually decreases as increases.

Heuristic satisficing is to use a fixed for all . That is, with

to find . It is found that, the value of heuristic satisficing has only a slight decrease from the optimal satisficing .

Satisficing can be converted into infinite horizon: Introduce a time cost of per unit time in heuristic satisficing. The value is then

It is found that, as increases, decreases. This reflects that the higher the time cost, the more relaxed the aspiration have to be.

## Bibliographic data

```
@incollection{
title = "On Optimal Satisficing: How Simple Policies can Achieve Excellent Results",
author = "J. N. Bearden and T. Connolly",
booktitle = "Decision Modelling in Uncertain and Complex Environments",
editor = "T. Kugler and J. C. Smith and T. Connolly and Y. J. Son",
address = "New York",
publisher = "Springer",
year = "2008",
}
```