page_title: Info-gap decision theory
section_title: Introducing uncertainty
hierarchical_section_title: Info-gap decision theory / Example: resource allocation / Introducing uncertainty
caption_attribution_description: Revenue function instance
context_page_description: Info-gap decision theory is a non-probabilistic decision theory that seeks to optimize robustness to failure – or opportuneness for windfall – under severe uncertainty, in particular applying sensitivity analysis of the stability radius type to perturbations in the value of a given estimate of the parameter of interest. It has some connections with Wald's maximin model; some authors distinguish them, others consider them instances of the same principle.
  It has been developed since the 1980s by Yakov Ben-Haim, and has found many applications and described as a theory for decision-making under "severe uncertainty". It has been criticized as unsuited for this purpose, and alternatives proposed, including such classical approaches as robust optimization.
context_section_description: However, this analysis does not take uncertainty into account. Since the revenue functions are only a (possibly rough) estimate, the actual revenue functions may be quite different. For any level of uncertainty (or horizon of uncertainty) we can define an envelope within which we assume the actual revenue functions are. Higher uncertainty would correspond to a more inclusive envelope. Two of these uncertainty envelopes, surrounding the revenue function of the red team, are represented in Figure 3. As illustrated in Figure 4, the actual revenue function may be any function within a given uncertainty envelope. Of course, some instances of the revenue functions are only possible when the uncertainty is high, while small deviations from the estimate are possible even when the uncertainty is small.
  These envelopes are called info-gap models of uncertainty, since they describe one's understanding of the uncertainty surrounding the revenue functions.
  From the info-gap models (or uncertainty envelopes) of the revenue functions, we can determine an info-gap model for the total amount of revenues. Figure 5 illustrates two of the uncertainty envelopes defined by the info-gap model of the total amount of revenues.
caption: Figure 4 – Revenue function instance
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