Info-gap’s decision model for robustness

Info-gap decision theory puts forward two types of decision-making models: one for decision-makers who are risk-averse and thus seek robustness, and one for decision-makers who are risk-takers and thus seek opportuneness.

Recall that according to info-gap decision theory, the robustness of decision x\in X is defined as follows:

\displaystyle \rho(x,\tilde{u}):= \max_{\rho\ge 0}\ \{\rho: r^{*}\le r(x,u),\forall u\in N(\rho,\tilde{u})\}

where

  • X = decision space.
  • u = parameter of interest whose true value is subject to severe uncertainty.
  • \tilde{u} = point estimate of the true value of u.
  • N(\rho,\tilde{u}) = neighborhood of size \rho around \tilde{u}.
  • r^{*} = critical performance level.
  • r(x,u) = performance level of decision x associated with the given value of u.

The greater the value of \rho(x,\tilde{u}), the more robust the decision.

Hence, insofar as decision-makers pursuing robustness are concerned, the best (optimal) decision is that whose robustness is the highest (largest). Therefore, info-gap’s decision model for robustness is as follows:

\begin{array}{rl} \displaystyle \rho(\tilde{u}):= &  \displaystyle \max_{x\in X} \rho(x,\tilde{u})\\    \displaystyle \equiv & \displaystyle  \max_{x\in X} \max_{\rho\ge 0}\ \{\rho: r^{*}\le r(x,u),\forall u\in N(\rho,\tilde{u})\}\\   \displaystyle \equiv & \displaystyle \max_{\substack{x\in X\\\rho\ge 0}}\ \{\rho: r^{*}\le r(x,u),\forall u\in N(\rho,\tilde{u})\} \end{array}

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