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Diffstat (limited to 'problem.tex')
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diff --git a/problem.tex b/problem.tex index 9d3fb9f..a3b54b4 100644 --- a/problem.tex +++ b/problem.tex @@ -83,10 +83,10 @@ matrices $R$ can be found in Section~\ref{sec:ext}. %Note that \eqref{dcrit} is a submodular set function, \emph{i.e.}, %$V(S)+V(T)\geq V(S\cup T)+V(S\cap T)$ for all $S,T\subseteq \mathcal{N}$; it is also monotone, \emph{i.e.}, $V(S)\leq V(T)$ for all $S\subset T$. -\subsection{Budgeted-Feasible Experimental Design: Full Information Case} +\subsection{Budget-Feasible Experimental Design: Full Information Case} -Beyond the cardinality constraint in classical experimental design discussed above, is -the budgeted version. +Beyond the cardinality constraint in classical experimental design discussed above, a + budgeted version can also be considered. %depart from the above classic experimental design setting by assuming that Each experiment is associated with a cost $c_i\in\reals_+$. Moreover, the experimenter $\E$ is limited by a budget $B\in \reals_+$. The cost $c_i$ can capture, \emph{e.g.}, the amount the subject $i$ deems sufficient to @@ -118,7 +118,7 @@ for all $S\subseteq\mathcal{N}$, since the matrix $\T{X_S}X_S$ is positive semi- \end{equation} the optimal value achievable in the full-information case. -\subsection{Experimental Design Problem: Strategic Case} +\subsection{Budget-Feasible Experimental Design: Strategic Case} We study the strategic case when $c_i$'s are specified by the subjects and they are strategic. In this case, the costs $c_i$ are {\em not} common knowledge and they are reported by the % their reporting can be manipulated by the |