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Diffstat (limited to 'problem.tex')
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diff --git a/problem.tex b/problem.tex index 347bce7..358c825 100644 --- a/problem.tex +++ b/problem.tex @@ -108,7 +108,7 @@ $w_i$, to an experiment with $x_i^2=w_i$.% Moreover, \eqref{modified} is submodu Note that \eqref{modified} 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 $S\subset T$, with -$V(\emptyset)=0$. Finally, it is also non-negative, \emph{i.e.}, $V(S)\geq 0$ +$V(\emptyset)=0$. Finally, it is non-negative, \emph{i.e.}, $V(S)\geq 0$ for all $S\subseteq\mathcal{N}$, since the matrix $\T{X_S}X_S$ is positive semi-definite for all $S\subseteq \mathcal{N}$. %Finally, we define the strategic version of \EDP{} (denoted by \SEDP) by adding the additional constraints of truthfulness, individual rationality, and normal payments, as described in the previous section. We denote by |