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authorThibaut Horel <thibaut.horel@gmail.com>2013-04-16 15:43:50 +0200
committerThibaut Horel <thibaut.horel@gmail.com>2013-04-16 15:43:50 +0200
commit6cc7d966aca5cd760309881a90125a9058cc3e61 (patch)
tree0a58fabadd10110e3655244085a820abcc2192e6 /problem.tex
parentf408c518fb2f6d0ec15c50c9e9be800b4311eff8 (diff)
downloadrecommendation-6cc7d966aca5cd760309881a90125a9058cc3e61.tar.gz
Fix some typos and inconsistent notations
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@@ -155,7 +155,7 @@ returns a vector of payments $[p_i(c)]_{i\in \mathcal{N}}$.
\item \emph{Truthfulness/Incentive Compatibility.} An experiment subject has no incentive to missreport her true cost. Formally, let $c_{-i}$
be a vector of costs of all agents except $i$. Then, % $c_{-i}$ being the same). Let $[p_i']_{i\in \mathcal{N}} = p(c_i',
% c_{-i})$, then the
-\begin{align} p_i(c_i,c_{-i}) - s_i(c_i,c_{-i})\cdot c_i \geq p_i(c_i',c_{-i}) - s(c_i',c_{-i})\cdot c_i, \label{truthful}\end{align} for every $i \in \mathcal{N}$ and every two cost vectors $(c_i,c_{-i})$ and $(c_i',c_{-i})$.
+\begin{align} p_i(c_i,c_{-i}) - s_i(c_i,c_{-i})\cdot c_i \geq p_i(c_i',c_{-i}) - s_i(c_i',c_{-i})\cdot c_i, \label{truthful}\end{align} for every $i \in \mathcal{N}$ and every two cost vectors $(c_i,c_{-i})$ and $(c_i',c_{-i})$.
\item \emph{Budget Feasibility.} The sum of the payments should not exceed the
budget constraint, \emph{i.e.}
%\begin{displaymath}