[freehaven-cvs] Added tables summarizing variables

[syverson@seul.org]

Update of /home/freehaven/cvsroot/doc/fc03
In directory moria.mit.edu:/tmp/cvs-serv19318

Modified Files:
	econymics.tex 
Log Message:
Added tables summarizing variables


Index: econymics.tex
===================================================================
RCS file: /home/freehaven/cvsroot/doc/fc03/econymics.tex,v
retrieving revision 1.49
retrieving revision 1.50
diff -u -d -r1.49 -r1.50
--- econymics.tex	17 Dec 2002 00:36:37 -0000	1.49
+++ econymics.tex	7 Mar 2003 22:41:51 -0000	1.50
@@ -11,8 +11,7 @@
 %\title{Issues in the Economics of Anonymity}
 %\title{Topics in the Economics of Anonymity}
 %\title{The Economics of Anonymity}
-\title{On the Economics of Anonymity\\
-(Pre-proceedings Draft)}
+\title{On the Economics of Anonymity}
 \author{Alessandro Acquisti\inst{1} \and Roger Dingledine\inst{2} \and Paul Syverson\inst{3}}
 \institute{SIMS, UC Berkeley
 \email{(acquisti@sims.berkeley.edu)}
@@ -363,6 +362,49 @@
 anonymity and reliability differently, and because in different
 scenarios anonymity and reliability for the same agent might have
 different impacts on her payoff.
+In Section~\ref{sec:application}, we will make a number of assumptions
+that will allow us to simplify this equation. 
+We present here for the reader's convenience a table summarizing those
+variables that will appear in both the complete and simplified
+equations, as well as one that describes the variables used only in
+the more complete equation above.
+
+
+\begin{center}
+\begin{tabular}{|c|cl|}
+\hline
+\multicolumn{3}{|c|}{Variables used in both full and simple payoff equations} \\ \hline
+\hline
+&$u_i$     & utility for agent $i$ \\ \cline{2-3}
+&$v_{a_i}$ & disutility $i$ attaches to message exposure \\ \cline{2-3}
+&$p_a$     & prob.\ that a sent message loses anonymity \\ \hline
+number of nodes&$n_s$     & sending agents (sending nodes) \\ \cline{2-3}
+(other than $i$)&$n_h$     & honest nodes \\ \cline{2-3}
+in mix-net&$n_d$     & dishonest nodes\\ \hline
+dummy variables:&$a^h_i$ & $i$ is an honest node and sending agent \\ \cline{2-3}
+$1$ if true, $0$ otherwise&$a^s_i$   & $i$ sends through the mix-net \\ \hline
+&$c_s$     & of sending a message through the mix-net\\ \cline{2-3}
+costs &$c_h$     & of running an honest node \\ \cline{2-3}
+&$c_n$     & of sending a message around the mix-net\\
+\hline
+\end{tabular}
+\end{center}
+\begin{center}
+\begin{tabular}{|c|cl|}
+\hline
+\multicolumn{3}{|c|}{Variables used only in full payoff equation} \\ \hline
+\hline
+&$v_{r_i}$ & value $i$ attaches to sent message being received \\ \cline{2-3}
+&$p_r$     & prob.\ that message sent through mix-net is received \\ \hline
+&$b_h$     & of running an honest node \\ \cline{2-3}
+{\raisebox{1.5ex}{benefits}} &$b_d$     & of running a dishonest node \\ \hline
+&$a^d_i$   & $i$ runs a dishonest node \\ \cline{2-3}
+dummy variables&$a^n_i$   & $i$ sends message around the mix-net \\ \cline{2-3}
+&$a^r_i$   & $1$ $i$ receives dummy traffic \\ \hline
+cost &$c_r$     & of receiving dummy traffic \\ \hline
+\end{tabular}
+\end{center}
+
 
 Note also that the costs and benefits from sending the message
 might be distinct from the costs and benefits from keeping the
@@ -522,8 +564,8 @@
 communications. We later comment on the addition reliability
 issues.
 
-These assumptions let us re-write the payoff function presented in
-Section \ref{sec:model} in a simpler form:
+%These assumptions let us re-write the payoff function presented in
+%Section \ref{sec:model} in a simpler form:
 \begin{equation*}
 u_{i}=-v_{a_{i}}\left( 1-p_{a}\left(
 n_{s},n_{h},n_{d},a_{i}^{h}\right) \right)

***********************************************************************
To unsubscribe, send an e-mail to majordomo@seul.org with
unsubscribe freehaven-cvs       in the body. http://freehaven.net/