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@@ -55,10 +55,32 @@ We believe that this framework, while inspired by eBay auctions, also has applic
 
 Therefore, our goal is as follows:
 
-\begin{goal} To define a formal model for an eBay-style ascending first-price auction with a reserve price and a \lq\lq Buy It Now\rq\rq option, relate it to prior work on dynamic (time-dependent) auctions, analyze its properties and equilibria, and attempt to find a simpler approximation model.\end{goal}
+\begin{goal} To define a formal model for an eBay-style ascending first-price
+auction with a reserve price and a \lq\lq Buy It Now\rq\rq option, relate it to
+prior work on dynamic (time-dependent) auctions, analyze its properties and
+equilibria, and attempt to find a simpler auction which approximates it.\end{goal}
 
 \section{Desiderata for Model}
 
+In order to formalize the setting we are interested in studying, we need to
+make some assumptions on the behaviors of the agents. Finding the right
+behavioral axioms is part of the project, but we list a few natural candidates
+that we are planning to consider:
+\begin{itemize}
+    \item each bidder not only has a utility function that expresses his utility at the
+        end of the auction, but also maintains a distribution on the
+        probability of being allocated.
+    \item at each time step, the bidders update their distribution based on
+        what has been observed at the previous step (hence the bidders'
+        distribution are a function of the past history up to this point)
+    \item at each time step, bidders place in order to maximize a function
+        which is increasing in the probability of being allocated and their
+        utility: contrary to 
+\end{itemize}
+
+
+
+
 \section{Relevant Prior Work}
 
 \end{document}