From eb3fed8f0f1b3d954b5ba26f397ab1541df04f7b Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Sun, 2 Nov 2014 18:24:23 -0500
Subject: Finish section 2

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 project/main.tex | 24 +++++++++++++++++++-----
 1 file changed, 19 insertions(+), 5 deletions(-)

(limited to 'project/main.tex')

diff --git a/project/main.tex b/project/main.tex
index 34a37f7..a0c58a6 100644
--- a/project/main.tex
+++ b/project/main.tex
@@ -71,11 +71,25 @@ that we are planning to consider:
         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 
+        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, if a bidder is not currently winning, she is
+        willing to sacrifice some expected utility to increase their
+        probability of being allocated. That is, the agents' are not fully
+        rational with respect to their ``outside-the-auction utility'': while
+        the auction is still running, the utility function that they are
+        maximizing puts a higher weight on simply winning the auction.
+\end{itemize}
+
+Under these behavioral axioms, we want to analyze the eBay-style auctions with
+respect to the following properties: truthfulness, envy-freeness, revenue
+optimality. One last property that we would like to analyze is \emph{regret}:
+we don't know yet how to define it properly, but a good notion of regret should
+be a function of the difference in utility induced by the ``non-rational''
+behavior of the agents: during the auction they are maximizing a different
+utility function (biased by the probability of winning); this might decrease
+their true utility.
+
 \end{itemize}
 
 \section{Relevant Prior Work} We are planning to consider prior work on first-price auctions where the bidders have multiple rounds of bidding over time, and various mechanisms that can capture this idea. One inspiration comes from the \lq\lq bid-your-utility \rq\rq auction described in the following paper: Hoy, D., Jain, K., \& Wilkens, C. A. (2013, June). A dynamic axiomatic approach to first-price auctions. In Proceedings of the fourteenth ACM conference on Electronic commerce (pp. 583-584). ACM.
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