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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. |