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\author{Thibaut Horel \& Paul Tylkin}
\title{Economics 2099 Project Proposal}

\begin{document}

\maketitle

\section{Motivation and Goals} The motivation for our idea comes from the eBay ascending first-price auction with a \lq\lq Buy It Now\rq\rq option. The auction works as follows:

\begin{itemize}
\item The seller sets a reserve price, a Buy It Now price, and a time duration for the auction.
\item The bidders can submit bids (\$$b_i$) at any time, starting from some minimum bid.
\item At any time during the auction, a buyer can choose to \lq\lq Buy It Now\rq\rq (for $\$B$) and end the auction.
\item At the end of the auction, if none of the bidders have exercised the \lq\lq Buy It Now\rq\rq option, the item is allocated to the bidder with the highest bid, if that bid exceeds the reserve price. If the highest bid does not exceed the reserve price, the item is not allocated.
\item The history of all bids is available to all of the bidders throughout the time of the auction.
\end{itemize}

We believe that this framework, while inspired by eBay auctions, also has applicability to numerous other contexts, such as home buyers bidding for homes (e.g. should they agree to the list price or risk an ascending bid war with other potential buyers), contract negotiations (e.g. should a government contractor agree to a particular value and sacrifice potential additional revenue or engage in negotiations and risk that another contractor will undercut them), etc.

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}

\section{Desiderata for Model}

\section{Relevant Prior Work}

\end{document}
