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diff --git a/project/main.tex b/project/main.tex index 84ca28b..69d3f24 100644 --- a/project/main.tex +++ b/project/main.tex @@ -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} |