Last Update: Dec. 4^{th}, 2015.
Earlier in 2011, Prof. Silvio Micali, Alessandro Chiesa and I discovered a new area in game theory, that is to study auctions (or more general games) when the participating players do not exactly know their valuations. This page is my attempt to keep track of all of our published papers and technical reports, and to resolve potential confusions on the model.
Through detailed notations and motivations can be found in our paper, the oneline version of our model is as follows.
Our Knightian Valuation Model. We focus on auctions where the designer has no information about the players, and in addition, the only information a player \(i\) has about the profile of true valuations, \(\theta^*\), consists of a set of distributions \(\mathcal{K}_i\), from one of which \(\theta^*_i\) has been drawn.
We refer interested readers to our paper for motivations and examples for such setting. Clearly, when \(\mathcal{K}_i\) is a singleton for each \(i\), this setting collapses to that of the classical secondprice, Vickrey, and VCG mechanisms. We observe in our paper that, at least in auctions, this model is mathematically equivalent to the following distributionfree version.
Our Knightian Valuation Model (distributionfree). Each player \(i\)'s sole information about \(\theta^*\) consists of a set of valuations \(K_i\) such that \(\theta^*_i \in K_i \subseteq \Theta_i\). We call \(K_i\) the candidate set of player \(i\) (or approximate valuation of player \(i\) in our earlier version of the paper).
Our goal is to study the socialwelfare efficiency of auction mechanisms, as a function of \(\delta\), the maximum inaccuracy of the candidate sets \(K_i\).
We have presented our results in two computer science conferences, ITCS 2012 and ACMEC 2014. We refer these two papers as [CMZ12] and [CMZ14]. Our journal version of the paper [CMZ15] is published in Econometrica. We have also produced 4 related technical reports [CMZbridge], [CMZvcgregret], [CMZvcgutility] and [CMZsingleparam] that we may choose to submit independently in the future. The table below provides a visual summary of these papers.
Results  Solution Concept  [CMZ12]  [CMZ14]  [CMZ15]  [CMZsingleparam]  [CMZvcgutility]  [CMZvcgregret] 
(1). dominantstrategy and expostNash mechanisms fail to work even for singlegood auctions  dominantstrategy expost Nash 
included  included  
(2). the secondprice mechanism produces great socialwelfare under undominated strategies for singlegood auctions  undominated strategies 
included  
(2'). 2 is essentially optimal among all finite mechanisms for singlegood auctions  undominated strategies 
included  
(3). there is a probabilistic mechanism that slightly outperforms the secondprice one for singlegood auctions  undominated strategies 
included  
(4). the Vickrey mechanism produces great socialwelfare under undominated strategies for multiunit auctions  undominated strategies 
included  
(4'). 4 is essentially optimal among all finite mechanisms for multiunit auctions  undominated strategies 
included  
(5). classical DST mechanisms continue to work under Knightian uncertainty in undominated strategies for singleparameter domains  undominated strategies 
included  
(6). the VCG mechanism performs poorly in undominated strategies for unrestricted combinatorial auctions  undominated strategies 
included  included  
(7). the VCG mechanism performs well in regretminimizing strategies for unrestricted combinatorial auctions  regretminimizing strategies 
included  included  
(7'). 7 continues to hold for utility maximizers who only resort to regret to break ties  regretelimination
after undominated strategies see [CMZbridge] 
included  included 






