Chapter 2. On the Numerical Solution of Equilibria in Auction Models with Asymmetries within the Private-Values Paradigm

We describe and compare numerical methods used to approximate equilibrium bid functions in models of auctions as games of incomplete information. In such games, private values are modeled as draws from bidder-specific type distributions and pay-your-bid rules are used to determine transactions prices. We provide a formal comparison of the performance of these numerical methods (based on speed and accuracy) and suggest ways in which they can be improved and extended as well as applied to new settings.