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 modelled as draws from bidder-specific type distributions and pay-your-bid rules are used to determine transactions...

In models of first-price auctions, when bidders are ex ante heterogenous, deriving explicit equilibrium bid functions is typically impossible, so numerical methods (such as polynomial approximations) are often employed to find approximate solutions. Recent theoretical research concerning...

Previous researchers have modelled the decision to accept a donor organ for transplantation as a Markov decision problem, the solution to which is often a control-limit optimal policy: accept any organ whose match quality exceeds some health-dependent threshold; otherwise, wait for another. When...

Using a clock model of a multi-unit, oral, ascending-price auction, within the commonvalue paradigm, we analyse the asymptotic behaviour of the transaction price as the number of bidders gets large. We find that even though the transaction price is determined by a (potentially small) fraction of...