Revenue implications of choosing discrete bid levels in a Japanese–English auction

We consider the set-up of a Japanese–English auction with exogenously fixed discrete bid levels for a specific game (the wallet game with two bidders, following Gonçalves and Ray in Econ Lett 159:177–179, 2017). We show that in this auction, partition equilibria exist that may be separating or pooling. We illustrate separating and pooling equilibria in games with two and three discrete bid levels and compare the revenues of the seller from these equilibria to find the optimal bid levels for these cases.