Revenue implications of choosing discrete bid levels in a Japanese-English auction (Q6541994)

The authors consider the set-up of a Japanese-English auction (JEA) with exogenously fixed discrete bid levels for a specific game (the wallet game with two bidders) and show that (symmetric) partition equilibria, involving weakly increasing strategies based on elements of a partition of the signal space, exist for the wallet game in JEA with discrete bid levels. The authors illustrate several such equilibria with only two or three discrete bid levels and find the necessary conditions that support them. These equilibria, however, yield a lower expected revenue for the seller than in the case of a continuous JEA. Despite this, it is shown that a revenue-maximizing second-best solution for this set-up exists; that is, the seller may choose these bid levels optimally to maximize the revenue, although it can never achieve the expected revenue of a continuous JEA (first-best).