Principal-agent models are pervasive in theoretical and applied economics, but their analysis has largely been limited to the ``first-order approach'' (FOA) where incentive compatibility is replaced by a first-order condition. This paper presents a new approach to solving a wide class of...

In the mobile video games industry, in-app purchases are a major source of revenue. A common in-app purchase is for additional "moves" or "time" in puzzle games. We call these in-app purchases "bonus actions". In some games, bonus actions can only be purchased in advance of attempting a level of...