Sham Kakade, Ilan Lobel, and Hamid Nazerzadeh
We consider the problem of designing optimal mechanisms for settings where agents have dynamic private information. We present the Virtual Pivot Mechanism, that is optimal in a large class of environments that satisfy a separability condition. The mechanism satisfies a rather strong equilibrium notion (it is periodic ex-post incentive compatible and individually rational). We provide both necessary and sufficient conditions for immediate incentive compatibility for mechanisms that satisfy periodic ex-post incentive compatibility in future periods. The result also yields a strikingly simple mechanism for selling a sequence of items to a single buyer. We also show the allocation rule of the Virtual Pivot Mechanism has a very simple structure (a Virtual Index) in multi-armed bandit settings. Finally, we show through examples that the relaxation technique we use does not produce optimal dynamic mechanisms in general non-separable environments.