Generalizing Obvious Dominance using the Sure-thing Principle

We offer a class of solution concepts for dynamic games by allowing obvious dominance (OD, Li, 2017) to be facilitated by players’ application of the sure-thing principle (STP, Savage, 1954) on relevant events in their contingent reasoning. In the resulting k-OD equilibrium, a lower k reflects a less demanding level of sophistication in applying STP. We present the class of gradual mechanisms, featuring dynamic information feedback, as a revelation principle for k-OD implementation. Applying k-OD to implement generalized median voter schemes, we show how an increasing sophistication level k extends the range of implementable social choice functions.