Obvious Dominance and Random Priority

We introduce a general class of simplicity concepts that vary the foresight abilities required of agents in extensive-form games, and use it to provide characterizations of simple mechanisms in social choice environments with and without transfers. We show that obvious strategy-proofness---an important simplicity concept included in our class---is characterized by clinch-or-pass games we call millipede games. Some millipede games are indeed simple and widely-used, though others may be complex, requiring significant foresight on the part of the agents, and are rarely observed. Weakening the foresight abilities assumed of the agents eliminates these complex millipede games, leaving monotonic games as the only simple games, a class which includes ascending auctions. As an application, we explain the widespread popularity of the well-known Random Priority mechanism by showing it is the unique mechanism that is efficient, fair, and simple to play.