Analyzing Games of Information

Abstract

A transparent example is twenty questions. In this game, a poser thinks of an object, and a guesser attempts to isolate it by the asking of at most twenty yes-no questions. Since any yes-no question is allowed, there is a winning strategy precisely if the set of set of potential objects is of size at most 220 ? 1,048,576. More generally, if n questions are allowed, there exists a winning strategy if and only if the number of feasible objects is at most 2n. One can routinely establish this by induction. At each stage, one simply asks a question that divides the remaining set of feasibilities evenly.