The traditional model of sequential decision making, for instance, in extensive form games, is a tree. Most texts define a tree as a connected directed graph without loops and a distingueshed node, called the root. But an abstract graph is not a domain for decision theory. Decision theory...

This paper addresses the question of what it takes to obtain a well-de?ned extensive form game. Without relying on simplifying ?niteness or discreteness assumptions, we characterize the class of game trees for which (a) extensive forms can be de?ned and (b) all pure strategy combinations induce...