extensive form game

noun1

1. •
   Informally, a representation of a game as a tree of decision nodes, with the game beginning at a unique initial node, and flowing through the tree along a path determined by the players until a terminal node is reached, where play ends and payoffs are assigned to all players; each non-terminal node belongs to a player; that player chooses among the possible moves at that node, each possible move is an edge leading from that node to another node.