Infinite Deterministic Graphical Games
V. J. Baston, F. A. Bostock · SIAM Journal on Control and Optimization · 1993
A deterministic graphical game is a two-person zero-sum game with perfect information played on a directed graph. Nodes with no successor are called terminal nodes and have a payoff associated with them. The other nodes are labelled to indicate which of the players chooses the successor node. Play starts at a specific node and only stops when a terminal node is reached at which point player 1 obtains the payoff corresponding to that node; if play never ends the payoff is zero. The paper shows that such games have a solution even when the graph has an infinite number of nodes.