Cycles in extensive form perfect information games

AbstractWe define and analyse a new class of perfect information games. The nodes of a directed graph G are partitioned into n player sets. Starting at a fixed node of G an infinite path is created as follows: If the current node belongs to player k, then player k chooses any successor node. A local reward n-vector is assigned to every arc. The payoff corresponding to the infinite path is the long term average of the local reward vectors. Such games are called DGA games. Negative and positive results are obtained for the existence of Nash equilibria in certain types of pure strategies (e.g., stationary and automated strategies). Applications to duopoly pricing models and “surveillance games” on graphs are given