We consider an infinite two-player stochastic zero-sum game with a Borel winning set, in which the opponent's actions are monitored via stochastic private signals. We identify two conditions of the signalling structure: Stochastic Eventual Perfect Monitoring (SEPM) and Weak Stochastic Eventual...

Define a continuous game to be one in which every player's strategy set is a Polish space, and the payoff function of each player is bounded and continuous. We prove that in this class of games the process of sequentially eliminating "never-best-reply" strategies does not terminate after the...