We consider a dynamic game where additional players (assumed identical, even if there will be a mild departure from that hypothesis) join the game randomly according to a Bernoulli process. The problem solved here is that of computing their expected payoff as a function of time and the number of players present when they arrive, if the strategies are given. We consider both a finite horizon game and an infinite horizon, discounted game. As illustrations, we discuss some examples relating to oligopoly theory (Cournot, Stackelberg, cartel).
