There exist situations where firms (identical or not) are in a state of renewed interaction and where, at each period, in addition to exits, new firms (identical or not) may arrive. In such cases, no one is able to know ex ante exactly how many firms there will be in each period. One of the questions an incumbent firm might therefore ask itself, in this context, is what expected payoff it can expect. Our paper aims to provide an answer to this question, in finite and infinite horizons, using a discrete-time dynamic game with random arrival(s) and exit(s) of different types of firm(s). We first propose a general model, which we then particularize by considering the types as composed of identical players. Within this framework, we address the case of a dynamic Cournot oligopoly with sticky prices, and provide numerical illustrations to underline the interest of this approach and demonstrate its operational character.
