Cournot model of oligopoly appears as a central model of strategic interaction between competing firms both from a theoretical and applied perspective (e.g antitrust). As such it is an essential tool in the economics toolbox and always a stimulus. Although there is a huge and deep literature on it and as far as we know, we think that there is a ”mouse hole” wich has not already been studied: Cournot oligopoly with randomly arriving producers. In a companion paper [Bernhard and Deschamps, 2016b] we have proposed a rather general model of a discrete dynamic decision process where producers arrive as a Bernoulli random process and we have given some examples relating to oligopoly theory (Cournot, Stackelberg, cartel). In this paper we study Cournot oligopoly with random entry in discrete (Bernoulli) and continuous (Poisson) time, whether time horizon is finite or infinite. Moreover we consider here constant and variable probability of entry or density of arrivals. In this framework, we are able to provide algorithmes answering four classical questions: 1/ what is the expected profit for a firm inside the Cournot oligopoly at the beginning of the game?, 2/ How do individual quantities evolve?, 3/ How do market quantities evolve?, and 4/ How does market price evolve?