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