On Cournot-Nash Equilibria with Exogenous Uncertainty

A large literature has accumulated which examines how the optimal solution of an agent maximising the expectations of a real-valued function depending on a rendom parameter p and the agents's behaviour x reacts to pertubations in the first and second moments of p. In this literature p is given exogenously, i.e. independent of x. We extend the theory in two aspects. First we allow there to be many agents and broaden our attention to regard market behaviour. Second, we allow p to depend on the behaviours of the participating agents, for example when p is a price vector relevant to an oligopoly. The method used is an extension of Ireland (2), in that an analogy is made between the effects on behaviour of uncertainty in p and the effects of a change in p. We study, in particular, the Cournot solution with respect to pertubations in the first two moments of two types of parameter defining a linear demand for industry - one parameter corresponding to ordinate intercept and the other to slope. This analysis immediately gives the old results as a corollary. We also apply the analysis to a cooperative of individuals where there is uncertainty in the return to communal work. In the applications we study the kind of simplifying assumptions necessary and the nature of the results.