Monopoly profit lower than oligopoly due to risk aversion

The industry profit is usually maximized under monopoly and falls with the number of firms in a Cournot oligopoly. However, demand uncertainty and risk aversion reduce firms' outputs, thus raising oligopoly profits and reducing monopoly one. Given a liner demand and costs and a mean-variance utility, we obtain the necessary and sufficient condition for a monopoly's profit and utility to be lower than an oligopoly. We also find such a condition for collusion to yield a lower profit. Finally, we provide a sufficient condition for a monopoly profit to be lower than an oligopoly given a general non-linear demand function.