The optimum behavior of competing firms is examined under price uncertainty. The firms want to maximize their expected profits and in order to reduce risk, they also want to minimize the variances of the profits. This two-objective problem is realized by optimizing the certainty equivalents. In addition, the firms also want to limit the probabilities of very low profits, which requirement is formulated as chance-constraints. Two methods are suggested to find the equilibrium output levels. Based on the Kuhn-Tucker conditions as feasible solutions of a system of equalities and inequalities have to be identified. The second method requires to solve a single-objective nonlinear programming problem.
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