Isoelastic oligopolies under uncertainty

Single-product oligopolies are examined with uncertain isoelastic price functions and linear cost functions. Each firm wants to maximize its expected profit and also wants to minimize its uncertainty by minimizing the variance. This multiobjective optimization problem is solved by the weighting method, where the utility function of each firm is a linear combination of the expectation and variance of its profit. The existence and uniqueness of the equilibrium of the resulting n-person game is proved and an efficient algorithm is suggested to compute the equilibrium. The asymptotic behavior of the equilibrium is also investigated. Complete stability and bifurcation analysis is presented. The theoretical results are verified by computer simulation.