### Analytic solutions of nonlinear Cournot duopoly game.

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For nonlinear difference equations, it is difficult to obtain analytic solutions, especially when all the eigenvalues of the equation are of absolute value 1. We consider a second order nonlinear difference equation which can be transformed into the following simultaneous system of nonlinear difference equations: ⎧ x(t+1) = X(x(t),y(t)) ⎨ ⎩ y(t+1) = Y(x(t), y(t)) where $X(x,y)=\lambda \u2081x+\mu y+{\sum}_{i+j\ge 2}{c}_{ij}{x}^{i}{y}^{j}$, $Y(x,y)=\lambda \u2082y+{\sum}_{i+j\ge 2}{d}_{ij}{x}^{i}{y}^{j}$ satisfy some conditions. For these equations, we have obtained analytic solutions in the cases "|λ₁| ≠ 1 or |λ₂| ≠ 1" or "μ...

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