On the Oscillations in Cournot Games with Best Response Strategies

The paper proves that, under linear inverse demand with non-negativity constraints, simultaneous best-response dynamics in an n-firm Cournot game converge only to a Nash equilibrium or a two-period cycle, and it gives a constructive characterization of all two-period patterns (see the stated contribution and the two-case proof using partial orders across time slices: Eq. (12)–(20)) . By contrast, the model’s antitone-map argument incorrectly treats the coordinatewise minimum and maximum of a finite periodic orbit S as elements of S, which need not hold in the product order. This gap breaks the key step f(m)=M, f(M)=m and invalidates the claimed exclusion of longer cycles by that route.