Two producers act on a market of some homogeneous product. The first of them has a position of the leader and the other a position of the follower. The demand for this product evolves according to a demand function:

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yd (p(t)) = -2p(t) +20, a(t), b(t) > 0. The total output by both producers matches the demand for the product reported by consumers by a given price: y (1) + y2 (t) = yd (p(t)). Production total costs for the leader and for the follower, respectively, are as follows: ki (y (t)) = c (t)y + 1, k(y2(t)) = 2.5y2(t) + 1,