Cournot Game

In the Parameterized Cournot Game, as defined in Oesterle and Sharon (in press), two players choose their production quantities \(\boldsymbol{q} = (q_1, q_2) \in \mathbb{R}^2\) for a good with the price defined as \(p(\boldsymbol{q}) = \max(p_{max} - q_1 - q_2, 0)\). Both players have a constant production cost of \(c \geq 0\) per unit. The players’ utilities, representing their profits, are given by \(u_i(\boldsymbol{q}) = q_i \cdot \left(p(\boldsymbol{q}) - c\right)\). The restrictor patiently waits until the agents’ strategies converge and then formulates an optimal restriction to increase social welfare.

The implementation can be found with instructions here.