Dynamics in International Subsidy Games with Unit-elastic Demand," mimeo

In this paper, we construct a three-country model with two govern-ments and two firms and consider dynamic behavior of the sequential sub-sidy game in which the governments determine their optimal trade policies and then the firms determine their optimal outputs. We first show the existence of an optimal trade policy under realistic conditions. In the case of symmetric firms, the governments adopt periodic mixed trade policy (i.e., one government gives subsidy and the other levies tax in one period and then the governments interchange their policies in the next period) if the adjustment is naive, and the governments adopt a stable mixed policy if adaptive. In the case of asymmetric firms, a firm receives subsidy if its cost is lower and pays tax if higher. If the Cournot output point under the optimal subsidy is locally stable, then its dynamics can be periodic which is synchronized with the periodic trade policy. If it is locally un-stable, then complex dynamics involving chaos emerges regardless of the cost difference.