A differential oligopoly game for optimal production planning and water savings

A production planning single-decision problem is extended to a production planning and water saving dual-decision problem. A differential oligopoly game in which product prices are sticky and water right trading occurs is used to study this problem. Unlike previous studies appeared in the literature, the decisions in this study are affected simultaneously by both the product and the water right prices. Static, open-loop, closed-loop and feedback equilibria are analyzed to show optimal production plans and water saving decisions. The impact of oligopoly competition on the social welfare is finally analyzed. Different optimal solutions as the values of the parameters change are also simulated numerically. The results show that the firms' optimal production plans and water saving decisions are strongly influenced by the water efficiency, initial water right allocations and water right reservation prices.