Cooperative Dynamic Games with Durable Controls: Theory and Application

Durable controls that have effects lasting over a certain period of time are prevalent in real-life situations. Revenue-generating investments, toxic waste disposal, durable goods, emission of pollutants, regulatory measures, coalition agreements, diffusion of knowledge, advertisement and investments to build up physical capital are vivid examples of durable controls. Durable controls may affect both the decision-makers’ payoffs and the evolution of the state dynamics. This paper develops a new class of cooperative dynamic games with multiple durable controls of different lag durations affecting both the players’ payoffs and the state dynamics. A novel dynamic optimization theorem involving durable controls is derived. Dynamically consistent cooperative solutions are provided. An illustration of a dynamic game with durable controls causing lagged effects in capital formation, pollution accumulation and revenue generation from investment is presented. The analysis widens the application of dynamic game theory in practical problems. Further theoretical developments and relevant applications along this line would be expected.