Identifying reaction functions in differential oligopoly games

We investigate the issue of strategic substitutability/complementarity and define the concepts of best reply function and dominant strategy in deterministic differential games. We prove that if a player's Hamiltonian is additively separable w.r.t. controls, then players follow dominant strategies at every instant. Otherwise, if the Hamiltonian is not additively separable w.r.t. controls, instantaneous best replies can be properly characterised. However, under additive separability, we show that strategic interaction via best replies can still be characterised at the steady state. Illustrative examples are Ramsey and Solow's growth models, reformulated as oligopoly games, and a Cournot differential game with sticky price.