On the (in)stability of nonlinear feedback solutions in a dynamic duopoly with renewable resource exploitation

- We study linear and nonlinear feedback equilibria in a differential duopoly game with resource extraction.
- We show that the degenerate tangency solution is unstable.
- The continuum of nonlinear equilibria is characterised using Rowat's (2007) procedure.
- The set of stable nonlinear equilibria is also identified.

We revisit Fujiwara's (2008) linear-quadratic differential duopoly game to show that the degenerate nonlinear feedback identified by the tangency point with the stationary state line is indeed unstable, given the dynamics of the natural resource exploited by firms. To do so, we fully characterise the continuum of nonlinear feedback solution via Rowat's (2007) method, thereby identifying the infinitely many stable nonlinear feedback equilibria. This entails that Rowat's method can be used in games where each player's instantaneous payoff depends quadratically on all players' controls.