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.
Lambertini, L., Mantovani, A. (2016). On the (in)stability of nonlinear feedback solutions in a dynamic duopoly with renewable resource exploitation. ECONOMICS LETTERS, 143, 9-12 [10.1016/j.econlet.2016.03.015].
On the (in)stability of nonlinear feedback solutions in a dynamic duopoly with renewable resource exploitation
LAMBERTINI, LUCA;MANTOVANI, ANDREA
2016
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
