Analysis of cap-and-trade mechanism represented by a piecewise dynamical system

In this paper, we derive the dynamics of cap-and-trade mechanism between firms considering corporate values associated with the carbon dioxide emission reduction. The relationship between the initial emission allowances and total reductions, and the necessary condition to achieve carbon neutrality are shown by the equilibrium state analysis. In the simplest case with 2 agents, the dynamics of the cap-and-trade mechanism are expressed as a piecewise nonlinear system, and the analysis is facilitated by nonlinear coordinate transformation and dimensionality reduction. Finally, we derive a stability condition for the piecewise linearized system and show a couple of types of possible behaviors of the firms in numerical examples.