Abstract
In general, a linear-quadratic game with a single state implies the existence of a continuum of infinitely many equilibria generated by infinitely many nonlinear strategies. I illustrate a linear-quadratic linear state game with multiple states, which (i) alternatively fits the analysis of GHG emissions and the extraction of living stocks, and (ii) lends itself to be solved for nonlinear feedback strategies as if each player were facing a single state equation. This representation of the game delivers a continuum of nonlinear feedback solutions. However, I also show that in general this solution does not coincide with that delivered by the standard method based upon undetermined coefficients. Using the latter, it can be proved that the complexity engendered by the first approach disappears, leaving entirely the stage to equilibrium unicity. These findings reveal that parceling out the stock (CO2 of fish) across firms can be a desirable policy tool.