More oligopolistic behavior

Even very simple models require attention to detail. In [link] we described simple model from the literature. A related model with a coupling constraint that limits pollution emissions is described in:

1. Jacek Krawczyk and James Zuccollo, NIRA-3: An improved MATLAB package for finding Nash equilibria in infinite games, Victoria University of Wellington, December 2006
2. Lars Mathiesen, Regulation of pollution in a Cournot equilibrium, The Norwegian School of Economics and Business Administration, Bergen, June 2008.

The Nash-Cournot model without pollution controls is simply:

Adding the pollution controls using taxes (or tradable quotas) is not that difficult:

Still for this simple model I get different results for the base case (no pollution controls). My results are:

----    135 PARAMETER results                       output      profit    emission       price no control  .j1      55.351      61.274 no control  .j2      14.914      13.345 no control  .j3      53.684      57.639 no control  .k1                             419.978 no control  .k2                             301.125 no control  .-                                            1.761 with control.j1      21.145       8.942 with control.j2      16.028      15.414 with control.j3       2.726       0.149 with control.k1                             100.000 with control.k2                              81.164 with control.-                                            2.601

The paper [1] has the following results:

The second part corresponds to my solutions, but the first part shows differences. As the problem with controls is an extension of the problem without controls, there is actually a reasonable chance my solution is correct.