Changes

In the first period, <math>P\,</math>'s best response to any <math>c\,</math> is <math>x^P\,</math>. <math>A\,</math> then maximizes utility by choosing <math>c_1\,</math> subject to this. However, as <math>z\,</math> is independent of <math>x\,</math> (and <math>y\,</math>), and as <math>A\,</math>'s utility is concave in <math>c\,</math>, but costs are convex, <math>A\,</math> chooses the interior maximum irrespective of <math>P\,</math>'s choice to maximize <math>z\,</math> and hence <math>u\,</math> (subject to the constraint that <math>x=x^p\,</math>). Any <math>y\,</math> can be choosen as it will have no effect.

===Specialized Capacity (SC)===

:<math>y^* \in [y_c,x^A]\,</math>

===Comparing GC and SC===