This is based on #45, where as discussed in #45 I noticed that maybe we can get away without costates in the merit function/linesearch. This basically amounts to using the sum of all players' objectives as a merit function. Clearly, local minimizers of this function include local minimizers of each individual players' objective, but not the other way around. If this works well, it indicates that we are still descending on this "more general" merit function. The benefit of using it is that it does not require costates.
Empirically, this new merit function + linesearch works at least as well as the previous method. At some point, we should try to incorporate costates but for now this is probably simplest.
This is based on #45, where as discussed in #45 I noticed that maybe we can get away without costates in the merit function/linesearch. This basically amounts to using the sum of all players' objectives as a merit function. Clearly, local minimizers of this function include local minimizers of each individual players' objective, but not the other way around. If this works well, it indicates that we are still descending on this "more general" merit function. The benefit of using it is that it does not require costates.
Empirically, this new merit function + linesearch works at least as well as the previous method. At some point, we should try to incorporate costates but for now this is probably simplest.