are playing their *worst possible strategy*. Thus it is highly undesirable for an algorithm to converge to this critical point. However for $\alpha = 1.0$, ConOpt does converge to $(0,0)$ which provides an example of the consensus regularization introducing spurious solutions. The other algorithms, instead, diverge away towards infinity, as would be expected. In particular, we see that SGA is correcting the problematic behavior of ConOpt, while maintaining its better convergence rate in the first example. As we increase $\alpha$ to $\alpha \in \{3.0,6.0\}$, the radius of attraction of $(0,0)$ under ConOpt decreases and thus ConOpt diverges from the starting point $(0.5,0.5)$, as well.

The first experiment shows that the inclusion of the competitive Term \[item:comp\] is enough to solve the cycling problem in the bilinear case. However, as discussed after Theorem \[thm:convergence\], the convergence results of existing methods in the literature are not break down as the interactions between the players becomes too strong (for the given $\eta$). The first experiment illustrates that this is not just a lack of theory, but corresponds to an actual failure mode of the existing algorithms. The experimental results in Figure \[fig:matrixGAN\] further show that for input dimensions $m,n > 1$, the advantages 