1.0$, all the other methods converge exponentially towards the equilibrium, with ConOpt and SGA converging at a faster rate due to the stronger gradient correction ($\gamma > \eta$). If we choose $\alpha = 3.0$, OGDA, ConOpt, and SGA fail. The former diverges, while the latter two begin to oscillate widely. If we choose $\alpha = 6.0$, all methods but CGD diverge.

-   In order to explore the effect of the consensus Term \[item:consensus\], we now consider the convex-concave problem $f(x,y) = \alpha(x^2 - y^2)$ (see Figure \[fig:quad\]). For $\alpha = 1.0$, all algorithms converge at an exponential rate, with ConOpt converging the fastest, and OGDA the slowest. The consensus promoting term of ConOpt accelerates convergence, while the competition promoting term of OGDA slows down the convergence. As we increase $\alpha$ to $\alpha = 3.0$, the OGDA and ConOpt start failing (diverge), while the remaining algorithms still converge at an exponential rate. Upon increasing $\alpha$ further to $\alpha = 6.0$, all algorithms diverge.

-   We further investigate the effect of the consensus Term \[item:consensus\] by considering the concave-convex problem $f(x,y) = \alpha( -x^2 + y^2)$ (see Figure \[fig:quad\]). The critical point $(0,0)$ does not correspond to a Nash-equilibrium, since both players 