Chicken (game) respectively. The line in graph on the left shows the optimum probability of playing the escalated strategy for player Y as a function of "x". The line in the second graph shows the optimum probability of playing the escalated strategy for player X as a function of "y" (the axes have not been rotated, so the dependent variable is plotted on the abscissa, and the independent variable is plotted on the ordinate). The Nash equilibria are where the players' correspondences agree, i.e., cross. These are shown with points in the right hand graph. The best response mappings agree (i.e., cross)
Shannon capacity of a graph The Lovász number ϑ("G") is a different graph invariant, that can be computed numerically to high accuracy in polynomial time by an algorithm based on the ellipsoid method. The Shannon capacity of a graph "G" is bounded from below by α("G"), and from above by ϑ("G"). In some cases, ϑ("G") and the Shannon capacity coincide; for instance, for the graph of a pentagon, both are equal to . However, there exist other graphs for which the Shannon capacity and the Lovász number differ. Haemers provided another upper bound on the Shannon capacity, which is sometimes better than Lovász bound: where