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)
Graph of a function should be taken into account. The graph of a function on its own doesn't determine the co-domain. It is common to use both words, function and graph of a function, since even if considered the same object, they indicate viewing it from a different angle. Given a mapping formula_1, in other words a function formula_2 together with its domain formula_3 and co-domain formula_4, the graph of the mapping is the set which is a subset of formula_6. The graph of the function formula_2 is the same set formula_8, which is, in the abstract definition of a function, the same as