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)
Paired opposites Paired opposites Paired opposites are an ancient, pre-Socratic method of establishing thesis, antithesis and synthesis in terms of a standard for what is right and proper in natural philosophy. Scalar ranges and coordinate systems are paired opposites within sets. Incorporating dimensions of positive and negative numbers and exponents, or expanding x, y and z coordinates, by adding a fourth dimension of time allows a resolution of position relative to the standard of the scale which is often taken as 0,0,0,0 with additional dimensions added as referential scales are expanded from space and time to mass and energy. Ancient systems frequently