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)
K-graph C*-algebra edges involved in the graph and additional factorization rules of 2-color equivalent classes should be defined. The factorization rule on k-graph skeleton is what distinguishes one k-graph defined on the same skeleton from another k-graph. k- can be any natural number greater than or equal to 1. The reason k-graphs were first introduced by Kumjian, Pask et. al. was to create examples of C*-algebra from them. k-graphs consist of two parts: skeleton and factorization rules defined on the given skeleton. Once k-graph is well-defined, one can define functions called 2-cocycles on each graph, and C*-algebras can be built from k-graphs