Algorithms for Payoff Trajectories in C1 Parametric Games

In 2009 ([4]) a new procedure to determine the payoff space of non-parametric differentiable normal form games has been presented. Then, the new procedure has been applied (in [1]) to numerically determine an original type of 3-dimensional representation of the family of payoff spaces in normal-form C1 parametric games, with two players.
In this work, the method in [4] has been pointed out and assumed with the aim of realizing an algorithm which (computationally) gives the real geometric representation of the payoff trajectory of normal-form C1-parametric games, with two players. The application of our algorithm to several examples concludes the paper. Our analysis of parametric games, also, allows us to pass from the standard normal-form games to their coopetitive extension, as already illustrated in several applicative papers by D. Carfì.