An Algorithm for payoff space in C1 parametric games

We present a new algorithm which determines the payoff-space of certain normal-form C1 parametric games, and - more generally - of continuous families of normal-form C1 games. This algorithm was implemented in MATLAB, and was applied to several real-life cases. It has the merit of providing the parametric expressions of the critical zone for any game in the considered family both in the bistrategy space and in the payoff space, and it allows to both graphically illustrate the disjoint union (with respect to the parameter set of the parametric game) of the family of all payoff spaces, and parametrically represent the union of all the critical zones. One of the main motivations of our paper is that, in the applications, many normal-form games naturally appear in a parametric form; moreover, some efficient models of coopetition are parametric games of the considered type. Specifically, our developed algorithm provides the parametric and graphical representation of the payoff space and of the critical zone of a parametric game in normal-form, supported by a finite family of compact intervals of the real line. It is a valuable tool in the study of simple normal-form C1-parametric games in two dimensions.