Border-collision bifurcations in a dynamic management game

Managerial systems often involve piecewise-linear relations associated with non-negativity conditions or other forms of restrictions to the decision variables. The bifurcations that take place in such systems differ qualitatively from the bifurcations that one can observe in smooth dynamical systems. The present paper provides an analysis of the bifurcation structure of the so-called BEER game, a dynamic management game developed at the Sloan School of Management to illustrate how the structure of a system determines its behavior. We show how the BEER model displays abrupt period-doubling bifurcations, truncated bifurcation cascades, and a variety of the so-called border-collision bifurcations. Particular emphasis is paid to the resonance structure observed in one- and two-sector versions of the model.