  The aim of this of this paper is to study infinite games and to prove
formally some properties in this framework. As a consequence we show that the
behavior (the madness) of people which leads to speculative crashes or
escalation can be fully rational. Indeed it proceeds from the statement that
resources are infinite. The reasoning is based on the concept of coinduction
conceived by computer scientists to model infinite computations and used by
economic agents unknowingly. When used consciously, this concept is not as
simple as induction and we could paraphrase Newton: "Modeling the madness of
people is more difficult than modeling the motion of planets".
