In this paper we intend to investigate the relationship between game theory and Fibonacci numbers. We call
Fibonacci games the subset of constant sum homogeneous weighted majority games whose increasing sequence of all type
weights and of the minimal winning quota is a string of consecutive Fibonacci numbers. Exploiting key properties of the
Fibonacci sequence, we obtain closed form results able to provide a simple and insightful classification of such games. In
detail: we show that the numerousness of Fibonacci games with t types is [(t+1)/2]; we describe unequivocally a Fibonacci game on the basis of its profile as a function of t and of a proper index z=1,...,[(t+1)/2];; we provide rules concerning
the behaviour of the total number n(t,z) of non-dummy players in a Fibonacci game. It turns out that there are two kinds of
Fibonacci games, associated respectively with z=1 (Fibonacci-Isbell games) and z>1.
