This paper considers games with two players for which it provides a sufficient condition on the responsiveness of the players' best replies around a Nash equilibrium that implies (i) a multiplicity of Nash equilibria; (ii) the non-isolatedness of this Nash equilibrium as rationalizable strategies; and (iii) the existence of non-trivial correlated equilibria arbitrarily close to it. This simultaneity of multiplicity, instability and vulnerability to sunspots parallels the same pattern observed in overlapping generations economies and finite economies with asymmetric information, and hints at some underlying relation between different avatars of the indeterminacy of economies and games that goes beyond the boundaries of any specific framework. Global links between multiplicity, instability and sunspots are also provided.