Games played on an illfounded membership relation

The epsilon-game as an attempt to salvage something from failure of foundation. Solitaire version gives rise to concept of wellfounded set and rank, binaire version gives us pseudofoundation and pseudorank. These both give rise to games defining a binary relation of relative rank (resp. pseudorank). Greatest and least fixed points. Natural constructions of models of epsilon-determinacy. A paradox of inductively defined sets.