This paper introduces the class of 2 × 2 × 2 trimatrix games with identical anonymous best-replies. For this class a complete classification on the basis of the Nash equilibrium set is provided.

This paper provides an overview of the various shapes the best- reply multifunctions can take in 2×2×2 trimatrix games. It is shown that, unlike in 2×2 bimatrix games, the best replies to the opponents’ pure strategies do not completely determine the structure of the Nash equilibrium set.

This paper introduces the class of 2 × 2 × 2 trimatrix games with identical anonymous best-replies. For this class a complete classification on the basis of the Nash equilibrium set is provided.