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.

This paper provides an overview of the various shapes the bestreply multifunctions can take in 2x2x2 trimatrix games. It is shown that, unlike in 2x2 bimatrix games, the best replies to the opponents pure strategies do not completely determine the structure of the Nash equilibrium set