On evolutionary 3-person prisoner's dilemma games on 2-D lattice

We investigate a system of interacting agents which play 3-person Prisoner's Dilemma game on a regular 2-dimensional lattice. The agents can choose between All-D, All-C, and TFT strategies. The peculiar structure of 3-person interactions gives rise to two different TFT strategies, which have different influence on the temporal evolution of the system. We introduce a formal setting for the relevant cellular automaton with the 3-person interactions, compare different TFT strategies, and discuss various properties of the 3-person games on the lattice.