Dynamic Supergames on Rectangle Lattice Based on Four Person Team Games

In this paper two classes of large supergames, i.e., infinitely repeated games played by many players on 2-dimensional rectangle lattice are studied. Each person located on the vertices of the lattice plays four 4-person team games or 4-person 2-pairs team games simultaneously with her neighbors. Under the conditions of the pre-specified updating rules and the transition probabilities, the strategy process forms a Markov Chain. The formula of invariant measures which represent the long-run equilibrium plays with symmetric payoffs are obtained.