This paper investigates N-person games with linear payoff functions, which are defined by four parameters each for the case when some of these parameters are equal to each other. Such cases represent transitions between different games. The participating agents are all greedy simpletons who imitate the behavior of the neighbor in their Moore neighborhood - nine neighbors, including themselves - that received the highest reward in the previous iteration. The results show that the solutions are non-trivial and represent quite irregular emergent behavior when the payoff functions are equal or cross each other.
The paper contributes the first logical analysis of borderline N-person games.