𝑁-Person Games with Crossing Externalities

Abstract

We report computer simulation experiments based on our agent-based simulation tool to model uniform N-person games with crossing payoff functions for the case when the agents are greedy simpletons who imitate the action of that of their neighbors who received the highest payoff for its previous action.

The payoff (reward/penalty) functions are given as two straight lines: one for the cooperators and another for the defectors. The payoff curves are functions of the ratio of cooperators to the total number of agents. Even if the payoff functions are linear, four free parameters determine them. In this investigation only crossing payoff functions are considered.

We have investigated the behavior of the agents systematically. The results show that the solutions are non-trivial and in some cases quite irregular. They show drastic changes in case of the Leader Game in the narrow parameter range of 1.72 â‰¤ P â‰¤ 1.75. This behavior is similar to that observed by [3] for the N-person Chicken Game. Irregular solutions were also found for the Reversed Stag Hunt Game.