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Agent-Based Simulation of *N*-Person Games with Crossing Payoff Functions

**Miklos N. Szilagyi**

**Iren Somogyi***Department of Electrical and Computer Engineering,**University of Arizona, Tucson, AZ 85721*

#### Abstract

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

The individual agents may cooperate with each other for the collective interest or may defect, that is, pursue their selfish interests only. After a certain number of iterations the proportion of cooperators stabilizes to either a constant value or oscillates around such a value.

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 nontrivial and in some cases quite irregular. They show drastic changes for the Leader Game in the narrow parameter range of 1.72 ≤ *P* ≤ 1.75. This behavior is similar to that observed in [1] for the *N*-Person Chicken Game. Irregular solutions were also found for the Reversed Stag Hunt Game.