Agent-based simulation of the N-person chicken game

We report computer simulation experiments using our agent-based simulation tool to model the multi-person Chicken game. We simplify the agents according to the Pavlovian principle: their probability of taking a certain action changes by an amount proportional to the reward or penalty received from the environment for that action. The individual agents may cooperate with each other for the collective interest or may defect, i.e., pursue their selfish interests only. Their decisions to cooperate or defect accumulate over time to produce a resulting collective order that determines the success or failure of the public system. 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 curves: 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. The actual shapes of the payoff functions depend on many factors. Even if we assume linear payoff functions, there are four parameters that are determined by these factors. The payoff functions for a multi-agent Chicken game have the following properties. (1) Both payoff functions increase with an increasing number of cooperators. (2) In the region of low cooperation the cooperators have a higher reward than the defectors. (3) When the cooperation rate is high, there is a higher payoff for defecting behavior than for cooperating behavior. (4) As a consequence, the slope of the D function is greater than that of the C function and the two payoff functions intersect. (5) All agents receive a lower payoff if all defect than if all cooperate. We have investigated the behavior of the agents under a wide range of payoff functions. The results show that it is quite possible to achieve a situation where the enormous majority of the agents prefer cooperation to defection. The Chicken game of using cars or mass transportation in large cities is considered as a practical application of the simulation.