Chaos and community evolution in social learning with multiple true states

Much of the existing researches on social learning assume that there is only one underlying true state, and consider whether and/or how the agents can learn the true state. The questions of how the opinion is going if there are multiple true states, and whether it can lead to community evolution in society, are more interesting and challenging. Motivated by this, in this paper we give a preliminary study on social learning with multiple true states, and develop a model in which different groups of agents receive signal sequences generated by different underlying true states. The agent updates his belief by combining his rational self-adjustment based on the received signals and the influence of his neighbors through their communication. If the communication network and the reliance of each agent on its neighbors are fixed, we observe chaos in opinion dynamics, and further find that the signal structure of interference state can transform chaos into convergence for the agent's belief while the signal structure of true state only influences the amplitude of the chaotic oscillations. If the agent changes the reliance on its neighbors according to the difference between their beliefs, communities can emerge from the society, where the agents influenced by the same external state are likely to gather together and form a community.