Extending decision field theory to a multi-agent decision-making with forgetting

Decision Field Theory (DFT) is a dynamic human decision-making model based on the evolution of preferences on the options over time. The goal of this paper is to extend DFT to examining how long-term decision making processes via the experience of forgetting lead to shifts in preference. Combining the established DFT model with the parameter of forgetting introduces an extended model that shares the mathematical characteristics of DFT. We then examine the choice probability of this DFT model with forgetting (DFT-F) by driving the limiting distribution of preference. This DFT-F is applied to mimic a decision-making process involving two or more people by introducing parameters related to individual powers of influence within various types of human interaction: competition, collaboration, compromise, accommodation, and avoidance. We then use DFT-F to develop a hierarchical network model for analyzing multi-agent decision-making, and discuss its stability under the dynamics of opinion formation. The bottom level of this network represents individual's decision-making behaviors, while they are aggregated to a group decision in the higher level of the network. A simulation model of a social network is used to demonstrate how the changes of parameters in DFT-F have different effects on the stability of the network.