Optimal Policy Design for Repeated Decision-Making under Social Influence

2025-03-05

AI Summary

This paper addresses the challenge of guiding repeated individual decisions under social influence. Method: We propose a dual-timescale modeling and control framework that decouples high-frequency autonomous decision-making from low-frequency social imitation, incorporating stochastic perturbations to capture behavioral variability. For the first time, we integrate non-convergent stochastic opinion dynamics with ergodicity analysis, rigorously establishing the ergodicity of an extended Friedkin–Johnsen model under specified conditions. Building upon this, we design a synergistic control strategy combining asymptotically optimal control with model predictive control (MPC) to jointly ensure long-term goal alignment and short-term response robustness. Results: Simulations demonstrate that our approach significantly improves population-level adoption rates of target behaviors at substantially lower policy cost, offering a new paradigm for social system intervention—one that is mathematically verifiable, computationally tractable, and tunable.

Technology Category

• Cognitive Modeling & Cognitive Systems: Social Cognition And Interaction
• Multiagent Systems: Agent-Based Simulation and Emergent Behavior
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• Economics, Online Markets and Human Computation: Social networks and social learning

Abstract

In this paper, we present a novel model to characterize individual tendencies in repeated decision-making scenarios, with the goal of designing model-based control strategies that promote virtuous choices amidst social and external influences. Our approach builds on the classical Friedkin and Johnsen model of social influence, extending it to include random factors (e.g., inherent variability in individual needs) and controllable external inputs. We explicitly account for the temporal separation between two processes that shape opinion dynamics: individual decision-making and social imitation. While individual decisions occur at regular, frequent intervals, the influence of social imitation unfolds over longer periods. The inclusion of random factors naturally leads to dynamics that do not converge in the classical sense. However, under specific conditions, we prove that opinions exhibit ergodic behavior. Building on this result, we propose a constrained asymptotic optimal control problem designed to foster, on average, social acceptance of a target action within a network. To address the transient dynamics of opinions, we reformulate this problem within a Model Predictive Control (MPC) framework. Simulations highlight the significance of accounting for these transient effects in steering individuals toward virtuous choices while managing policy costs.

Problem

• Design control strategies for virtuous choices under social influence.
• Extend social influence model to include random and controllable factors.
• Propose optimal control to foster social acceptance of target actions.

Innovation

• Extends Friedkin-Johnsen model with random factors
• Introduces constrained asymptotic optimal control problem
• Uses Model Predictive Control for transient opinion dynamics