Optimal policy design for innovation diffusion: shaping today's incentives for transforming the future

TL;DR

The paper addresses promoting diffusion of innovations in social-influence networks by extending Friedkin–Johnsen opinion dynamics to incorporate both short-memory incentives and long-term incentives with memory that decays exponentially. The design problem is formulated as a model-predictive control (MPC) over an augmented state, yielding a convex quadratic program with linear constraints. Key contributions include two budget-aware incentive-design strategies and a validation via numerical simulations on real data (sustainable mobility) showing that receding-horizon control achieves higher adoption while efficiently using resources. The work offers a scalable framework for shaping incentives to steer large-scale diffusion trajectories toward transformative outcomes.

Abstract

In this paper, we propose a new framework for the design of incentives aimed at promoting innovation diffusion in social influence networks. In particular, our framework relies on an extension of the Friedkin and Johnsen opinion dynamics model characterizing the effects of (i) short-memory incentives, which have an immediate yet transient impact, and (ii) long-term structural incentives, whose impact persists via an exponentially decaying memory. We propose to design these incentives via a model-predictive control (MPC) scheme over an augmented state that captures the memory in our opinion dynamics model, yielding a convex quadratic program with linear constraints. Our numerical simulations based on data on sustainable mobility habits show the effectiveness of the proposed approach, which balances large-scale adoption and resource allocation

Figures (3)

• Figure 2: $x(t)$, $u^\ell(t)$ and $u^s(t)$, varying $\alpha$ for $\rho = 0.7$ and $\beta = 200$. The dashed lines represent the mean across agents.
• Figure 3: $x(t)$, $u^\ell(t)$, and $u^s(t)$, varying $\rho$, for $\alpha = 0.5$ and $\beta = 200$. The dashed lines represent the mean across agents.
• Figure 4: Increased budget: $x(t), ~u^\ell(t), ~u^s(t)$ for $\alpha=0.5$, $\rho=0.7$, and $\beta=400$. The dashed lines represent the mean over the agents.