Targeted incentives for social tipping in heterogeneous networked populations

TL;DR

The paper addresses how to design targeted incentives to trigger endogenous social tipping in populations with heterogeneous networks and preferences under real-world constraints. It introduces a game-theoretic agent-based model where individuals choose between two options based on intrinsic preferences and local social influence, analyzed via Markov chains and mean-field methods. The study finds that targeting amenable individuals often yields the lowest cost to achieve high adoption (e.g., $90\%$), but optimal strategies depend on network structure, resistance to change, and homophily, with trade-offs between backsliding and spillovers. These insights offer policymakers a framework to tailor incentives under budget, speed, and equity considerations, and the results are validated across synthetic and empirical networks.

Abstract

Many societal challenges, such as climate change or disease outbreaks, require coordinated behavioral changes. For many behaviors, the tendency of individuals to adhere to social norms can reinforce the status quo. However, these same social processes can also result in rapid, self-reinforcing change. Interventions may be strategically targeted to initiate endogenous social change processes, often referred to as social tipping. While recent research has considered how the size and targeting of such interventions impact their effectiveness at bringing about change, they tend to overlook constraints faced by policymakers, including the cost, speed, and distributional consequences of interventions. To address this complexity, we introduce a game-theoretic framework that includes heterogeneous agents and networks of local influence. We implement various targeting heuristics based on information about individual preferences and commonly used local network properties to identify individuals to incentivize. Analytical and simulation results suggest that there is a trade-off between preventing backsliding among targeted individuals and promoting change among non-targeted individuals. Thus, where the change is initiated in the population and the direction in which it propagates is essential to the effectiveness of interventions. We identify cost-optimal strategies under different scenarios, such as varying levels of resistance to change, preference heterogeneity, and homophily. These results provide insights that can be experimentally tested and help policymakers to better direct incentives.

Figures (15)

• Figure 1: Strategies need to account for the distribution of preferences The most cost-effective strategies to achieve 90% adoption are plotted for different preference distributions modeled using a transformed Beta distribution, $\text{Beta}(\alpha, \alpha)$, symmetrically centered around the average preference strength. The parameter shape parameters are the same, and $\alpha$ controls homogeneity. In A, the preference distributions are plotted corresponding to 5 points in the parameter space depicted using stars in B with matching colors. We test strategies based on information about preference distribution (B), networks (C), and the random targeting strategy. We then compare all strategies in D. Among strategies based on preferences (B) the amenable strategy is cost-effective across all preference distributions. In C, we see that in case of high resistance to change, it is better to target the highly connected nodes while targeting peripheral nodes when the population is more amenable to change. In D, we see that as preference distribution gets more heterogeneous, the amenable strategy outperforms network-based strategies over a greater range of average preferences. The population size is 1000 and is connected via a Barabási-Albert network (min $k$=10) with social influence parameter $\omega =0.5$.
• Figure 2: Optimal strategies in segregated and clustered populations The most cost-effective strategies to achieve 90 % adoption are plotted for varying average preferences for change and levels of homophily in the network. In A, networks corresponding to corner cases and the center of the parameter space are depicted. We test strategies based on information about preference distribution (B), networks (C), and the random targeting strategy. We then compare all strategies in D. In B, we see that while amenable strategy works for low homophily networks, for more segregated networks random strategy works better in case of high resistance while targeting resistant individuals works when the population is more amenable on average. In C, we see that homophily doesn't change the ordering of network-informed strategies. In D, we see that as the networks get more segregated, the network-informed strategies outperform preference-informed strategies over a greater range of average preferences. The population size is 1000 and is connected via a homophilous Barabási-Albert network (min $k=10$) with social influence parameter $\omega = 0.5$ and the preference distribution is given by a transformed $\text{Beta}(\alpha, \alpha)$, with $\alpha=2$.
• Figure 3: Time taken for 90% adoption The time taken to reach 90% adoption is plotted against the cost of implementing different heuristics for Barabási-Albert networks (A, B) and Barabási-Albert networks with homophily = 0.45 (C, D). In A, C the cost and time taken by minimum intervention using different strategies is plotted. Time is measured in generations ($N$ time steps). Each point represents the average value for a given configuration of network and preference distribution over 50 replicates. We consider 2500 configurations for each heuristic (50 networks and 50 preference distributions). The 5-95 percentile bands are shown along both axes. The average minimum interventions sizes which are indicated as percentages of the population. In B(D), as intervention sizes are increased beyond the minimum levels observed in A(C), the cost vs time plot shows an inflection point for all the tested heuristics. In the homophilous networks, all strategies take more time to achieve 90% adoption. Further, the resistant strategy becomes cost-effective while taking significantly more time. The population size is 1000, with a preference distribution given by a transformed $\text{Beta}(\alpha, \alpha)$, with $\alpha=2$ centered around average preference = 1.
• Figure 4: Gini coefficient of incentives The Gini coefficient of the incentives given is plotted for the target group (A, B) and the whole population (C, D).In A and C, the Gini coefficient is plotted against the cost of the minimum intervention sizes. As intervention sizes are increased beyond the minimum levels observed in \ref{['fig:figc']}. In B we see that the Gini coefficient within the target group increases with greater intervention size for network-informed strategies, and converges to the random strategy which remains unaffected by increasing intervention size being representative of the population heterogeneity. Thus smaller target groups are more relatively more homogeneous. In D, we see the intuitive result that greater intervention size decreases the Gini coefficient for the population( target and non-target group). The population size is 1000 connected by a Barabási-Albert network, with a preference distribution given by a transformed $\text{Beta}(\alpha, \alpha)$, with $\alpha=2$ centered around average preference = 1.
• Figure S1: Adoption trajectories from theory Using a Markov Chain analysis (described in supplemental text), the trajectory of adoption is plotted for 5 different targeting strategies: amenable (A), resistant(B), high-degree nodes (C), low-degree nodes(D) and random (E). The fraction of adoption within both target and non-target group is plotted and the minimum intervention sizes are identified which are marked on the respective colorbars. The preference and degree distributions considered are the same as Fig 3. In panel F the fixed points corresponding to the Eq.S11 are plotted and we see that unstable fixed point $x^* \approx 0.4$ equals $\phi_{min}$ in panels A, B and E.