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Optimal diversification strategies in the networks of related products and of related research areas
Aamena Alshamsi, Flavio L. Pinheiro, Cesar A. Hidalgo
TL;DR
Related activities make entry into new economic activities more likely, but optimal diversification strategies balancing related and unrelated activities are not well understood. The paper models diversification as strategic diffusion under complex contagion and finds that highly connected activities are most useful to target at an intermediate stage, in line with country patterns in exports and research.
Problem
Although related activities increase the likelihood of entering new activities, how to optimally balance related and unrelated diversification remains unclear.
Source: Introduction · p. 1Method
The paper models economic diversification as strategic diffusion under complex contagion and studies optimal strategies across network topologies.
Source: Introduction · p. 1Results
Strategies minimizing diversification time target highly connected activities at an intermediate step, and countries’ export and research patterns are similar to the model’s predictions.
Source: Introduction · p. 2, Empirical Validation · p. 7Takeaways & Limitations
Optimal diversification depends on when to target highly connected activities, which is at an intermediate, relatively low level of diversification.
Source: Discussion · p. 8The model excludes strategic interactions among multiple diffusion processes competing for the same network nodes.
Source: Modelling Strategic Diversification · p. 4
Abstract
from arXiv · showhide
Countries and cities are likely to enter economic activities that are related to those that are already present in them. Yet, while these path dependencies are universally acknowledged, we lack an understanding of the diversification strategies that can optimally balance the development of related and unrelated activities. Here, we develop algorithms to identify the activities that are optimal to target at each time step. We find that the strategies that minimize the total time needed to diversify an economy target highly connected activities during a narrow and specific time window. We compare the strategies suggested by our model with the strategies followed by countries in the diversification of their exports and research activities, finding that countries follow strategies that are close to the ones suggested by the model. These findings add to our understanding of economic diversification and also to our general understanding of diffusion in networks.
Introduction
The paper frames economic diversification as a complex-contagion problem: related activities shape entry, but the optimal strategy for traversing this landscape remains unclear. Its model finds that diversification is fastest when highly connected activities are targeted at an intermediate step, consistent with observed country strategies.
- Regions face a trade-off between targeting activities that leverage local knowledge and taking riskier steps that may open new development paths.Source: Introduction · p. 1
- Economic activity entry is more likely when related activities are already present, but optimal strategies for traversing these path-dependent landscapes remain an open question.Source: Introduction · p. 1
- Complex contagion, where transmission is reinforced by multiple sources, better represents knowledge diffusion than simple contagion, which requires contact with one individual.Source: Introduction · p. 1
- The paper formalizes diversification as strategic diffusion under complex contagion and explores the problem across simple and complex network topologies.Source: Introduction · p. 1
- Strategies that minimize diversification time target highly connected activities at an intermediate step, and country export and research strategies are similar to the model’s predictions.Source: Introduction · p. 2
Results
The paper models diversification as strategic diffusion over networks where related activities make entry more likely. Its optimal strategies target highly connected activities at intermediate stages, and countries’ export and research strategies broadly resemble the model’s predictions.
Path Dependencies in Networks of Related Activities
- Entry probabilities rise as a slightly super-linear power of related-activity share: y ≈ 0.16x^1.03 for products and y ≈ 0.74x^1.09 for research.Product entry is characterized over four years and research-area entry over three years.Source: Path Dependencies in Networks of… · p. 2
Modelling Strategic Diversification
- The model assigns activities active, potentially active, or inactive states, with activation probability increasing as a power of the share of related activities already present.The probability rule uses α to adjust the strength of path dependence.Source: Modelling Strategic Diversification · p. 2
- The optimization selects an ordered sequence of targets to minimize total activation time across wheel, generalized-wheel, and scale-free networks, benchmarked against five simple strategies.The benchmarks are random, high-degree, low-degree, greedy, and majority targeting.Source: Modelling Strategic Diversification · pp. 2, 4
- The analysis focuses on minimizing activation time and excludes competing diffusion processes; other objective functions are left for future work.The paper motivates the no-interaction assumption by noting that new entrants represent less than 1% of a product’s global market on average.Source: Modelling Strategic Diversification · p. 4
- For wheel networks, optimal hub timing is about 7% active at α = 1 and 10–15% of peripheral nodes at α = 2; its window shifts later as relatedness strengthens.The optimal window is less risky to miss by being late than by targeting the hub too early.Source: Modelling Strategic Diversification · pp. 5–6, Figure 2 · p. 5
- In the most heterogeneous generalized-wheel networks, equation 4 activates all nodes in 80% of greedy and majority time and 70% of random-strategy time.The advantage of choosing the right dynamic strategy grows with network heterogeneity.Source: Figure 2 · p. 5, Modelling Strategic Diversification · p. 6
- In scale-free networks, a greedy–majority mix beats all five benchmark strategies, performs relatively better as α rises, and targets high-degree nodes earlier than greedy does.The optimal mix changes with α.Source: Figure 2 · p. 5, Modelling Strategic Diversification · p. 6
Empirical Validation
- Countries’ export and research diversification follows an inverse-U pattern, broadly matching the model, though export targeting overshoots hubs early and undershoots at intermediate stages.For research, the simulated optimum is close to the theoretical prediction.Source: Empirical Validation · p. 7, Figure 3 · p. 7
Discussion
Because activity entry is more likely when related activities are present, the paper asks how to optimize diversification under network-constrained knowledge diffusion. Its findings indicate that strategies are dynamic, with highly connected activities best targeted at an intermediate, relatively low level of diversification.
Discussion
- Although related activities commonly agglomerate and knowledge diffusion is a proposed driver, optimal diversification strategies under network constraints remain little understood.Entry probability increases with the number of related activities present locally or nearby.Source: Discussion · p. 7
- The analysis uses diversification as a baseline objective in which all activities have equal value, while noting that other objective functions could be considered.Examples include export contribution to GDP, economic complexity, and carbon intensity.Source: Discussion · pp. 7–8
- Strategies for maximizing diversification are dynamic: highly connected activities should be targeted at an intermediate, relatively low level of diversification.The strategy depends on when activities are targeted, not only which activities are chosen.Source: Discussion · p. 8