Modeling for the Dynamics of Human Innovative Behaviors

How to promote the innovative activities is an important problem for modern society. In this paper, combining with the evolutionary games and information spreading, we propose a lattice model to investigate dynamics of human innovative behaviors based on benefit-driven assumption. Simulations show several properties in agreement with peoples’ daily cognition on innovative behaviors, such as slow diffusion of innovative behaviors, gathering of innovative strategy on “innovative centers”, and quasi-localized dynamics. Furthermore, our model also emerges rich non-Poisson properties in the temporal-spacial patterns of the innovative status, including the scaling law in the interval time of innovation releases and the bimodal distributions on the spreading range of innovations, which would be universal in human innovative behaviors. Our model provide a basic framework on the study of the issue relevant to the evolution of human innovative behaviors and the promotion measurement of innovative activities.

💡 Research Summary

The paper proposes a minimal lattice‑based model that captures the evolution of human innovative behavior by integrating a cost‑driven benefit structure, information spreading, and evolutionary game dynamics. Each node on an L×L periodic lattice represents an individual who adopts one of two strategies: Innovator (I) or Follower (F). Innovators generate a new piece of information (an “innovation”) at each macro‑time step t, while followers randomly select a neighbor and adopt the most recent information they encounter. Within a single macro‑step, each agent updates its information at most once, creating a competitive diffusion process.

Both innovators and followers receive a benefit proportional to the number of agents whose information ultimately originates from them (denoted M_i). Innovators pay a higher cost C_I = a (a ≥ 1) reflecting the greater effort required to create new ideas; followers pay a unit cost C_F = 1. The net payoff is therefore P_i = M_i − C_i. After all agents have updated, each node compares its payoff with those of its four nearest neighbors and imitates the strategy of the neighbor (or itself) with the highest payoff, breaking ties randomly. This imitation rule is the standard replicator dynamics used in evolutionary games.

Extensive Monte‑Carlo simulations reveal several robust phenomena. First, the steady‑state fraction of innovators R_I declines as an inverse power of the innovation cost, R_I ∝ a^−1, essentially independent of lattice size. Analytical reasoning shows that at equilibrium the average payoff of innovators equals that of neighboring followers, leading to the condition M_I ≈ 2(a − 1)·m_F (with m_F ≥ 2 the average number of follower neighbors). Substituting N = L² yields the observed scaling.

Second, innovators self‑organize into small, persistent clusters that the authors term “innovation centers.” These clusters display two basic geometric motifs (cross‑plaid and chessboard‑like) and remain localized for many time steps, producing a quasi‑localized dynamics. The spatial spread of the I‑strategy grows sub‑diffusively: the cumulative visited area A_I(t) follows a power law A_I ∝ t^0.7, markedly slower than the linear growth of a random‑walk baseline.

Third, temporal statistics of innovation events are non‑Poissonian. The inter‑event time τ_I between successive adoptions of the I‑strategy follows a cumulative distribution p_c(τ_I) ∝ τ_I^−0.5, corresponding to a probability density exponent ≈ −1.5, a hallmark of bursty human activity. The duration an agent remains an innovator also obeys a similar scaling, indicating short bursts of innovative activity interspersed with longer follower periods.

Fourth, the distribution of spreading sizes S (the number of agents reached by a single innovation) is bimodal. For low cost a, the distribution is dominated by a power‑law tail p(S) ∝ S^−1.5; as a increases, a secondary peak emerges that is well described by a Gaussian component centered at S_0, with S_0 scaling linearly with the inverse innovator fraction (S_0 ∼ R_I^−1). This reflects two regimes: frequent small‑scale diffusion within dense follower regions and occasional large‑scale cascades originating from sparsely populated innovation clusters.

Overall, the model demonstrates that a simple combination of higher innovation cost, payoff proportional to diffusion reach, and local imitation suffices to reproduce key empirical features of human innovation: clustered “hot spots,” slow spatial propagation, bursty temporal patterns, and mixed‑scale diffusion outcomes. The findings suggest that policy measures aiming to stimulate innovation should consider not only reducing creation costs but also fostering connectivity among existing innovation centers to enhance their diffusion potential.