Post-Disaster Resource Redistribution and Cooperation Evolution Based on Two-Layer Network Evolutionary Games

TL;DR

This work tackles post-disaster resource scarcity by modeling cross-layer cooperation between shelters and victims using a coupled two-layer network. It combines an upper-layer continuous public goods game for shelters with a lower-layer binary cooperation game for victims, enabling cross-layer feedback analyzed via Monte Carlo simulations on Barabási–Albert and Beijing shelter networks. Key findings show that moderate enhancement factors and subsidies promote cooperation, while excessive incentives trigger free-riding; credible punishment effectively suppresses defection, and hub-targeted punishment enhances diffusion under resource constraints. The results provide policy guidance on calibrated incentives, enforceable sanctions, and structurally targeted interventions to foster rapid, robust cooperation during early post-disaster recovery.

Abstract

In the aftermath of large-scale disasters, the scarcity of resources and the paralysis of infrastructure raise severe challenges to effective post-disaster recovery. Efficient coordination between shelters and victims plays a crucial role in building community resilience, yet the evolution of two-layer behavioral feedback between these two groups through network coupling remains insufficiently understood. Here, this study develops a two-layer network to capture the cross-layer coupling between shelters and victims. The upper layer uses a post-disaster emergency resource redistribution model within the framework of the public goods game, while the lower layer adopts a cooperative evolutionary game to describe internal victim interactions. Monte Carlo simulations on scale-free networks reveal threshold effects of incentives: moderate public goods enhancement and subsidies promote cooperation, whereas excessive incentives induce free-riding. In contrast, credible and well-executed punishment effectively suppresses defection. Targeted punishment of highly connected shelters significantly enhances cooperation under resource constraints. A comparative analysis using a network generated from the actual coordinates of Beijing shelters confirms the model's generality and practical applicability. The findings highlight the importance of calibrated incentives, enforceable sanctions, and structural targeting in fostering robust cooperation across organizational and individual levels in post-disaster environments.

Figures (14)

• Figure 1: Schematic of the coupled two-layer "shelter--victim" network.
• Figure 2: Moderate enhancement promotes cooperation, excessive $r$ reduces it. (a)–(b) Evolution of $\theta(t)$, $\mu(t)$ under $r \in \{1.05,\,1.10,\,1.30,\,1.60\}$. Moderate values accelerate convergence and yield higher cooperation, whereas large $r$ weakens incentives. (c)–(d) Steady-state of $\theta(t)$, $\mu(t)$ over $r \in [1.0, 3.0]$, showing a non-monotonic trend: shelter input rises slightly with $r$, while victim cooperation declines monotonically. Each result from 256 runs over 25 000 steps, with steady-state values averaged over the final 1000 steps. Parameters: $\sigma=0.40$, $\gamma_1=0.50$, $\alpha=0.50$, $\gamma^0=0.90$, and $\beta=0.50$.
• Figure 3: Higher subsidy $\sigma$ weakens lower-layer cooperation. (a)–(b) Evolution of $\theta(t)$, $\mu(t)$ under $\sigma \in \{0.30,\,0.40,\,0.45,\,0.50\}$. Shelters respond weakly to subsidies, but victims become less cooperative as $\sigma$ increases. (c)–(d) Steady-state of $\theta(t)$, $\mu(t)$ over range $[0,\,1)$. Default parameters, $r=1.30$, the simulation settings unchanged.
• Figure 4: Punishment effect: $\gamma^0$ dominates, $\alpha$ has a secondary effect, and $\gamma_1$ shows a relatively weak impact. Rows 1 and 2: the evolution of $\theta(t)$ and $\mu(t)$ as each parameter varies independently. Row 3: steady-state of $\mu(t)$ for each parameter. Default parameters, $r=1.30$, $\sigma=0.40$, the simulation settings unchanged.
• Figure 5: Joint punishment maximizes cooperation. (a)–(b) Evolution of $\theta(t)$ and $\mu(t)$ under seven punishment configurations. Single-parameter punishment is insufficient, and only full penalty combination sustains high cooperation. Default parameters, the simulation settings unchanged.