The effect of social welfare system based on the complex network

With the passage of time, the development of communication technology and transportation broke the isolation among people. Relationship tends to be complicated, pluralism, dynamism. In the network where interpersonal relationship and evolved complex net based on game theory work serve respectively as foundation architecture and theoretical model, with the combination of game theory and regard public welfare as influencing factor, we artificially initialize that closed network system. Through continual loop operation of the program, we summarize the changing rule of the cooperative behavior in the interpersonal relationship, so that we can analyze the policies about welfare system about whole network and the relationship of frequency of betrayal in cooperative behavior. Most analytical data come from some simple investigations and some estimates based on internet and environment and the study put emphasis on simulating social network and analyze influence of social welfare system on Cooperative Behavio.

💡 Research Summary

The paper investigates how a social‑welfare system influences cooperative behavior within a complex social network by combining game‑theoretic modeling with network science. Individuals are represented as nodes in an undirected graph, each adopting either a cooperative (C) or defecting (D) strategy in a repeated Prisoner’s Dilemma interaction with their neighbors. Strategy updates follow a probabilistic rule that weights the average payoff of neighboring nodes together with an external welfare incentive, denoted by the scalar parameter β. A higher β corresponds to a stronger welfare boost for cooperative actions.

The authors initialize a closed network and run synchronous rounds: in each round every node plays the two‑person game with all adjacent nodes, accumulates payoffs, and then possibly switches strategy according to the β‑adjusted rule. To explore the role of network topology, three graph types are examined: (1) an Erdős‑Rényi random graph, (2) a Watts‑Strogatz small‑world network with high clustering and short path lengths, and (3) a hierarchical community network that mimics clustered social groups.

Simulation results reveal a clear threshold effect of β. When β≈0 (no welfare incentive), defectors dominate and the average cooperation level stays below 20 %. Once β exceeds roughly 0.3, cooperation spreads rapidly, reaching over 70 % average cooperation. The small‑world and community graphs display lower critical β values than the random graph, indicating that clustered structures amplify the welfare impact. Conversely, higher network density dampens the reduction of defection, suggesting that densely connected societies may require stronger or more targeted welfare measures to suppress betrayal.

Empirical input for the model comes from a modest online survey (≈200 respondents) and a set of environmental estimates used to calibrate initial conditions. This limited data set constrains the external validity of the parameter choices, particularly the initial proportion of cooperators and the realistic magnitude of β. Moreover, reducing the multifaceted nature of welfare policies to a single scalar overlooks distinctions among cash transfers, education subsidies, health benefits, and other components that may affect behavior differently.

Methodologically, the study’s strength lies in its systematic comparison across multiple network topologies, highlighting how structural properties modulate policy effectiveness. However, the model assumes a static, closed network and ignores exogenous shocks such as economic crises or policy revisions, which are common in real societies. The strategy‑update mechanism is a simple probabilistic rule rather than a more sophisticated learning process (e.g., Bayesian updating or reinforcement learning), limiting its ability to capture bounded rationality and heterogeneous risk attitudes.

In conclusion, the paper provides quantitative evidence that higher welfare incentives can substantially increase cooperation and reduce betrayal in simulated social networks, especially when those networks exhibit clustering or community structure. Nonetheless, the findings should be interpreted cautiously due to data limitations, oversimplified welfare representation, and the absence of dynamic network evolution. Future work would benefit from incorporating real‑world social‑connection data (e.g., social‑media or telecom records), disaggregating welfare into multiple policy levers, and allowing nodes to enter or leave the network over time. Such extensions would improve the model’s realism and enhance its usefulness for policymakers seeking to design welfare systems that promote collective cooperation.