The multilayer garbage disposal game extends the classical garbage disposal game to multilayer social networks. Each layer represents a distinct type of social relationship among a fixed set of individuals. At each time step, agents redistribute a quantity called "garbage" by averaging their current amount and offloading equal proportions to their neighbors in each layer. The game models a decentralized and non-strategic system: agents act uniformly across time and layers without strategic optimization.

We analyze this model from a mathematical rather than game-theoretic perspective. Our focus is on the case where all agents follow the same averaging rule across connected social graphs, each with at least three nodes. Under these conditions, we prove that the amount of garbage held by each agent in each layer converges to the initial global average—defined as the average garbage across all agents and layers at time zero.

This convergence result reveals that simple local averaging and redistribution mechanisms can produce stable and predictable outcomes in decentralized, multilayer settings. Furthermore, agents whose initial total garbage exceeds the global average retain a long-term advantage, highlighting the role of initial conditions in shaping persistent disparities.

This model offers a framework for studying how information, influence, or other transferable quantities spread and stabilize across overlapping social structures. It opens the door to further investigations into how network topology, redistribution rules, or initial heterogeneity affect long-term system behavior.

Authors:
Hsin-Lun Li, National Sun Yat-sen University, Taiwan

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Posted by James Alexander Gordon

Last updated: 2023-02-23 23:45:00

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