Distribution Concepts Under Duplicated Structure

In the context of standard states, contributors are typically either fully engaged or not engaged at all under interactions with other contributors. However, in real-world situations, contributors may exhibit varying degrees of involvement and operational capacities. Additionally, related influence may differ across various situations. Therefore, this paper introduces distribution concepts utilizing duplicated structures and weights to address these complexities. To examine the mathematical precision and practical applicability of these distribution concepts, we introduce a specific reduction and its analogues, which provide axiomatic characterizations and dynamic processes.