Resource Exchange and Link Formation in Decentralized Networks

Abstract

Decentralized sharing systems rely on strategic decisions of the agents, such as how much of their resources to give and to whom. Agents may benefit from creating new connections with other agents, but those additional links may involve costs and future value uncertainty caused by changes of the network in the future or other allocation decisions. We capture these ideas in a model in which agents allocate resources to their active neighbors and may unilaterally strategically create or renew links with costs when it benefits them. The model distinguishes between initial links, which are always available, and newly formed links, which may be permanent or temporary and may lose quality over time. Two allocation rules are considered: an egalitarian strategy, where agents split resources equally among neighbors, and a proportional strategy, where agents allocate more resources to neighbors
from whom they previously received more. Both methods are evaluated using Eisenberg-Gale welfare and Jain’s fairness index. We observe that instead of a classic equilibrium, the systems may enter a recurring cycle of states denoted by allocations and network structure. Moreover, we prove that the egalitarian rule reaches an exact cycle under some assumptions and observe that the proportional rules converge to a cycle, in which the per-period change in allocations falls below a constant.

In simulations on sparse, dense, and small-world graphs, link formation improves fairness, especially in sparse graphs where Jain’s index rises from 0.72 to 0.88. While dense initial graphs already perform well with few additional links, sparse graphs create more links and do not reach a cycle within the simulation horizon as often. Based on strategies, the proportional ones perform better in terms of fairness, and the strategy where the new links are helped by a decreasing function reaches a cycle more often, 81.5% of the time, compared with 51.9% for the simpler proportional rule. Link formation affects welfare unevenly: it raises welfare on initially sparse graphs (Eisenberg–Gale welfare rises from 33.0 to 34.2) but can slightly reduce it on already-dense graphs (35.8 to 35.6), because links degrade and a degraded link carries less throughput.