New paper proves circular networks are optimal for shared cost information sharing

In a new arXiv preprint, computer scientists Juan M.C. Larrosa and Fernando Tohmé (Universidad Nacional del Sur, Argentina) develop a noncooperative model of directed network formation where agents create links to access valuable information while sharing the costs generated along the paths through which information is obtained. Each agent has a positive amount of information and simultaneously chooses which other agents to contact. A directed link initiated by one agent allows her to access the information of the contacted agent and that agent's reachable network, but each link in the resulting information path incurs a unit cost. Payoffs depend on the total value of accessible information net of accumulated connection costs.

The central result is that strict Nash equilibria must take the form of circular directed networks — a directed cycle where every agent is connected in a loop. Moreover, these circular networks are exactly the Nash networks that use the minimum number of links while allowing every agent to access all available information. Although noncircular weak Nash networks may exist, they are structurally redundant and do not satisfy the same minimality property. The model also shows that strict Nash networks are both Pareto optimal and efficient in terms of aggregate welfare, meaning no agent can be made better off without another being made worse off, and total payoffs are maximized.

The paper compares this framework with the influential Bala & Goyal (2000) model, emphasizing that shared path costs and heterogeneous information values generate different equilibrium implications. While Bala & Goyal's model allowed for stars and other structures under certain cost regimes, Larrosa & Tohmé's sharing of costs along paths forces the emergence of circles. The analysis supports the equivalence between strict stability (no unilateral deviations) and minimal connectivity in directed information networks — a finding with practical implications for designing efficient peer-to-peer systems, communication protocols, and decentralized information networks where users share transmission costs.