PPubMed15 Sep 2016Cited 4×

Economic returns in forming stable R&D networks

Mohamad Alghamdi

Abstract

The aim of this paper is to study the individual and social benefits behind constructing stable R&D networks. We find that the equilibrium outcomes of a stable network are related to the number of competitors. As they increase, the individual outcomes and the total welfare decrease. This implies that in the individual and social perspectives, small stable networks are more desirable than the large ones. Furthermore, when comparing the stability of the components of a network with a complete network, we conclude two main observations. The first observation shows that the stability of the components of a network does not necessarily guarantee a stable overall network. The second observation suggests that firms prefer to be part of a complete network rather than part of a stable component of a network. This preference depends on the profit of firms where it is maximized when firms are belong to the complete network.

A figure from Economic returns in forming stable R&D networks — fig. from the paper

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In stable R&D networks, larger size lowers firm profits and total welfare, making small networks more beneficial.

What’s new

i.Theoretical analysis of how network size affects economic returns in stable R&D networks
ii.Proof that individual outcomes and total welfare decrease as the stable network grows
iii.Demonstration that stability of network components does not guarantee overall network stability
iv.Identification that firms prefer complete networks over stable components when profits are maximized
v.Derivation of profit, consumer surplus, and welfare trends for complete versus empty networks

How they did it

The authors built a theoretical model based on the Goyal‑Moraga‑Gonzalez linear‑quadratic Cournot framework with homogeneous goods. They derived equilibrium expressions for R&D effort, output, profit, consumer surplus and total welfare, and analytically examined how these outcomes change with the number of firms (network size). Proofs and propositions were used to establish monotonic relationships and compare complete and empty networks.

What they found

Proposition 1: R&D effort, quantity and profit are monotonically decreasing functions of network size n (shown for a=2, c̄=1, γ=1, n=3‑30)
Proposition 2: The profit gap between complete (Kₙ) and empty (Eₙ) networks shrinks as n increases
Proposition 3: Industry profit and total welfare fall with larger n, while consumer surplus rises (a=2, c̄=1, γ=1)
Corollary 2: As n→∞, firm profit approaches a very small positive value δ
Figures 1‑3 illustrate the declining profit, effort and quantity and the rising consumer surplus as n grows from 3 to 30

Caveats

✕The analysis assumes homogeneous goods and a linear‑quadratic utility function, limiting applicability to heterogeneous product markets
✕Link formation costs are assumed negligible, ignoring real‑world transaction costs
✕The study is purely theoretical with no empirical validation of the model predictions
✕Only complete and empty network structures are examined, not more complex or dynamic network formations

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