1

From Network Microeconomics to Network Infrastructure Emergence 

V. Marbukh 

National Institute of Standards and Technology 

100 Bureau Drive, Stop 8920 

Gaithersburg, MD 20899-8920 

marbukh@nist.gov 

Abstract – This paper suggests that evolutionary models of 

network infrastructure in a market economy can be derived from 

the underlying selfish behavior of users and providers of network 

services in the same way as non-equilibrium thermodynamics is 

derived from the underlying statistical physics of interacting 

particles. This approach may be useful for overcoming 

restrictions of existing models failing to account for the effect of 

the details of user/provider selfish behavior on the infrastructure 

evolutionary path. Network security considerations may be a 

part of this user/provider behavior. Our main assumption is 

that “almost perfect competition” keeps the system close to 

the “social optimum”. 

Keywords—network, economics, infrastructure, emergence. 

I. INTRODUCTION 

In a market economy network evolution is driven by 

technological constraints and self-interests of the 

participants. Each user generates demand in attempt to 

maximize its net utility, which is the difference between the 

utility of obtaining service and the service price while each 

service provider attempts to maximize its profit, which is 

the difference between its revenue and expenses. We 

model a network by a capacitated graph with links/nodes 

owned by different providers. The key feature of our 

model is that providers not only can expand/reduce 

network capacity within the infrastructure represented by 

the network graph, but also have the option to modify the 

network infrastructure by adding/eliminating network 

links. While capacity expansion within a fixed 

infrastructure can be done at the marginal cost of the 

resources, growing network infrastructure by adding 

links/nodes requires initial and typically significant 

investment, e.g., for putting fiber underground. 

This initial investment typically destroys convexity 

and causes a multiplicity of Nash equilibrium 

infrastructures in the natural game-theoretic formalization 

of the selfish user/provider behavior, making interpretation 

of this game-theoretic model difficult. This difficulty has 

led to using game-theoretic models of selfish user/provider 

behavior only for fixed network infrastructure when the 

corresponding game typically has a unique Nash 

equilibrium in demand, pricing, investments, and 

capacities. Separate modeling of infrastructure growth 

typically relies on phenomenological random graph models 

[1]-[3]. 

However, accounting for the effect of user/provider 

economic incentives on the network infrastructure 

evolution may be essential. For example, the result of 

selfish investment in the network security [4] can be 

affected if network users and providers have an option of 

disconnecting from providers who create or propagating 

security risk. Another example is selfish investment in the 

bandwidth within existing infrastructure. The inefficiency 

of the competitive equilibrium in the bandwidth pricings 

and offerings [5] may be a result of inefficient network 

infrastructure, which prevents provider competition. In 

both examples provider ability to modify infrastructure 

may significantly affect the emerging network 

infrastructure. 

 This paper suggests that infrastructure evolutionary 

models can be derived from the underlying game-theoretic 

model of selfish user/provider behavior in the same way as 

non-equilibrium thermodynamics is derived from the 

underlying statistical physics of interacting particles. We 

assume time scale separation between “fast” convergence to 

user/provider equilibrium for a given network infrastructure 

and “slow” infrastructure evolution modeled by a Markov 

process. We consider the situation of almost perfect 

competition in which a large number of providers compete 

for demand generated by the same users [6]. Based on 

results from economics [6], as well as results for some 

particular networks [7]-[9], we conjecture that selfish 

user/provider behavior maximizes the aggregate user utility 

subject to provider profitability. 

Exploiting similarities between utility maximization 

and entropy maximization in a closed physical system with 

fixed energy [10], we propose to model the infrastructure 

evolution by a time-reversible Markov process. The 

proposed model includes a possibility of selfish investment 

in network security and is open to various generalizations. 

The paper is organized as follows. Section II discusses 

user/provider competitive and socially optimal equilibria. 

Section III proposes network infrastructure models 

consistent with the underlying selfish user/provider 

interactions. Finally, Section IV briefly summarizes and 

outlines directions of future research. 

II. NETWORK ECONOMIC MODEL 

This Section describes economics driving user/provider 

strategic interactions. Subsection A describes the network 

model. Subsection B describes the bandwidth 

supply/demand model. 

A. Network 

We model the network by a directed capacitated graph 

with set of nodes N and set of links 
2

L {L : n N,k N \ n} = nk ∈ ∈ where links Lnk l ∈ directly 

connect node n to node k . The network infrastructure is 

determined by network graph g = (N,L) and ownership of 

network elements. Let dim{ } nk Lnk s = be the number of 

links directly connecting node n to node k , and Cnk be the 

aggregate capacity of these links. 

Limited link capacities impose constraints on the feasible 

end-to-end throughputs (n,k ) x from nodes n ∈ N to nodes 

k ∈ N \ n

 ∑⊂

= Rnk r

n k r x x ( , ) , (1) 

 ij

r i j r R

Yij xr C

nk

= ∑ ≤ :( , )∈ ⊂

, (2) 

where Ynk is the aggregate rate through links Lnk l ∈ , vector 

x (x ,r R) = r ∈ characterizes end-to-end flow rates on all 

feasible routes Un k

R Rnk , = , and the set of feasible routes 

from node n∈ N to node k ∈ N \ n is Rnk . 

For simplicity of exposition we assume that all links 

Lnk l ∈ directly connecting node n to node k are identical 

with respect to their capacities: l nk nk c = C s and carried 

load: l nk nk y = Y s . In our economic model these 

assumptions are justifiable when the cost of providing 

bandwidth c , is the same (c) φnk , for all links Lnk l ∈ . In 

this case bandwidth providers are inclined to charge the same 

price for bandwidth pnk on all links Lnk l ∈ and users are 

indifferent to using links Lnk l ∈ [8]-[9]. Generalization to a 

case when the cost of providing bandwidth on different links 

Lnk l ∈ may be different is straightforward. 

We assume that bandwidth costs (c) φnk are nondecreasing in c ≥ 0 . Communication bandwidth costs 

φnk (c); n∈ N,k ∈ N \ n are concave in c ≥ 0 , e.g., 

 φnk (c) = ank + bnk c, n∈ N,k ∈ N \ n (3) 

where ank ≥ 0 characterizes the fixed cost, e.g., cost of 

putting the fiber underground and bnk ≥ 0 characterizes the 

marginal capacity cost. 

Our model can be easily generalized to incorporate 

constraints imposed by limited node processing capacity 

Cnn , n∈ N . It is natural to assume that costs of the 

processing bandwidths φnn (C),n∈ N are convex in C ≥ 0

due to technological constraints. For example, considered in 

[11] is the case of hard processing bandwidth constraints 

* Cnn ≤ C corresponding to processing cost φnn (C) = 0 if 

* C ≤ C , and φnn (C) = ∞ if * C > C . In this paper we 

uniformly refer to network nodes and links as network 

elements. 

B. Bandwidth Users and Providers 

We model the effect of investment in the network security 

by assuming that traffic of rate x traversing network element 

l faces security risk xh (q) l , where q (q ,l L) = l ∈ is the 

vector of levels of investment in the security of network 

elements l is. We assume functions h (q) l to be decreasing 

in all vector q components due to positive externalities, i.e., 

improving security of a network element not only improves 

this element security; but also is beneficial for the security of 

the entire network [4]. 

Assuming that the owner of a network element l

charges users price pl for a unit of this element's 

bandwidth, the profit generated by network element l is 

 ( ) ( ) :

ll l

r l r

l l l r f = p − q ∑x −φ c ∈

 (4) 

Generally, there are S service providers, with service 

provider s ∈ S owning network elements Ms l ∈ . Each 

network element is owned by some provider: M L s S s ≡ U ∈ . 

Each provider s ∈ S attempts to maximize its aggregate profit 

 ∑∈

= M s l

s l F f (5) 

We assume that each user is uniquely identified by the 

origin-destination pair (n,k),n∈ N,k ∈ N \ n . Let 

u (x) nk be user (n,k) ’s utility of obtaining end-to-end 

bandwidth x from node n to node k . Utility functions 

u (x) nk are assumed to be monotonously increasing and 

concave in x ≥ 0 at least in the case of file transfers. For 

example, weighted (α,w) - fair bandwidth allocation [12] is 

based on user utilities 

 

⎩

⎨

⎧

=

− ≠ =

−

ln 1

(1 ) 1 ( , )

1

α

α α

α

α

w x if

wx if

u x w (6) 

where α,w > 0 are some parameters. In a particular case of 

proportional fairness, when α =1, parameters w = wnk can 

be interpreted as user (n,k) ’s willingness to pay for end-toend bandwidth x from node n to node k . 

User (n,k) net utility is its gross utility of having end-toend bandwidth minus expenses and expected losses due to 

security risks: 

 ∑ ∑ ∑[ ] ∈ ∈ ∈

− + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ =

nk Rnk r r l

r l nk l

r R

Unk unk xr x p η h (q) (7) 
3

where parameter ηnk ≥ 0 quantifies user (n,k) ’s sensitivity 

to the security risk. Each user (n,k) attempts to maximize 

its net utility (7) over the vector of flow rates ( , ) r Rst x r ∈ , 

given security risks h (h ,l L) = l ∈ and prices 

p ( p ,l L) = l ∈ . 

III. USER/PROVIDER EQUILIBRIA 

This Section introduces notions of user/provider 

equilibria. Subsection A describes user/provider best 

responses. Subsection B discusses multiplicity of the 

competitive (Nash) equilibria of the user/provider game. 

Subsection C conjectures that under perfect competition 

these competitive equilibria approach the social optimum. 

A. User/Provider Best Responses 

It is easy to see that user net utility (7) maximization 

results in minimum cost routing where the adjusted cost of 

a route is the sum of the adjusted costs of network elements 

comprising the route 

 ∑∈

=

l r

dr dl (η) (η) (8) 

and network element l adjusted cost is 

 d ( ) p h (q) l η = l −η l (9) 

Assuming sufficient capacity, the entire user (n,k)

aggregate demand 

 x [u x d x] nk nk x nk

*

0

*

( ) = argmax ( ) − ≥

 (10) 

is sent over minimum cost routes 

{ : , } * *

nk r nk Rnk R = r d = d r ∈ , where 

 min ( ) *

r nk r R

dnk d

nk

η ∈ = (11) 

Users are indifferent between feasible routes of minimum cost. 

If there is a single minimum cost route: * *

nk nk R = r , the entire 

user (n,k) demand is carried on this route: 

 

⎩

⎨

⎧ = = otherwise

x if r r

x nk nk

r 0

* *

* (12) 

In the particular case of user utilities (6): 

( ) ( , ) nk nk wnk u x = u xα , user (n,k) aggregate demand is 

 ( ) st

nk nk nk x w d 1 α * *

( ) = (13) 

Further we assume that users always generate the best 

response demand, and thus element l generates profit 

⎥

⎦

⎤ ⎢

⎣

⎡ = ∑ − − ∑ ∈ r l∈r

l l r

r l r

fl p q pl xr p q q x p q :

*

:

* * ( , ) ( , ) φ ( , ) (14) 

Expression (14) implies that the optimal provider responses 

ensure tightness of the capacity constraints (2). Indeed, 

providers have incentive to eliminate any spare capacity to 

reduce expenses while in a case of insufficient capacity the 

provider can increase its revenue by raising the price. 

B. Competitive Equilibria 

Consider a non-cooperative game of providers s ∈ S

attempting to maximize their profits 

 ∑∈

= M s l

s l F ( p,q) f ( p,q) * * (15) 

over pricing pl , and investment in security ql of their assets 

Ms l ∈ , where ( , ) * fl p q are given by (14). Typically, this 

game has multiple Nash equilibria corresponding to different 

network infrastructures defined by a combination of network 

topology and ownership of network elements. These Nash 

equilibria are associated with attractors of the following 

evolutionary/learning provider adjustments [13]: 

l s l l s l Ms q = ∂F (q, p) ∂q , p = ∂F (q, p) ∂p l ∈ * * & & (16) 

Note that since best user response (8)-(12) ( , ) * x = x q p is 

discontinuous in a case of equal minimum cost multipath 

routing, the differential equations (16) may have 

discontinuous right-hand sides. It can be shown that in this 

case system (16) should be understood as a differential 

inclusion [14] describing sliding modes along the 

discontinuity hyperplanes. 

Bertrand's model of user/provider equilibria [9], [15] 

assumes that in "fast" time users/providers achieve 

equilibrium over user demands x (x ,r R) = r ∈ , 

bandwidth pricing ( ) p = pl and investment in security 

( ) q = ql subject to the capacity constraints (2) for fixed 

capacities ( )l c = c . On a "slow" time scale bandwidth 

pricing and investment in security become functions of the 

network element capacities: ( ) * p = p c and ( ) * q q c l = . 

Nash equilibrium capacities * c = c are associated with 

attractors of the following bandwidth adjustments [9]: 

 cl = ∂Fs [q (c), p (c)] ∂cl l ∈ Ms, s ∈ S * * * & (17) 

 Figure 1 demonstrates multiplicity of provider equilibria 

achieved by adjustment process (17) on an example of two 

providers competing for the same demand [9]. 

Fig. 1. Capacity adjustments by two competing providers. 

C1

C2
4

Three equilibria are possible: one equilibrium with both 

providers supplying bandwidth and two equilibria with only 

one provider supplying bandwidth and another provider driven 

out of business. 

C. Perfect Competition: Social Optimum 

In competitive equilibrium providers ensure profitability 

by charging users a competitive price which is higher than the 

marginal bandwidth price. It is known from economics [6] 

that as the number of providers competing for the same 

demand increases, the competitive prices drop approaching the 

corresponding marginal prices. This increase in competition 

squeezes the provider profit margins but increases user net 

utilities as shown in Figures 2 and 3 respectively for N

parallel links competing for demand generated by the same 

users [8]-[9]. 

Fig. 2. Provider profit vs. number of competing providers N

 

Fig. 3. User net utility vs. number of competing providers N

One may expect that in the limit of perfect competition 

with a large number of providers competing for the same users 

the competitive equilibria will approach a social optima which 

maximizes the aggregate user utility 

 max ( , , )

( , , )

U x p q x p q

Σ (18) 

 Σ = ∑

( , )

( , , ) ( , , ) n kU x p q Unk x p q (19) 

subject to provider profitability 

 ( ) 0 : :

⎥ ≥

⎦

⎤ ⎢

⎣

⎡ ⎟

⎠

⎞ ⎜

⎝

⎛ = ∑ ∑ − ∑ − l r ∈ ∈ M s ∈ r l

l r

r l r

M l l r F p q x φ x (20) 

Note that for bandwidth cost function (3) constraints (20) take 

the following form: 

 ( ) 0 :

≤⎥

⎦

⎤ ⎢

⎣

⎡ ∑ ∑ + + − ∈ ∈ M s l r r l

l l l l r a b q p x (21) 

It is easy to see that due to the assumed concavity of the 

communication bandwidth costs φnk (c); n∈ N,k ∈ N \ n , 

at a social optimum (18)-(20) no more than one link nk l = l

connects node n∈ N to node k ∈ N \ n . This observation 

allows us to assume in (18)-(20) that at most one link nk l = l

connects a node n∈ N to a node k ∈ N \ n . However, it 

poses a fundamental question since the social optimization 

(18)-(20) views system performance from the user perspective, 

assuming that providers only recover their expenses without 

making any profit, and this may occur only close to perfect 

competition with a large number of providers competing for 

demand generated by the same users [6]. The rest of this 

Subsection qualitatively demonstrates that low barriers to 

entering the market are necessary for this situation to occur and 

for the optimization problem (18)-(20) to approximate the 

competitive equilibria. 

Consider N providers competing for the same demand 

generated by a user with utility function u(x) = wlog x

disregarding network security (η = 0) . Each provider 

charges the user a competitive price p xN for bandwidth x , 

while the provider’s own expense for supplying this bandwidth 

is a + bx . Since the user’s individual optimization results in 

demand w pN x = equally divided among all N providers, 

the provider profitability condition pN x N > a + b x N

takes the form ( )(1 ) N < w a − b pN . Since pN ↑ b as 

N ↑ ∞ (see [9]), the profitability condition imposes an upper 

bound on the number of competing providers * N < N . 

Optimization problem (18)-(20) implies a large number of 

providers * N driving provider profit down to zero, and it is 

easy to see that in our simple case this can occur only if the 

barrier for a provider to enter the market a is much less than 

user willingness to pay w : a << w . It can be shown that this 

qualitative conclusion holds for general topology networks. 

IV. INFRASTRUCTURE MODELS

Given set of network nodes N , we characterize 

network infrastructure by a binary vector 

( : l (n,k),n N,k N \ n) δ = δ l = ∈ ∈ , where δ nk =1 if 

directed link nk l = l from node n to node k exists and 

δ nk = 0 otherwise. This Section proposes equilibrium and 

evolutionary models for δ = δ (t) under assumptions that 

“almost perfect” competition keeps the network infrastructure 
5

close to socially optimal. The proposed models are based on 

the underlying economic model of user/provider interactions. 

Subsection A introduces infrastructure social utility ( ) * W δ , 

which is the result of maximization of the social welfare over 

bandwidth demand/supply for a given vector δ . Subsection B 

suggests an entropy-based equilibrium model for vector δ

with ( ) * W δ playing the role of the negative energy. 

Subsection C suggests an approximation of infrastructure 

evolution by a time-reversible Markov process δ = δ (t) used 

in physics to describe evolution of interacting spins. 

A. Infrastructure Utility 

Optimization problem (18)-(20) is non-convex due to the 

assumed concavity of the communication bandwidth cost 

functions φnk (c); n∈ N,k ∈ N \ n . It is known that this 

non-convexity leads to multiple local maxima of the aggregate 

utility (19). However, given the vector (x) ( (x)) δ = δ l , 

 

⎪⎩

⎪

⎨

⎧ > = ∑∈

otherwise

if x

x r l r

r

l

0

1 0

δ ( ) : , (22) 

describing network infrastructure, the aggregate utility 

maximization (18)-(20) typically becomes a convex 

optimization problem. The corresponding maximal aggregate 

utility is a function of vector δ (x) = δ : ( ) * UΣ δ assuming 

that infrastructure δ (x) = δ can support provider 

profitability (20). It is natural to interpret ( ) * UΣ δ as the social 

utility of infrastructure δ . Of course actual evaluation of 

( ) * UΣ δ is computationally infeasible, and in the rest of this 

subsection we briefly discuss some approximations. 

 Consider the Lagrangian of the optimization problem 

(18)-(20) 

 ∑ ∑ ∑ ∈ ∈ ∈

Σ ⎥

⎦

⎤ ⎢

⎣

⎡ ⎟

⎠

⎞ ⎜

⎝

⎛ = − − − M s l r r l

l r

r l r

M l l r W U p q x x : :

γ ( ) φ (23) 

where ( p,q) M M γ = γ are the Lagrange multipliers solving 

the corresponding dual problem. Let ( ) * W δ be the 

maximum of function (23) over ( p,q, x) for a given vector 

δ . Due to non-convexity, solutions to the primal (18)-(20) 

and the corresponding dual problems may differ, and thus 

U −W ≠ const Σ ( ) ( ) * * δ δ (utilities are defined up to additive 

constant). Nevertheless, the function ( ) * W δ can be viewed as 

an approximation of the infrastructure utility. The 

computational advantage of the function ( ) * W δ over 

( ) * UΣ δ is that to evaluate ( ) * W δ one has to solve only one 

optimization problem rather than solve an optimization 

problem for each vector δ to evaluate function ( ) * UΣ δ . 

 In a case of low barriers to entering the market, further 

simplification is possible since (23) can be approximated by 

the difference between the aggregate user utility (18) and 

aggregate provider expenses: 

 ∑ ∑ ⎥

⎦

⎤ ⎢

⎣

⎡ ⎟

⎠

⎞ ⎜

⎝

⎛ = − + ∈

Σ

l r r l

l l r W x q U x q q x :

( , ) ( , ) φ (24) 

In a case of bandwidth cost function (3) social welfare (24) 

takes the following form: 

∑ ∑∑ ∑

∑ ∑

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡ −⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+⎥

⎦

⎤ ⎢

⎣

⎡ = − + +

∈ ∈ ∈

= ∈

( ) , ) ( ) (

: : 1

( )

( , , ) ( )

n R k r r l

nk r l

r R

nk r

l r r l

l l l r

nk nk

l

u x x h q

W q x a b q x

δ δ

δ

η

δ

 (25) 

where the set of available routes from node n∈ N to node 

k ∈ N \ n conditioned on infrastructure δ is 

 I ⎭

⎬

⎫

⎩

⎨

⎧ = ∏ = ∈

( ) : 1

l r

nk nk l R δ R r δ . (26) 

Define the social utility of infrastructure δ to be the 

maximum value of social welfare (20) achievable for this 

infrastructure: 

 ( ) max ( , , ) ,

* W W q x

q x

δ = δ (27) 

Infrastructure utility (25) can be evaluated effectively and even 

explicitly under realistic assumptions. Due to limited space we 

only note that in a case of network security insensitive users 

( = 0) ηnk with utilities u x w x nk nk ( ) = log the 

infrastructure utility (25) is 

 

∑∑ ∑

∑ ∑

= ∈ ∈ ∈

∈ ∈

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡ ⎟

⎠

⎞ ⎜

⎝

⎛ − +

⎟ −

⎠

⎞ ⎜

⎝

⎛ =

: 1 ( , ): ( ) ( )

( , ) ( )

*

*

min

( ) log min

l nk

nk

nk

l n k l r l r

l r R l l nk

n r k l

l r R nk

a b w b

W w b

δ δ δ

δ

δ

 (28) 

where user (n,k) optimal route is 

 ∑∈ ∈ = l r

l r R

rnk b nk ( )

* ( ) arg min

δ

δ (29) 

B. Equilibrium Infrastructure 

We model unavoidable uncertainties present in large 

networks by assuming that vector δ is a binary random 

variable with some probability distribution Ω(δ ) and entropy 

 = −∑ Ω Ω δ H (δ )log[ (δ )] (30) 

Social optimization either maximizes the infrastructure 

expected social utility 

 = ∑ Ω δ (δ ) (δ ) * * W W (31) 

subject to low bound on entropy (30) or, equivalently, 

maximizes entropy (30) subject to low bound on the expected 

infrastructure utility (31). 
6

Solution to these dual optimization problems is 

 * 1 ( ) *

( ) β δ δ W Z e − Ω = (32) 

where the parameter β > 0 is determined by the 

corresponding optimization constraint and Z is the 

normalization constant. As uncertainty decreases: H → 0 or 

equivalently β → ∞ , the distribution (32) recovers the 

optimal network infrastructure. Similar to approach [2] we 

define an equilibrium graph distribution by the entropy 

maximization procedure. The difference is that in our case the 

graph energy ( ) ( ) * E δ = −W δ is derived from user/provider 

microeconomics. This opens a possibility of exploring the 

effect of microeconomics, including network security 

considerations, on the network infrastructure emergence. 

C. Infrastructure Emergence 

We assume that competitive pressures may result in 

elimination of some network elements 

:( =1) → ( = 0) l l l δ δ due to un-profitability and/or adding 

some network elements :( = 0) → ( =1) l l l δ δ due to 

potential profit. Let vector l δ be the result of flipping 

component l δ l :δ l →1− δ in vector δ , i.e., infrastructure 

described by vector l δ contains (does not contain) link l if the 

infrastructure described by vector δ does not contain 

(contains) link l . Otherwise vectors l δ and δ are identical. 

Viewing vector ( ) δ = δ l as a system of interacting 

spins with energy ( ) ( ) * E δ = −W δ , we model infrastructure 

evolution by a Markov process (t) ( (t)) δ = δ l , with 

continuous time t ∈[0,∞) and transitions l δ →δ with 

rates ( , ) exp[ ( )] * μ l δ = Δl

W δ , where the infrastructure 

utility change due to this transition is 

( ) ( ) ( ) * * * W δ W δ W δ l Δl = − [16]. Process δ (t) is time 

reversible and satisfies conditions of detailed balance. This 

Markov evolutionary model is consistent with the entropybased equilibrium model (32) since the process δ (t)

distribution converges to distribution (32) as t → ∞ . 

Moreover, process δ (t) ’s relative entropy 

∑ Ω Ω Ω δ ( ,δ )log[ ( ,δ ) (δ )] * t t , where 

Ω(t,δ ) = Pr{δ (t) = δ}, monotonously decreases with time. 

 Process δ (t) , which describes infrastructure drift 

towards infrastructure utility increase perturbed by random 

fluctuations, can provide a foundation for phenomenological 

models of network growth. Connecting a new node n to the 

network can be viewed as creating link l from node n to 

some already connected to the network node k ∈ N : 

( = 0) → ( =1) δ l δ l . The corresponding change in the 

infrastructure utility ( ) * Δl

W δ weights the benefit of 

connectivity to a specific node against cost of this connection. 

It can be shown that, after some simplifying assumptions, 

network growth based on infrastructure utility gain ( ) * Δl

W δ

takes the form of “heuristically optimized” [3]. 

V. CONCLUSION AND FUTURE RESEARCH

Assuming that the network infrastructure is represented by 

the network graph and ownership, this paper suggests that 

network infrastructure modeling should be based on the 

network microeconomics. The paper argues that 

methodologies used in transitions from statistical physics of a 

large number of interacting particles to thermodynamics of a 

small number of macro-variables may prove applicable to the 

networking domain. The proposed approach assumes that 

“almost perfect competition” keeps the system close to social 

optimum, which maximizes the aggregate user utility subject 

to provider profitability. Future research will be concentrated 

on demonstrating the practical validity of the proposed 

approach and extending this approach to competitive 

user/provider equilibria far from perfect competition. 

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