An Individual View An Individual View on Cooperation Networkson Cooperation Networks

Institute of Information SystemsJ. W. Goethe University, Frankfurt

http://www.is-frankfurt.de

Tim Weitzel, Daniel Beimborn, Wolfgang König

Equilibria in Networks

Simulation Model

Results and Further Research

Equilibria in Networks

Simulation Model

Results and Further Research

Equilibria in NetworksEquilibria in Networks

network benefits

synergies, network effects …

example: EDI

but…

coordination problems (multiple equilibria)

example: EDI

equilibrium analysis

existence and efficiency of equilibria (where, and how to get there?)

evaluation of solution mechanisms (centralized, decentralized)

theoretical foundation and literaturetheoretical foundation and literature

Coordination problems (network effects as externality):

multiple equilibria, path dependencies [Arthur 1983; 1989; 1996] [David 1985] [Liebowitz/Margolis 1998]

market failure (discrepancy private and collective gains)[Kindleberger 1983; Farrell/Saloner 1986]

excess inertia [Katz/Shapiro 1985; 1986]

tippy networks, monopoly [Besen/Farrell 1994] [Shapiro/Varian 1998]

increasing returns multiple equilibria

which one will and should be achieved

as individual agent? as entire network (owner or other aggregate entity)?

Equilibrium conceptsEquilibrium concepts

Pareto efficiency:

an equilibrium is called Pareto-efficient if no one can be made better off without at least someone being worse off

in neo-classical economics, markets move towards Pareto efficiency

Kaldor-Hicks efficiency:

in networks, there are multiple Pareto-efficient equilibria. The Kaldor-Hicks criterion describes a preference order for Pareto-efficient equilibria

an equilibrium is called Kaldor-Hicks-efficient when changing towards it from the present state, the gainers could compensate the losers and still be better off

equilibriaequilibria

player 2

player 1 s21 s22

s11 (3,4) (2,3)

s12 (1,2) (5,3)

game has two Nash equilibria: (s11,s21) and (s12,s22)

both are Pareto-efficient

only (s12,s22) is Kaldor-Hicks efficient

Equilibria in Networks

Results and Further Research

Simulation Model

ModelModel

network participation as trade-off between

network participation costs (technology adoption, customizing, converters, etc.)

and benefits (direct network effects, cost savings due to a deeper integration with business partners, reduced friction costs)

Example: EDI network, electronic marketplace, iMode services

ModelModel

Idealistic network engineering by centralized coordination

omniscient central planner seeks overall optimum no agency costs “monolithic” decisions, collective objective function

vs.

realistic networks by decentralized coordination

autonomous agents embedded in individual network neighborhood opportunistic behavior individual information sets

Individual benefits Ei (ex post) Individual benefits Ei (ex ante)

Network-wide (centralized) savings

Centralized solution

simulation modelsimulation model

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s.t.

2 ijji yxx jinji ;, 1 iji yx 1 ijj yx jinji ;,

0ijy 1ijy jinji ;, 0ix 1ix ni

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individual consequencesindividual consequences(mostly no side payments necessary)(mostly no side payments necessary)

individual consequencesindividual consequences(magnified)(magnified)

findingsfindings

efficiency gap

centralized control: scarce cases of agents that are forced to participate against their will (or that would require compensations ex post in a decentralized context)

not only the whole network but also the vast majority of individuals are better off getting the optimal solution from a central principal

consequence: substantial number of “win-win” situations: if there are no Ei(z) < 0 centralized solution is Pareto-superior to decentralized

Equilibria in Networks

Results and Further Research

Simulation Model

Main resultsMain results

two cases of network inefficiency:

1. either agents wrongly anticipated their environments' actions

reducing uncertainty is in principal sufficient, i.e. designs aimed at enhancing the "information quality" (i.e. to solve the renowned start-up problem).

2. or some agents that should join a network from a central perspective are individually worse off doing so

some form of redistribution needs to be established

substantial fraction of first case promising concerning “severity” of network coordination problems: cheap talk (information intermediation) often does it!

future extensions:

network topology, density

negative effects and other dependencies

detailsdetails

appendixappendix

Externality

an externality is considered to be present whenever the utility function Ui(.) of some economic agent i includes real variables whose values are chosen by another economic agent j without particular attention to the welfare effect on i’s utility

Pareto efficiency:

an equilibrium is called Pareto-efficient if no one can be made better off without at least someone being worse off.

formally: an allocation x is considered to be Pareto-optimal if and only if no other allocation y exists which is weakly preferred over x by all individuals and strongly preferred by at least one individual

Standardisierungsmodell (Grundlagen)Standardisierungsmodell (Grundlagen) Agent i (i{1,...,n}) entscheidet über Nutzung des Standards q Standardisierungskosten Kiq vs. Standardisierungserlöse cij methodischer Vergleichsrahmen für institutionelle Mechanismen: Zentrale

(globale) vs. dezentrale (lokale) Koordination

1K1=10

2K2=20

c12 = 9

c21 = 30

1K1=10

2K2=20

c12 = 30

c21 = 30

Dezentra les Entscheidungskalkül

Zentra le (benchm ark) solution

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Kostenanteex

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default network consists of 35 agents corresponding to 630 variables and 2,415 restrictions

normally distributed costs and network effects

analogous results for other network sizes (e.g. n = 1,000) and distributions

50 repetitions per parameter constellation figure results from 4,500 simulation runs

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expected individ. utility (ex ante)

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costs anteex

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network-wide savings

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centralized objective function

Einige ErgebnisseEinige Ergebnisse

Netzwerksimulationen

Standardisierungsnutzen(Netzeffekte)(C) = 1000 (C) = 200

Standardisierungskosten(K) = 1000 (K) = var.

Netzgröße n = 35

Zeithorizont T = 35

Netzdichte V = var.

Netztopologie = var.

Installed Base B = var.

Anzahl Standards Q = 4

Die StandardisierungslückeDie Standardisierungslücke(einfaches Modell)(einfaches Modell)

-200000

0

200000

400000

600000

800000

1000000

1200000

1400000

050001000015000200002500030000350004000045000

GE

GE(z) GE(dz)

FehlentscheidungenFehlentscheidungen

0

0,1

0,2

0,3

0,4

0,5

140001500016000170001800019000

(K)

f

fpos

fneg

FehlentscheidungenFehlentscheidungen

1900

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1850

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1800

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1750

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1700

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f(t=3)

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(K)

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ModelModel

challenge: synchronize individual and aggregate objective functions

classic solution: profit sharing or a network ROI guaranteeing each participating agent “fair” returns on their participation costs

rests upon the assumption that

1. there are sufficient network gains to be redistributed

2. redistribution design can actually be developed to ensure e.g. positive ROI

In economic equilibrium analysis 1) implies that eventual allocation is Kaldor-Hicks-superior to the former and 2) that it is Pareto-superior.