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Introduction Model Analysis Summary On interdisciplinarity

Globalization and Social Networks

Georg Durnecker Fernando Vega-Redondo

University of Mannheim European University Institute

September 14, 2012

Duernecker & Vega-R. (Mannheim & EUI) Globalization and Social Networks September 14, 2012 1 / 20


Motivation

Globalization, a distinct (economic) phenomenon of our times

What is globalization? From a social network viewpoint:

short distances on the social network (a “small world”)long -range links supporting far-away interaction

Why is it important?

local opportunities become soon exhaustedhence expansion requires turning global: need for fresh opportunitiesthe social network (key support for exploration & exploitation of neweconomic opportunities) must also turn global!

Some of the questions addressed by the model:

How & when such globalization happens?What is the role of geography?Is it a robust/irreversible phemomenon?Is there a role for policy?



Related literatureEmpirical

Different specific measures on globalization:trade: Dollar & Kray (2001), Kali & Reyes (2007), Fagiolo et al (2010)direct investment: Borensztein et al (1998)porfolio holdings: Lane and Milesi-Ferreti (2001)

Integrated (multidimensional) measures: Dreher et al (2006)

TheoreticalDixit (2003):

agents located along a ring, play a repeated Prisoner’s Dilemmaopportunities improve with distance but observability deterioratesexternal enforcement is needed – it only pays if economy is large

Tabellini (2008):same spatial setup as Dixit’s, with altruism (decaying with distance)social evolution of preferences a la Bisin-Verdier (2001)preferences evolve, possibly reinforcing cooperation

� Both anchor enforceability or altruism to (fixed) geography/space

� Here, to endogenous network (formation depends on network+space)



Outline

1 The model

Basic frameworkDynamics: innovation and volatilityGame-theoretic microfoundation

2 The analysis

Some illustrative simulationsBenchmark theory (large-population limit)General theory (finite population)

3 Summary and conclusions



Basic framework

Finite (large) population N, placed along a ring in fixed position

Continuous t ≥ 0, state is the social network g(t) = {{i , j} ⊂ N}each link ij ∈ g(t), an ongoing valuable projectthe link eventually becomes obsolete and vanishes



Law of motion: innovation and volatility

Innovation (link creation)At each t, every agent i gets an idea at rate η to collaborate withsome other j . Such j is selected with probability pij ∝ 1

[d(i ,j)]α .

The link ij is actually formed if(1) it is not already in place(2) agents i & j are close either

geographically: d(i , j) ≤ ν(= 1),socially: δg(t)(i , j) ≤ µ, µ ∈ N

Volatility (link destruction)At each t, every existing link ij ∈ g(t) vanishes at rate λ(= 1).

parametersη: rate of “invention” (arrival of new ideas)α: “cohesion” (parametrizes importance of geography)µ: “institutions” (efficacy of social network in supporting cooperation)



A game-theoretic microfoundation – outline

A link is conceived as a repeated partnership with two phases:

1 The setup stage: a Prisoner’s Dilemma to cover setup coststhe project starts only if at least one agent“cooperates”

2 The operating phase: repeated coordination gamehigh- and low-effort equilibria – partnership ends at rate λ.

The population game can be played under two norms/equilibria:

Bilaterally independent: cooperation in PD supported bilaterally

Network-embedded: idem supported by third party punishment,when the social distance from the latter to deviator no higher than µ.

The N-embedded norm induces, at equilibrium, postulated law of motion(assume neighbors’ setup costs are lower and can be bilaterally supported)



A first appetizer: simulating a low cohesion scenario

α  = 0.5 µ = 3 n =1000



A second appetizer: simulating a high cohesion scenario

α  = 2 µ  = 3

n =1000



Benchmark large-population theory (I):steady state condition

Given a steady state, let φ be the conditional linking probability of arandomly selected node and let z denote the average degree

Steady State Condition (SSC):

φ η n = λz

2n

Assume family steady-state (random) networks can be parametrized by z .

Then, given the parameters of the model (η, µ, and λ(= 1)) we can makeφ = Φ(z) and write the SSC as

Φ(z) η =1

2z

which induces an equation to be solved in z .



Benchmark theory (II): Two cohesion-related scenarios

Depending on the value of α, two scenarios:

Low Geographical Cohesion (LGC): α ≤ 1

High Geographical Cohesion (HGC): α > 1

Key contrast: whether, as n→∞, the space-decaying probability ofselecting any finite set of nodes is zero (LGC) or positive (HGC).It all hinges upon whether

limn→∞

(n−1)/2∑d=1

1

dα= lim

n→∞ζ(α, n) = ζ(α)

is infinite (LGC, α ≤ 1) or finite (HGC, α > 1).



Benchmark theory (III): large-population assumptions

Maintained hypothesis:Steady states can be represented as random networks for large populations.

Then, building upon the theory of random networks, the followingassumptions can be made on the function Φ(z) by taking limit n→∞on counterpart properties applying for finite populations:

A1 Let α ≤ 1. Then, ∃z > 0 s.t. for all z ≤ z , Φ(z) = 0.

A2 Let α > 1. Then, Φ(0) = [ζ(α)]−1 > 0.

Also, we make some regularity assumptions (differentiability, monotonicity)on the function Φ(z)



Benchmark theory (IV): results

We posit the dynamical system:

z = ηΦ(z ; α)− z

2Proposition 1

Let α ≤ 1. Then, the state z = 0 is asymptotically stable.

Proposition 2

Let α >1. Then, if η > 0, the state z = 0 is not asymptotically stable.Furthermore, there is a unique state z∗ > 0 which satisfies:

∃ε > 0 s.t. ∀z(0) ∈ (0, ε), $[z(0), t]→ z∗.

Therefore, whether or not the social network can be “built from scratch”depends on whether or not there is sufficient geographic cohesion.



Benchmark theory (V): results, cont.

Proposition 3

Given any α > 1, denote by z∗(η) the unique limit state z∗ establishedabove. For any z , there exists some η such that if η ≥ η, then z∗(η) ≥ z .

Proposition 4

∃α such that if 1 < α < α, the function z∗(·) is upper-discontinuous atsome η = η0 > 0.

Therefore, if geographic cohesion is above the required threshold (α > 1)the steady-state connectivity can be made arbitrarily large as η grows.Furthermore, if such cohesion is not too large, such dependence on ηdisplays an upward discontinuity at some η0.

Recall this behavior was observed in our earlier illustrative simulations.



General theory (I)

To understand better the role of local congestion and institutions,we need to consider a general (finite-population) framework.

But, for finite populations, an analytical approach is intractableso we pursue a numerical computation of equilibriathat involves a numerical determination of the function Φ(z)

This allows a precise computation of the equilibria and, correspondingly,a full-fledged comparative analysis.

Here, we focus on two issues:

The role of institutions and innovation rate on optimal cohesion α∗

The effect of institutions on long-run connectivity



General theory (II): numerical determination of equilibrium

Having computed Φ(z) for every α, η, µ, find z∗ s.t. Φ(z∗) = z∗/(2η)

Graphically:

Finite population (n = 1000) induces significant local saturation -- mainly for high α



General theory (III): optimal degree of cohesion

Trade-off between better environmental conditions (higher µ and η)and the optimal degree of cohesion α∗ (n = 1000)

Op#

mal value

α*

Ins#tu#ons µ

Innova#on rate η

=5η =10η =20η



General theory (IV): the role of institutions

The effect of institutions on long-run network connectivitydisplays a step-like form:

α  =0.3 α  =0.5

α  =0.7 α  =1



Summary

Our stylized model stresses the following features of globalization:

1 It is a property of social networks: short network paths spanninglong geographic distances and connecting a large disperse population

2 It must underlie dense economic activity/collaborationby overcoming local saturation & expanding the set of opportunities

3 Robust phenomenon that, under low cohesion, arises abruptly(by triggering self-feeding effects on network formation)

4 Importance of social (“geographic”) cohesion:some is crucial, but beyond a point it is detrimental

5 Equilibrium multiplicity & hysteresis opens up a role for policy:temporary measures (e.g. rise in η) may produce persistent effects



Some reflections on methodology and interdisciplinarity

Question: Can economics [that must extricate itself from its currentconceptual crisis] benefit from methods/insights of other disciplines?

Answer: Yes, in particular can profit from (statistical) methods developedto study large systems of interacting entities... and this is an example!

But a number of very important caveats, often ignored by non-economists!Here, I emphasize just two, underlying historical success of the discipline:

1 Economic systems consist of rational (purposeful) individuals:

(a) incentives are essential component of economic insight(b) payoffs are unavoidable basis for welfare analysis & policy evaluation

2 Economic agents are forward looking:

(a) expectations are essential component of economic insight(b) “coherent” formation of expectations (possibly through learning) must

underlie useful welfare/policy analysis: Lucas critique


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