The Encyclopedia of Economic Principals

Chapter 90

Networks, Trust, Enforcement, and Collective Behavior

What ties carry, what they enforce, and which ones get built.

Four of the chapter's hypothetical cases, made interactive: a nonredundant acquaintance, closure as enforcement, a bridge no one sponsors, and reputation with a bond.

Every example here is a constructed teaching example: it uses the hypothetical numbers of the chapter's worked examples, plus a few values added for comparison and labelled as such in each panel. Nothing here measures a real market, firm or household.

Demonstration 1 of 4

The value of a nonredundant acquaintance

How much does a weak tie into a different information pool add to the chance of a job lead?

A tie is valuable for the news it carries that the rest of the network lacks. Overlap, not contact frequency, erodes that value.

Equation, written in LaTeX: 0.30(0.50)=0.15.

Equation, written in LaTeX: 1-(1-0.40)(1-0.15)=0.49.

Equation, written in LaTeX: 1-(0.60)(0.97)=0.418.

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Lina's close circle yields a lead with chance 0.40. Omar sees a suitable opening with chance 0.30 and forwards it with the chosen chance; overlap is the share of his leads Lina's circle already has. Pools are independent.

Predict first. If Omar moves into Lina's industry (80 percent overlap), how much of the 9-point gain survives?

Your prediction

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Figure: The value of a nonredundant acquaintance. Two bars: 0.40 with the close circle only and 0.490 with Omar's tie.
Omar's overlap with local pool: 0, Chance he forwards: 0.5
Constructed example: the book's hypothetical search has 0.40, 0.30, forwarding 0.50 and overlap 0 and 0.80; overlap 0.5 and forwarding 1.0 are added.

Calculated values

Omar's nonredundant contribution
0.150
Chance of a lead
0.490
Added by the tie
9.0 points

Omar sees openings with chance 0.30, forwards 50% of them and overlaps 0% with Lina's circle, so his new information is 0.30 x 0.50 x 1.00 = 0.150. Lina's chance of a lead rises from 0.40 to 1 - 0.60 x 0.850 = 0.490.

Worked steps

  1. Contribution = 0.30 x 0.50 x (1 - 0.00) = 0.150
  2. P(lead) = 1 - (1 - 0.40)(1 - 0.150) = 1 - 0.60 x 0.850 = 0.490
  3. Added = 0.490 - 0.40 = 0.090

Use the idea

When choosing whom to keep in touch with, weigh how different their information is, not only how close the relationship feels.

Where the conclusion applies

Independent pools and a fixed forwarding chance; leads still need qualifications to become jobs, as the chapter notes.

Check your understanding: With overlap 0.5 and forwarding 1.0, what is the chance of a lead?
Contribution 0.30 x 1.0 x 0.5 = 0.15, so 1 - 0.60 x 0.85 = 0.49.

Chapter 90 source: section "Strength of weak ties".

Demonstration 2 of 4

Closure as enforcement

When do shared trading partners make default on trade credit a losing move?

Enforcement requires the product of detection and sanction to exceed the private gain. Better information alone fails when the available consequence is small, and many ties alone fail when they neither detect nor punish.

Equation, written in LaTeX: d\leq p(C_{ij})S(C_{ij}).

Equation, written in LaTeX: 0.20(\$1{,}500)=\$300,

Equation, written in LaTeX: 0.80(\$2{,}000)=\$1{,}600,

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d = $1,000 is the gain from keeping the invoice, p the chance that default is detected and S the future surplus put at risk. Closure among partners can raise p, S or both.

Predict first. With shared partners (p = 0.80) whose only response is a $300 sanction, is default deterred?

Your prediction

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Figure: Closure as enforcement. Two bars: the gain from default, $1,000, and the expected consequence, $1,600.
Detection probability: 0.8, Sanction at stake ($): 2,000
Constructed example: the book's hypothetical retailer faces a $1,000 gain, p of 0.20 and 0.80 and sanctions of 300, 1,500 and 2,000; p = 0.50 is added.

Calculated values

Expected consequence pS
$1,600
Margin pS - gain
$600
Retailer
Repay

Detection 0.80 times a sanction of 2,000 dollars gives an expected consequence of 0.80 x 2,000 = 1,600 dollars against the 1,000 dollar gain, so repaying is better by $600.

Worked steps

  1. pS = 0.80 x 2,000 = 1,600
  2. Margin = 1,600 - 1,000 = 600
  3. Result: repaying is better by $600

Use the idea

To judge whether a community can sustain credit, estimate both how likely a default is seen and how much business it would cost.

Where the conclusion applies

A risk-neutral retailer and a one-time comparison of gain and expected loss, as in the chapter's hypothetical case.

Check your understanding: At p = 0.50 and S = $2,000, does the retailer repay?
pS = 0.50 x 2,000 = 1,000, exactly the gain: indifferent at the boundary.

Chapter 90 source: section "Network closure as an enforcement mechanism".

Demonstration 3 of 4

The bridge nobody builds

Why can a link that adds total surplus go unbuilt, and what fixes it?

The sponsor pays the whole cost but captures only its own benefit. A transfer from the other beneficiary, or a lower cost, aligns private and social incentives.

Equation, written in LaTeX: 10-12=-2.

Equation, written in LaTeX: 10+10-12=8.

Equation, written in LaTeX: 10+3-12=1

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A bridge to specialist D costs the sponsoring firm the chosen amount. It is worth 10 to A and 10 to B. B may pay A a transfer for sponsoring; D gains nothing.

Predict first. At cost 12, does a 3-unit transfer from B get the bridge built?

Your prediction

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Figure: The bridge nobody builds. Three bars: A's payoff -2, B's 10 and total 8.
Bridge cost: 12, Transfer B pays A: 0
Constructed example: the book's hypothetical firms have values 10 and 10, costs 12 and 8 and a 3-unit transfer; a cost of 16 is added.

Calculated values

A's private payoff
-2
B's payoff
10
Social surplus
8
Built
No

At cost 12 with a transfer of 0 from B, A's payoff from sponsoring is 10 + 0 - 12 = -2 and total surplus is 10 + 10 - 12 = 8, so no one builds the bridge although it would add 8 units: a transfer of at least 2 would be needed.

Worked steps

  1. A: 10 + 0 - 12 = -2
  2. B: 10 - 0 = 10
  3. Social: 10 + 10 - 12 = 8
  4. Result: no one builds the bridge although it would add 8 units: a transfer of at least 2 would be needed

Use the idea

Before subsidizing a missing connection, identify who else benefits and whether a feasible transfer could pay for it.

Where the conclusion applies

Fixed values, one possible sponsor at a time and an enforceable transfer.

Check your understanding: At cost 16 with a 3-unit transfer, is the link built, and is it efficient?
A gets 10 + 3 - 16 = -3, not built; social 20 - 16 = 4 > 0, so a transfer of at least 6 is needed.

Chapter 90 source: section "Strategic network formation".

Demonstration 4 of 4

Reputation, bonds, and the honest agent

Do future business and a posted bond together deter an agent from diverting a shipment?

Reputation and bonds work only through the chance that misconduct is detected and acted on. Shared origin matters only insofar as it raises that chance.

Equation, written in LaTeX: 0.9(6{,}000)(1+0.9+0.9^2+0.9^3)=18{,}570.60.

Equation, written in LaTeX: 0.4(6{,}000)(3.439)=8{,}253.60,

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Diverting pays 20,000 now. Honest service keeps four later opportunities of 6,000 each, discounted at 0.9 a year. Misconduct is detected with chance p, and a posted bond is forfeited when it is.

Predict first. When detection falls to 0.4, does the 3,000 bond still deter diversion?

Your prediction

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Figure: Reputation, bonds, and the honest agent. Stacked bar: expected lost business 18,570.60 and expected bond loss 2,700.00, against a line at the 20,000 diversion gain.
Detection probability: 0.9, Bond posted: 3,000
Constructed example: the book's hypothetical agency has a 20,000 gain, four 6,000 opportunities, discount 0.9, detection 0.9 and 0.4 and a 3,000 bond; detection 0.65 and bonds of 0 and 6,000 are added.

Calculated values

Expected lost business
18,570.60
Expected bond loss
2,700.00
Total consequence
21,270.60
Honest
Yes

With detection 0.90, cheating forfeits 0.90 x 6,000 x 3.439 = 18,570.60 of future business plus 0.90 x 3,000 = 2,700.00 of bond, 21,270.60 in all against a 20,000 gain, so honest service is privately better.

Worked steps

  1. 1 + 0.9 + 0.9^2 + 0.9^3 = 3.439
  2. Lost business = 0.90 x 6,000 x 3.439 = 18,570.60
  3. Bond loss = 0.90 x 3,000 = 2,700.00
  4. Total = 18,570.60 + 2,700.00 = 21,270.60 against 20,000: honest service is privately better

Use the idea

Value a reputation as detection probability times discounted future business, and check it against the one-time gain from cheating.

Where the conclusion applies

Four fixed opportunities, a constant discount factor and a bond forfeited only on detection.

Check your understanding: At p = 0.65 and a bond of 6,000, is honesty preferred?
0.65 x 6,000 x 3.439 = 13,412.10 plus 0.65 x 6,000 = 3,900 gives 17,312.10 < 20,000: not deterred.

Chapter 90 source: section "Diaspora Networks and Middleman Minorities".