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1 − δ
> u
(4)
Proof: Consider a “community enforcement” strategy according to which
all network members agree to trade honestly. Any defection from hon-
est trade is to be punished by a suspension of future trade between
the cheater and all other network members, with the provisos that (i)
if any other player defects in the future, that player is subsequently
punished while all previous defections are forgiven, and that (ii) si-
multaneous deviations are ignored (these conditions ensure subgame
perfection).
With this enforcement regime, an individual considering cheating has
an incentive to cheat all of those with whom she trades. So, defection
nets the defector a maximum one-shot gain of Ku; the net loss in each
future period is Kz (assuming all other network members adhere to
the community enforcement strategy). Therefore, defection is optimal
unless (4) holds. Conversely, suppose (4) holds. Then the “commu-
nity enforcement” strategy described above can support trade as a
subgame-perfect equilibrium.
The community enforcement strategy used in the proof, in which
players adopt a “social norm” that an individual who cheats any other
network member is to be ostracized from future trade, is based on that
described by Kandori (1992:67). As Kandori showed, to enforce hon-
est trade, “changing partners itself is unimportant and the crux of the
matter is information transmission among the community members”
(Kandori 1992:64) (thus, (4) is the same as (2)). Here, we have sim-
ply assumed perfect and costless information transmission within each
network.
Now assume that, in each period, a finite number of pairs of indi-
viduals are randomly selected from the entire (infinite) population, to
play one-shot briber‟s dilemmas. How will social structure be related
to corruption in this model?
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Lemma 3.2. When two members of the same network play a briber’s
dilemma, an agreement not to pay bribes can be sustained in a subgame-
perfect equilibrium through strategic linkage if and only if
R
2
+ c ≤ KS(u,z,δ)
(5)
Proof: Consider a strategy according to which defection in the briber‟s
dilemma, or cheating in trade, is punished by exclusion from all fu-
ture trade. When a defection occurs, all previous defections are for-
given; and simultaneous defections are ignored. With this enforce-
ment regime, after an official has chosen d, an individual considering
defecting would prefer to defect in all K trade games and the briber‟s
dilemma simultaneously. The player can expect to be excluded from all
future trade (assuming that all other network members never cheat).
A player will therefore prefer to defect unless
R + K(2u + z) +
δ
1 − δ
(Ku) ≤
120
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