The name is absent

z + 3^{( h - z} )^-[^{l +} 3⁽ y ^{- l )]} ≥ ^δ 3^(V3 ^- V4)

⇒ δ ≤ 3×^{2( z -1} )^{+( h -} y )
h-z

since from (1) we have V₃ - V₄ = 3(h - z). It is easy to see that for our parameterization this

is satisfied by all δ∈(0,1) since -²(^z—l)^{+ (}h—^y) = 34.
h-z

Finally, consider V₂ ≥ V^~ ₂ . This inequality is immediately rewritten as:

2  22

z + Ξ( h - z )-[ l + 2 ( y - l )] ≥ δ 3 (V3-V4 )

3 z - l + 2(h - y)
⇒ δ ≤ ××--------—

2 h-z

which always holds for all parameters since ^z l⁺²⁽h ^y) = 34.

h-z

The intuition is simple. Cooperating instead of sanctioning after observing a defection
may be helpful to the player, since it delays the spread of the sanction. However, doing so
generates a current loss to the player since he earns y (instead of h ) if he meets a
cooperator, and l (instead of z ) if he meets a deviator. Therefore, the player must be
sufficiently impatient to prefer play of Z to Y—clearly, the smaller l and y , the greater
the incentive to follow with the sanction. Our parameterization insures that this incentive
exists for all δ∈(0,1) .

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