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NTU Management Review Vol. 33 No. 2 Aug. 2023

Recall that in our basic model, the marginal probabilities for the type-H and type-L
creators to meet the threshold are p = β e and q=β e , respectively. When the two events
L
L
H
H
are independent, the joint probability for both creators to meet the threshold P should
HL
be pq=β e β e . To make the two events dependent while maintaining the marginal
L
L
H
H
probabilities unchanged, we now assume that P = pq + η, P =p(1-q)-η , P =(1-p)q-η, and
H
HL
L
P =(1-p)(1-q)+η, where η is an exogenous parameter measuring the dependency between
0
the two creators’ videos. If the parameter η is positive, the two events are positively
correlated (maybe because the two creators’ styles are similar). On the contrary, if η is
negative, the two events are negatively correlated. Note that when η = 0, the two events
are independent, and the model is the same as our basic model. Table 3 lists the marginal
and joint probabilities for all possible events.
Table 3 The Joint Probability Table under Dependency
Type-L creator
Type-H creator Marginal probability
Meets Does not meet
Meets P HL = pq + η P H = p(1 - q) - η p
Does not meet P L = (1 - p) q - η P 0 = (1 - p) (1 - q) + η 1-p
Marginal probability q 1 - q

We analyze the new setting results in the following proposition. It turns out that the
degree of dependency does not affect any player’s decision.
Proposition 5: For any reasonable value of η, the equilibrium effort exertion, contract
design, and advertorial allocation decisions are all identical.
With the new setting of probabilities, the two creators’ effort exertion problems

remain unchanged. This is because each of them only cares about whether her/himself may
meet the threshold, and the marginal probabilities remain unchanged. It then follows that
the equilibrium effort levels will still be those derived in Proposition 1. More interestingly,
though the MCN company’s contract design problem is changed, the MCN company’s
decisions remain unchanged. To explain this, let’s say η > 0 for a while. In this case, the
additional benefit that may be earned when both creators meet the threshold is offset by
the additional loss that will happen when only one creator meets the threshold with only

an exogenous amount ηA deducted from the MCN company’s total profit. The opposite
happens if η < 0. It then follows that all our major findings remain valid with dependency
between the two events (except that the MCN company’s profit will be affected by an
exogenous amount).

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