Channel Choice in Live Streaming Commerce

(1) p D D S ≥ p D and q D D S ≤ q D ≤ q D S always hold. (2) p D D S , θ D S , q S D S , q D S , and π F D S increase in τ S . (3) If t < t 1 , p S D S increases in τ S ; otherwise, p S D S decreases in τ S . (4) When C < C 3 , π F D S > π F D ; otherwise, π F D S ≤ π F D . Where t 1 = 2 + r k S ( 4 − 4 β + ( 6 − 4 β + 4 r ( β − 2 ) ( β − 1 ) k S − τ S ) τ S ) r k S ( 2 − 4 τ S + r k S ( 4 − 4 β + ( 4 β − 4 − τ S ) τ S ) ) , C 3 = k S ( 2 β − 2 − 2 t + τ S ) 2 4 r k S ( 4 β − 4 − τ S 2 ) − 8 .

(1) For any slotting fee F D T ∈ ( α λ k T ( 2 + 2 t − 2 β λ − τ T ) 2 4 r k T ( 4 β λ − 4 − τ T 2 ) − 8 + k T ( 2 + 2 t − 2 β λ − τ T ) ( 2 t − 2 β λ + τ T − 2 r k T ( 2 ( t − β λ ) ( β λ − 1 ) + τ T ( t − ( 1 + t − β λ ) τ T ) ) ) 2 ( 2 + r k T ( 4 − 4 β λ + τ T 2 ) ) 2 , k T ( 2 + 2 t − 2 β λ − τ T ) 2 ( 2 − 2 α λ + r α λ k T ( 4 β λ − 4 − τ T 2 ) ) 4 ( 2 + r k T ( 4 − 4 β λ + τ T 2 ) ) 2 ] , the optimal revenue-sharing ratio can be set by ϕ D T = k T ( 2 + 2 t − 2 β λ − τ T ) 2 ( 2 − 2 α λ + r α λ k T ( 4 β λ − 4 − τ T 2 ) ) − 4 F D T ( 2 + r k T ( 4 − 4 β λ + τ T 2 ) ) 2 4 k T ( 2 + 2 t − 2 β λ − τ T ) ( 1 − τ T + r k T ( 2 ( t − β λ ) ( β λ − 1 ) + τ T ( t − ( 1 + t − β λ ) τ T ) ) ) . (2) For any revenue-sharing ratio ϕ D T ∈ [ 0 , ( 2 + 2 t − 2 β λ − τ T ) ( 2 − 2 α λ + r α λ k T ( 4 β λ − 4 − τ T 2 ) ) 4 − 4 τ T + 4 r k T ( 2 ( t − β λ ) ( β λ − 1 ) + τ T ( t − ( 1 + t − β λ ) τ T ) ) ] , the optimal slotting fee can be set by F D T = α λ k T ( 2 + 2 t − 2 β λ − τ T ) 2 4 r k T ( 4 β λ − 4 − τ T 2 ) − 8 − 2 ϕ D T k T ( 2 + 2 t − 2 β λ − τ T ) ( 1 − τ T + r k T ( 2 ( t − β λ ) ( β λ − 1 ) + τ T ( t − ( 1 + t − β λ ) τ T ) ) ) + k T ( 2 + 2 t − 2 β λ − τ T ) 2 2 ( r k T ( 4 β λ − 4 − τ T 2 ) − 2 ) 2 .

(1) p D D T ≥ p D and q D D T ≤ q D ≤ q D T always hold. (2) p D D T , θ D T , q T D T , q D T , π F D T , π S D T , and π T D T increase in τ T . (3) If λ < λ 3 , p T D T increases in τ T ; otherwise, p T D T decreases in τ T . (4) When λ 5 < λ < λ 4 , π F D T > π F D ; otherwise, π F D T ≤ π F D . Where λ 3 = 1 + τ T + r k T ( ( 3 + t ) τ T − t ) + ( r k T ( t − τ T ) − 1 ) ( r k T ( t + τ T ( t τ T − 1 − 2 t ) ) − 1 − τ T 2 ) 2 r β k T τ T , λ 4 = 2 r t k T − 1 + r t k T τ T − r k T τ T 2 r β k T τ T , and λ 5 = max ( 2 + 4 r k T + r k T τ T 2 4 r β k T , 2 + 2 t − τ T 2 β ) .

Proposition 6:

(1) When λ 5 < λ < λ 4 , if C > C 4 , where C 4 = k S ( 2 β − 2 − 2 t + τ S ) 2 4 r k S ( 4 β − 4 − τ S 2 ) − 8 − ( 1 − α λ ) k T ( 2 β λ − 2 − 2 t + τ T ) 2 4 r k T ( 4 β λ − 4 − τ T 2 ) − 8 , the firm preferscChannel DT; otherwise, channel DS is preferred. (2) When λ ≥ λ 4 or λ ≤ λ 5 , if C > C 3 , the firm prefers channel D; otherwise, channel DS is preferred.

Proposition 6 sets out the effects of λ and C on the channel choice for an established firm, as graphically illustrated in Figure 11. From Figure 11 we find that when C is larger than a threshold (i.e., C ≥ C 3 ), channel DS cannot bring additional benefit to channel D due to the high channel encroachment cost, and so the firm will choose between channels DT and channel D. Again, as shown in proposition 5, the firm can benefit from channel DT only when the third-party streamer's popularity is moderate (i.e., λ 5 < λ < λ 4 ); otherwise, channel D dominates. However, when C is smaller than the threshold (i.e., C < C 3 ), channel DS outperforms channel D through the increased price and sales, as well as the lower channel encroachment costs associated with the live streaming channel. In regions where both channels DS and DT benefit the firm more than channel D ( C < C 3 and λ 5 < λ < λ 4 ), the choice between channels DT and DS depends on C. Channel DT outperforms channel DS when C is lower than a certain value (i.e., C < C 4 ); otherwise, channel DS dominates.

OPEN IN VIEWER

Figure 11.

The effects of λ , C, and τ on the established firm's channel choice ( t = 0.8 , k T = 0.5 , k S = 0.5 , β = 1.5 , α = 0.3 , τ S = 0.1 ) . (a) T τ = 0.15 , r = 2 ; (b) T τ = 0.2 , r = 2 ; (c) T τ = 0.2 , r = 2.3 .

In addition, we find that the cross-channel spillover from channel S or T to channel D, and the price sensitivity, r, will post impacts on the threshold values of λ and C. Comparing the cases in Figure 11(a) τ T = 0.15 and (b) τ T = 0.2 , we can see that as τ T increases, the tolerance for the top streamer's popularity decreases ( λ 4 ( 2 ) < λ 4 ( 1 ) ) , while the tolerance for the small streamer increases ( λ 5 ( 2 ) < λ 5 ( 1 ) ) . This is because introducing an additional live streaming channel brings channel competition. When collaborating with a top streamer, the heightened demand on the live streaming channel means the competition between the two channels will be intensified, resulting in a lower price in the live streaming channel (see proposition 5(3)). That is, a greater spillover effect intensifies competition. However, channel competition is negligible when collaborating with a less popular streamer; the greater spillover effect is the extra traffic spilling over from the live streaming channel to the traditional channel, leading to higher sales in both channels in channel DT. They both lead to smaller regions where channel DT dominates. Furthermore, we also find that as price sensitivity increases, consumers are more sensitive to price, and the cost associated with the live streaming channel will push up the price (note that p D D T ≥ p D and p D D S ≥ p D ), and thus the benefit from the extra demand with live streaming channel will be insufficient to justify the channel encroachment cost, resulting in a larger region where channel D dominates (compare the cases in Figure 11(b) r = 2 and (c) r = 2.3 ).

5 Extensions