The booming live-streaming commerce has significantly changed the traditional e-commerce model,thus attracting much attention from both industry and academia.In recent years,an increasing number of scholars have appli...The booming live-streaming commerce has significantly changed the traditional e-commerce model,thus attracting much attention from both industry and academia.In recent years,an increasing number of scholars have applied analytical models to explore live-streaming strategies for firms in different scenarios.However,the previous literature mainly considers monopolists,while in the real world,competition is not rare.To fill this gap between the literature and practical observations,this paper applies a game theoretical model to study live-streaming adoption and pricing strategy for firms under competitive environments.The results show that,for competitive firms,the equilibrium strategy depends on the relation between the commission rate and the intensity of the market expansion effect.Additionally,compared to the case in which no firm adopts live-streaming,competitive firms do not always benefit from the adoption of live-streaming selling.The paper also shows that competition plays a negative role in inducing a firm to adopt live-streaming.展开更多
A t-container Ct(u,v)is a set of t internally disjoint paths between two distinct vertices u and v in a graph G,i.e.,Ct(u,v)={P_(1),P_(2),···,Pt}.Moreover,if V(P_(1))∪V(P_(2))∪···∪V(Pt...A t-container Ct(u,v)is a set of t internally disjoint paths between two distinct vertices u and v in a graph G,i.e.,Ct(u,v)={P_(1),P_(2),···,Pt}.Moreover,if V(P_(1))∪V(P_(2))∪···∪V(Pt)=V(G)then Ct(u,v)is called a spanning t-container,denoted by C_(t)^(sc)(u,v).The length of C_(t)^(sc)(u,v)={P_(1),P_(2),···,Pt}is l(C_(t)^(sc)(u,v))=max{l(P_(i))|1≤i≤t}.A graph G is spanning t-connected if there exists a spanning t-container between any two distinct vertices u and v in G.Assume that u and v are two distinct vertices in a spanning t-connected graph G.Let D_(t)^(sc)(u,v)be the collection of all C_(t)^(sc)(u,v)’s.Define the spanning t-wide distance between u and v in G,d_(t)^(sc)(u,v)=min{l(C_(t)^(sc)(u,v))|C_(t)^(sc)(u,v)∈D_(t)^(sc)(u,v)},and the spanning t-wide diameter of G,D_(t)^(sc)(G)=max{d_(t)^(sc)(u,v)|u,v∈V(G)}.In particular,the spanning wide diameter of G is D_(κ)^(sc)(G),whereκis the connectivity of G.In the paper we provide the upper and lower bounds of the spanning wide diameter of a graph,and show that the bounds are best possible.We also determine the exact values of wide diameters of some well known graphs including Harary graphs and generalized Petersen graphs et al..展开更多
基金supported by the National Natural Science Foundation of China(72171219,72201264,71921001,71801206,71971203)the Fundamental Research Funds for the Central Universities(WK2040000027)+1 种基金the New Liberal Arts Fund of USTC(FSSF-A-230104)the Four Batch Talent Programs of China.
文摘The booming live-streaming commerce has significantly changed the traditional e-commerce model,thus attracting much attention from both industry and academia.In recent years,an increasing number of scholars have applied analytical models to explore live-streaming strategies for firms in different scenarios.However,the previous literature mainly considers monopolists,while in the real world,competition is not rare.To fill this gap between the literature and practical observations,this paper applies a game theoretical model to study live-streaming adoption and pricing strategy for firms under competitive environments.The results show that,for competitive firms,the equilibrium strategy depends on the relation between the commission rate and the intensity of the market expansion effect.Additionally,compared to the case in which no firm adopts live-streaming,competitive firms do not always benefit from the adoption of live-streaming selling.The paper also shows that competition plays a negative role in inducing a firm to adopt live-streaming.
基金supported by the National Natural Science Foundation of the People's Republic of China“On disjoint path covers of graphs and related problems”(12261085)Natural Science Foundation of Xinjiang Uygur Autonomous Region of China“On spanning wide diameter and spanning cycle ability of interconnection networks”(2021D01C116)。
文摘A t-container Ct(u,v)is a set of t internally disjoint paths between two distinct vertices u and v in a graph G,i.e.,Ct(u,v)={P_(1),P_(2),···,Pt}.Moreover,if V(P_(1))∪V(P_(2))∪···∪V(Pt)=V(G)then Ct(u,v)is called a spanning t-container,denoted by C_(t)^(sc)(u,v).The length of C_(t)^(sc)(u,v)={P_(1),P_(2),···,Pt}is l(C_(t)^(sc)(u,v))=max{l(P_(i))|1≤i≤t}.A graph G is spanning t-connected if there exists a spanning t-container between any two distinct vertices u and v in G.Assume that u and v are two distinct vertices in a spanning t-connected graph G.Let D_(t)^(sc)(u,v)be the collection of all C_(t)^(sc)(u,v)’s.Define the spanning t-wide distance between u and v in G,d_(t)^(sc)(u,v)=min{l(C_(t)^(sc)(u,v))|C_(t)^(sc)(u,v)∈D_(t)^(sc)(u,v)},and the spanning t-wide diameter of G,D_(t)^(sc)(G)=max{d_(t)^(sc)(u,v)|u,v∈V(G)}.In particular,the spanning wide diameter of G is D_(κ)^(sc)(G),whereκis the connectivity of G.In the paper we provide the upper and lower bounds of the spanning wide diameter of a graph,and show that the bounds are best possible.We also determine the exact values of wide diameters of some well known graphs including Harary graphs and generalized Petersen graphs et al..
