Study on the Price Competition between E2commerce Retailer and Conventional Retailer

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1 2006 : (2006) , 2, 2 (, ; 2, ) :,,,.,. :,,, ;,,. : ; ; ; : C93 : A Study on the Price Competition between E2commerce Retailer and Conventional Retailer CHEN Yun, WANG Huan2chen 2, SHEN Hui2zhang 2 (China Executive Leadership Academy Pudong, Shanghai 20204, China ; 2Management School, Shanghai Jiao Tong University, Shanghai , China) Abstract: Considering the impacts of implementation degree of electronic commerce on retailers behaviors, this paper applies a two2stage game model to study the price competition between an e2commerce retailer and a conventional retailer. Expressions for optimal prices, profits and consumers distribution in equilibrium are derived. Some propositions are proved and discussed. This paper points out that, when the critical valuation of e2commerce consumer is more than or equal to that of conventional consumer, the product price of both retailers will decrease with implementation degree of electronic commerce ; when the critical valuation of e2commerce consumer is less than that of conventional consumer, the profits of e2commerce retailer will be more than that of conventional retailer if implementation degree of electronic commerce is more than a critical value. Key words : electronic commerce ; retailer ; price competition ; consumers valuation of goods,, ( ),., ; ( ),.,. :?., [ 4 ], 999,Smith, Bailey & Brynjolfsson : : ( ) : (975 - ),,, ; (933 - ),,, ; (958 - ),,, China Academic Journal Electronic Publishing House. All rights reserved.

2 [5 ]., [6 8 ], [9 ]. Friberg et al (2000, 200), CD, ( Internet ) ( Internet ) [6,7 ]. Pan et al (2002) Hotelling, [8 ]., (200), [9 ]., [ 6 8 ] ( v,0 < v ), [ 6,7 ] v = ; [9 ] ( ),, (, ), [ 6,7 ] ( [ 6, 7 ], )., [6,7 ],, ( [6,7 ] ). : 2 ; 3 4 ; 5. : ;, ( ). 2,.,, ;, ;, ;,., : : u ( ) = - T - p e, - t -, 0, ) (0, ) ; = [0, ], [ 0, ] ;, [ 0, ] ; 2) p e ; ; 3) T ( ) ( ) ; 4) t ( ) (0 < t < ), t ; t, [6 ]. ( ) v (0 < v ), v, ( - v)., u ( ) 0., () China Academic Journal Electronic Publishing House. All rights reserved.

3 37, u ( ) = - T - p e 0, e ( p e ) ( e ) e ( p e ) = p e + T ;, u ( ) = - t - 0, t ( ) ( t ) t ( ) = - t.. ) e t, v ( - e ),., - T - p e - t - 0, ( p e, ) ( ) : ( p e, ) = min t ( p e + T - ),. (2), v ( - ), ( - v) ( - ) + ( - t )., e t,. 2) e < t, t. : e < t, p e + T < - t ; 0 < t <, p e + T - t < t ( - t) -, t t ( p e + T - ) < - t, < t.,,., v ( - e ), ( - v) ( - t ), 2. t ( e t ) 2 ( e < t ) c e, c t,. e t e < t. 3 e t., : D e ( p e, ) = v t ( + t - p e - T) ; D t ( p e, ) = - v + v t ( p e + T) -, : e ( p e, ) = ( p e, : p 3 e = p 3 t = : v + t - vt t ( - t). (3) - c e ) D e ( p e, ) ; t ( p e, ) = ( - c t ) D t ( p e, ), (4) 3 v + 4 t - 3 vt [ ( v + t - vt) (2 c e + c t + t - T) + t ( - T) ], (5) 3 v + 4 t - 3 vt [ v ( - t) ( c e + T) + 2 ( v + t - vt) c t + ( - t) (2 t - vt) ]. (6) China Academic Journal Electronic Publishing House. All rights reserved.

4 e ( p 3 e, p 3 t ) = 3 t ( p 3 e, p 3 t ) = v t (3 v + 4 t - 3 vt) 2 [ ( v + 2 t - vt) ( c e + T) - ( v + t - vt) ( c t + t) - t ] 2, (7) v + t - vt t ( - t) (3 v + 4 t - 3 vt) 2 [ v ( - t) ( c e + T) - ( v + 2 t - vt) ( c t + t) + 2 t ] 2. (8), : 3 ( p 3 e, p 3 t ) = 3 t ( p 3 t ) = 3 e ( p 3 e ) = D 3 e ( p 3 e, p 3 t ) = D 3 t ( p 3 e, p 3 t ) = t (3 v + 4 t - 3 vt) [ ( v + 2 t - vt) ( c e + T) - ( v + t - vt) c t - t ( + 2 vt - 2 v - 3 t) ], ( - t) (3 v + 4 t - 3 vt) [ v ( - t) ( c e + T) + 2 ( v + t - vt) c t + t ( - t) (2 - v) ], (0) 3 v + 4 t - 3 vt [ ( v + t - vt) (2 c e + 2 T + c t + t) + t ], () v t (3 v + 4 t - 3 vt) [ - ( v + 2 t - vt) ( c e + T) + ( v + t - vt) ( c t + t) + t ], (2) v + t - vt t ( - t) (3 v + 4 t - 3 vt) [ v ( - t) ( c e + T) - ( v + 2 t - vt) c t + t ( - t) (2 - v) ]. c e T ( c e + T), : e t, ( c e + T) : c e + T ( + t) ( v + t - vt) c t + t ( - t) ( + vt - t - 2 v) ( - t) ( v + 2 t - 2 vt), ( v + t - vt) ( c t + t) + t v + 2 t - vt ) 3 e 3 t, : 3 e - 3 t = t ; k ( - t) (3 v + 4 t - 3 vt) 0 ; : k = ( - t) ( v + 2 t - 2 vt) ( c e + T) - ( + t) ( v + t - vt) c t - t ( - t) ( + vt - t - 2 v) ; 0 < v,0 < t <, c e + T ( + t) ( v + t - vt) c t + t ( - t) ( + vt - t - 2 v) ( - t) ( v + 2 t - 2 vt) 2), - 3 = c e + T ( v + t - vt) ( c t + t) + t v + 2 t - vt = c e T a ; k 2 t (3 v + 4 t - 3 vt) 0, : k 2 = - ( v + 2 t - vt) ( c e + T) + ( v + t - vt) ( c t + t) + = c e T b ; 3) [ c e T a, c e T b ] - t -. (9) (3) 0, ( - t) ; [ 0, ], 0, ( - t), ( - t - ) 0 ;, = 0, - t - > 0 ; > 0, ( - t), > 0, - t - 0., 0, - t c t 0, c t, - t - c t 0. c e T b - c e T a = t ( v + t - vt) (3 v + 4 t - 3 vt) ( - t - c t ) ( - t) ( v + 2 t - 2 vt) ( v + 2 t - vt) [ c e T a, c e T b ]., c e + T [ c e T a, c e T b ],.. 2 e t,, ( v ), ;, 0,, : China Academic Journal Electronic Publishing House. All rights reserved.

5 39 ) v > t ( - 2 c e + 2 T + c t - 3 t) ( - t) ( c e - 2 T - c t + 2 t) T < c e - c t + t ; 2 2) c e > v + 2 t - vt [ ( v + t - vt) (2 T + c t - 2 t) + t ( - t) ] ; 3) T < ( v + 2 t - vt) c e - t ( - t) 2 ( v + t - vt) - 2 ( c t - 2 t). p 3 e p 3 t v, : 5 p 3 e 5 v = - t ( - t) (3 v + 4 t - 3 vt) 2 (3 - c t - t - 2 c e - 2 T) 0 ; 5 p 3 t 5 v = - 2 t ( - t) (3 v + 4 t - 3 vt) 2 (3 - c t - t - 2 c e - 2 T) 0 ;, : p 3 e - p 3 t = 3 v + 4 t - 3 vt k 3, : k 3 = v ( - t) ( c e - 2 T - c t + 2 t) - t ( - 2 c e + 2 T + c t - 3 t) ;, p 3 e - p 3 t > 0, k 3 > 0, ) v > t ( - 2 c e + 2 T + c t - 3 t) ( - t) ( c e - 2 T - c t + 2 t) T < c e - c t + t, p 3 e > p 3 t ; 2 2) c e > v + 2 t - vt [ ( v + t - vt) (2 T + c t - 2 t) + t ( - t) ], p 3 e > p 3 t ; 3) T < ( v + 2 t - vt) c e - t ( - t) 2 ( v + t - vt) - 2 ( c t - 2 t), p 3 e > p 3 t.. 2, c t + t = c e + T =,.,,,,,. 2,, ( ),. 2 Internet [0 2 ], Lee (998) AUCNET, [0 ]. 4 e < t e t,., : D e ( p e ) = v ( - e ) = v ( - p e - T) ; D t ( ) = ( - v) ( - t ) =, : e ( p e ) = ( p e, : : - t ( - v) ( - - t). (4) - c e ) D e ( p e ) ; t ( ) = ( - c t ) D t ( ). (5) p 3 e = 2 ( + c e - T) ; p 3 t = 2 ( + c t - t). (6) 3 e ( p 3 e ) = 4 v ( - c e - T) 2 ; 3 t ( p 3 t ) =, : 3 e ( p 3 e ) = 2 ( + c e + T) ; 3 t ( p 3 t ) = 4 ( - t) ( - v) ( - c t - t) 2. (7) 2 ( - t) ( + c t - t), (8) China Academic Journal Electronic Publishing House. All rights reserved.

6 D 3 e ( p 3 e ) = 2 v ( - c e - T) ; D 3 t ( p 3 t ) = 2 ( - t) ( - v) ( - c t - t). (9) e < t. 3 e < t, ( c e + T), c e + T < - t. e < t 3 e ( p 3 e ) 3 t ( p 3 t ),. c t. 4 e < t, v, v - t 2 - t,., = 4 v ( - c e - T) 2-3 e ( p 3 e ) - 3 t ( p 3 t ) = 4 v ( - c e - T) 2-4 ( - t) ( - v) ( - c t - t) 2, 4 ( - t) ( - v) ( - c t - t) 2. c t c e + T = - t, = ( - c t - t) 2 4 ( - t) 2 [ v (2 - t) - ( - t) ] 0, v - t 2 - t < 0, v < - t 2 - t c t c e + T < - t v - t 2 - t, 3 e ( p 3 e ) - 3 t ( p 3 t ) > ( - c t - t) 2 4 ( - t) 2 [ v (2 - t) - ( - t) ] 0.. 4,,,,,,. 5 Friberg et al (2000,200), v, e t e < t ( Friberg et al v = e t ),,., e t,,,,, ;,. e < t,,, v,.,, : ; ;.,. : [ ] Bakos J Y. Reducing buyer search costs : Implications for electronic marketplaces [J ]. Management Science, 997, 43 (2) : China Academic Journal Electronic Publishing House. All rights reserved.

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