Gladkova Margarita Graduate School of Management St. Petersburg State University, Russia E-mail: rita.gladkova@gmail.com Supervisor: Nikolay A.Zenkevich GAME-THEORETICAL MODEL “QUALITY-PRICE” UNDER COMPETITION ON THE INDUSTRY MARKET December, 2007 Model assumptions • Customer: i N , N {1,2}; s2 s1 , 1, 0 s p, U ( p, s ) 0, p s p s • Decision-making process: si si si s0 , si s, si , pi 0 pi Company’s profit function i pi , p j , si , s j , si , s j pi Di pi , p j , si , s j csi F si ; i, j 1,2 pi , Di ( pi , p j , si , s j ), c( si ), F ( si ) si s0 , si s, si , pi 0 Cost functions: 2 1. c( si ) ksi , k 0 2 2. F ( si ) bsi s0 , b 0 Covered market: D1 ( p1 , p 2 , s1 , s 2 ) p 2 p1 s 2 s1 p 2 p1 D2 ( p1 , p 2 , s1 , s 2 ) s 2 s1 Uncovered market: D1 ( p1 , p 2 , s1 , s 2 ) p 2 p1 p1 s 2 s1 s1 p 2 p1 D2 ( p1 , p 2 , s1 , s 2 ) s 2 s1 Covered market. Solution If (2 ) 2 [ s, s 0 ] 18k s1 * s0 * s 2 s0 * 2 2 2 s p1 3 18k 2 p * 2 2 s 18k 2 3 s1* s 2 * (2 ) s2 18k * 2 D1 3 D2* 2 3 * 2 2 (2 ) 2 2 s k s 1 9 18k 4 2 (2 ) 2 * 2 s 324k 9 Covered Market Parameters (2 ) [ s, s 0 ] 18k Quality ranges Firm 1 Firm 2 2 s s s (2 ) 2 s0 18k 0 s 0 Differentiation level s, s s2* s s, s s0 s s, s s2 s * 2 s 0 NE quality levels 0 0 0 s * 2 * 2 * Uncovered Market Parameters 0.0241 0.1266 k 0.1266 k 0.1266 0.1266 2 k s , s0 s, s, s0 s , s0 , Firm 1 s 0 Firm 2 s s s s 0 0 s2 s, s s s0 s s2 0 0 * 0 2 k s , s s2* s1* s s2** s1** ** 1 0 s 0 Differentiation level * 2 0 s 0 NE quality levels * 1 s0 2 k 2 k 0.0241 2 k s , s0 , 2 k 0.0241 2 0.0241 2 Quality ranges ** s *** 1 , s2** *** 2 ,s s2*** s1*** s, s s0 s s, s s2 s 0 ** 2 **