J. JASKOLD GABSZEWICZ, J.-F. THISSE ON THE NATURE OF COMPETITION WITH DIFFERENTIATED PRODUCTS. ( 0 9. Shaked, Sutton, 1985).

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1 б * J JASKOLD GABSZEWICZ J-F THISSE ON THE NATURE OF COMPETITION WITH DIFFERENTIATED PRODUCTS 0 б (883) (95) б б (Hotelling 99) б б (d Asremont et al 979) б : б ( б ) б б б б б б б б : * Economic Journal 986 Vol 96 P 60 C б б ( 0 9 Shaked Sutton 985)

2 б б б б б : б б б б б б б б б б б б б б б 0 I б ( б ) 0 6 б ( [0 ]) б (979)

3 б I II б 0 s б 0 s s э s s s й S I = [ 0 ] ( ) б б 0 s щ б 0 s щ s s s 0 S II = [ ч [ б ( I) б s s ( б ) б б s s s б б б ( II) t s s Д б tss Д ( ) : tss ( Д) = cs 6с s Д + ds ( 6с s Д ) c> 0 d> б 0 6 c > 0 d = c = 0 d > ( 0 9 d Asremont et al 979)

4 б б б б б ; II б I б б s = 6с a s = + a э a э б б ( ) б ( ) б б x( ) б x( ) : + cs 6с x + d( s 6с x) = + cs 6с x + d( s 6с x) x( ) x( ) x( ) s s б б б б 0

5 б б ( s < x( ) < s) 0 0 б : 0 8 ( ) = щ Д = + ac + ad; I = 6с + ac + ad Д > щ Д Д = + ac + 4a d; = 6с + c + ad Д Д > щ Д Д Д = 6с ac 6с 4a d; + c = 6с + ad 6с ac Д Д Д > щ Д Д Д Д = 6с ac 6с ad; = Д Д Д Д > щ б = Д Д Д б б s = + a

6 б : б i Pi( i j) = = i = i i( i j) ( ) ( I) 0 0 б б б б б ( ) б б б б б

7 б a ( ) c d ( б ) ( ) б ( б б б б б б б ) б ( ) б 0 б б б б б ( ) I II б x( ) x( ) ( ) б x : c( s 6с x) + d( s 6с x) = + c( s 6с x) + d( s 6с x) x( ) = ( ) ( ) ds ( 6с s) 6с + c s 6с s + d s 6с s (978) б б

8 : 0 8 ( ) = щ + c( s 6с s ) + d( s 6с s ) = Д ; 6с c + d( s + s) = ds ( 6с s) d II = Д Д > щ 0; ( )( ) ( ) Д > щ Д Д = + c 6с d s 6с s + d s 6с s ; б б б (modified zero conjectural variation ZCV) б б б ZCV б б б

9 б ( ) = щ + ( d 6с c)( s 6с s ) 6с d( s 6с s ) = Д ; 6с d 6с c 6с d( s + s) = ds ( 6с s) d = Д Д > щ 0 ( ) ( ) Д > щ Д Д = 6с c s 6с s 6с d s 6с s ; i i( i j) = 0 8 ( ) i = P = i i i j б б s s б б (99) б б : б ( б ) б ( s s ) [ ( ) s s ( s s ) ] i ( j ) s i (s j ) : ( ) ( ) = ( ) 0 8 ( ) ( ) P ; ; i 6В5 6В7si sj i si sj j si sj 6В8 6Ь0 i si sj i 6В5 6В7si sj i si sj j si sj 6В8 6Ь i () б i б s s [( ) ( )]

10 s й S ( 0 5 S ) i = : 6я6 i I II I) = ( s s ) = ( s s ) II) P s s; ( s s ) ( s s ) щ P s s ; ( s s ) ( s s ) 6В5 6В7 6В8 6Ь0 6В5 6В7 6В8 6Ь0 i i j i i j j i j i i j i i j j i j si й SI ( 0 5 S II ) б б б б б б I б ( s s ) б б б б б б 0 9 б б б II? б ( s s ) : ds ( ) ( ) ( ) + s + + c s s = s 6с s (Selten 975)

11 б d ( ) ( ) ( 4 6с s ) 6с s 6с c s s = s 6с s c/ d < 4 6с s 6с s ( s s ) = ( s 6с s )[ d( s + s 6с ) + c] ( s s ) = c/ d щ 4 6с s 6с s d э c P [ ( ) s s; s s ( s s ) ] б P [ ( ) s s; s s ( s s ) ] s б 0 s 0 9 S II s й SII [( s )( s )] = = ({ ( s 6с ) [ d( s 6с ) + c] } ( s 0) ) d э c d > c s б б c/ d < 4 6с s 6с s s s й SII s = s dp [ s; ( s) ( s) ] ds = 0 0 s = ( d 6с c/ 3 d) d > c d > c ( ) ( ) 6Ж9 6Ь d 6с c 6В5 d 6с c 6В8 6Ь5 [( s ) ( s ) ] = 6В0 6Ь 4 d + + c 6Ь6 6В 6Ь3 9d 6В7 6В6 3 6Ь0 6Ь7 6В9 6Ь ( d 6с c) ( d 6с c) 6В5 ( d 6с c) 6В8 6Ь5 6В 6Ь + d 6с 6с c 6Ь6 6В3 6Ь3 3d 9d 6В6 6В7 3 6В9 6Ь0 6Ь7 6В c/ d щ 4 6с s 6с s б

12 б (d э c) б б 9 III б б б 0? б б б ( ) б б б s s Д t s 6с s Д б б (Gabszewicz Thisse 979) б ; 0 0 б б б б II ( ) (98) t

13 б б б t б б I II б б x( ) б I x : + t( x 6с s ) = + t( x 6с s ) II x : + t( s 6с x) = + t( s 6с x) б I б 0 6 x s s б б 0 6 dx t Д Д ( x 6с s) 6с t Д Д ( s 6с x) = 6с 3 d [ t Д ( x 6с s ) + t Д ( s 6с x) ] ( ) = x( ) б б x б dx/ d э > t( s s) Д = + t( s s) б 0 x( Д ) = s Д Д = 6с t( s s) б x( Д Д ) = s : dx d dx = 6с d ( Д ) ( Д Д ) б 0 6 x ;

14 б 0 б dx / d [ Д Д Д ] б dx/ d x б б 0 dx t Д Д ( s 6с x) 6с t Д Д ( s 6с x) = d [ t Д ( s 6с x) 6с t Д ( s 6с x) ] б б б 0 б i б x б б I dx / d б t Д Д I II 0 9 б б I б б 0 б б I II б б б б II 0 0 б (985) б б б

15 б I Ж9 c 6В a э 0 8 и м 6В0 6В3 ( 0 8) 6В3 d + c 6В ( ) : ( ) D = {( ); / 6с a э x( ) э / + a} D x( ) с + ad + c + c 6с + ad + c P( ) = + c 6с + ad + c P( ) = + c б = = ad + c P ( ) = ad + c б : { ;0 ( ) } D = э x < 6с a ( ) x 6с + ad + ac = { ;/ ( ) } D = + a < x э ( ) x 6с + ad 6с ac = б б x [0 ч ) б 0 % = ad + ac + c б 0 6 x( % ) > 6с a б D 0 D ( )

16 б D ( 0 8) б P ( ) x( ) = 0 5 = c( 6с a) 0 7 б ( 0 8) б 0 P( ) > P( ) 0 6 D б : ( ) D 0 0 D = {( ); / + a < x( ) э } 6с + ad 6с ac x( ) = 6с + ad 6с ac P( ) = 6с + ad + ac P( ) = б ( dp d = 0 dp d = 0) x( ) > + a ( ) D x( ) = б P ( ) = D б : ( ) й D = {( ); 0 э x( ) < 6с a} б б б II б : ds ( ) ( ) ( ) + s + + c s s = s 6с s 3 d ( ) ( ) ( 4 6с s ) 6с s 6с c s s = s 6с s 3

17 б c 4 s s d < 6с 6с ( 0 8) ( s s ) = ( s 6с s )[ d( s + s 6с ) + c] ( s s ) = 0 c 4 s s d щ 6с 6с ( 0 83) ( ) ( б ) б ( 0 8) D = {( ); 0 8 ( ) > ( ) > 0} : 0 8 ( ) = ( ) ( ) ( ) ds ( 6с s) 6с + c s 6с s + d s 6с s 0 8 ( ) = ( ) ( ) ( ) ds ( 6с s) 6с + ds 6с s 6с cs 6с s 6с ds 6с s й D : dpi = 0 d i = i ds ( ) ( ) ( ) + s + + c s s = s 6с s 3 d ( ) ( ) ( 4 6с s ) 6с s 6с c s s = s 6с s ( 0 8) й D б > ( )

18 i i j > i i j i б i j б б 0 6 P( ) P( ) i = { ; ( ) 0} D = 0 8 = i i j i j = ( s 6с s )[ d( s + s 6с ) + c] 3 i ( 0 8) б 0 б 0 6 P( ) P( ) ( ) й D > ( 0 83) б 0 6 ( ) D = {( ); 0 8 ( ) = } б б б L = ( s 6с s )[ d( s + s 6с ) + c] L ( 0) = б L < б 0 6 L dp d < > ( 0 83) = L Bertrand J Th orie math matique de la richesse sociale // Journal des Savant 883 Vol 48 P 499 C508 d Asremont C Jaskold Gabszewicz J Thisse J-F On Hotelling s stability in cometition // Econometrica 979 Vol 47 P 45 C 50 3 Eaton B C Lisey R G Freedom of entry and the existence of ure rofits // Economic Journal 978 Vol 88 P 455 C469 4 Edgeworth F The ure theory of monooly // 0 0 : Paers Relating to Political Economy London : Macmillan 95 Vol P C 4 5 Hotelling H Stability in cometition // Economic Journal 99 Vol 39 P 4 C57 6 Jaskold Gabszewicz J Thisse J-F Price cometition quality and income disarities // Journal of Economic Theory 979 Vol 0 P 340 C 359

19 б Jaskold Gabszewicz J Shaked A Sutton J Thisse J-F Price cometition among differentiated roducts: a detailed study of Nash equilibrium // London School of Economics ICERD DP Lancaster K Variety Equity and Efficiency New York : Columbia University Press MacLeod W B On the non-existence of equilibria in differentiated roduct models // Regional Science and Urban Economics 985 Vol 5 P 45 C6 0 Selten R Re-examination of the erfectness concet for equilibrium oints in extensive games // International Journal of Game Theory 975 Vol 4 P 5 C55 Shaked A Sutton J Relaxing rice cometition through roduct differentiation // Review of Economic Studies 98 Vol 69 P 3 C3 Shaked A Sutton J Product differentiation and industrial structure // London School of Economics ICERD DP

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