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1 = − 2 1<br />
2<br />
; 2 = 2<br />
2 − 1 +− 2<br />
2<br />
− 2 2<br />
2<br />
(17)<br />
From maximizing the private platform’s profit,wecanobtaintheprivate<br />
platform 2’s advertising level, so:<br />
2 = 2 − 1 + <br />
(18)<br />
2<br />
By substituting the level of advertising (18) in the profit functions (17)<br />
we obtain the profits:<br />
1 = − 2 1<br />
2<br />
; 2 = ( 2− 1 +) 2<br />
− 2 2<br />
8 2<br />
<br />
We now consider the platforms’ quality choices, so the publicly-owned<br />
platformmaximizesthesocialwelfareandtheprivateonemaximizesher/his<br />
profit. Taking into account that platform 1 does not obtain any revenue from<br />
advertising, the social welfare ( )atthefirst stage is now given by:<br />
= 2 − 2 + ( 1− 2 +3)(3( 1 − 2 )+)<br />
16<br />
+ (−1)( 2− 1 +) 2<br />
8<br />
− 2 1<br />
2<br />
− 2 2<br />
2<br />
(19)<br />
where the platforms’ profits () and consumer surplus ()aregivenby:<br />
= 1 + 2 = ( 2 − 1 + ) 2<br />
8<br />
− 2 1<br />
2 − 2 2<br />
2<br />
(20)<br />
= 2 − 2 + ( 1 − 2 +3)(3( 1 − 2 )+)<br />
16<br />
− ( 2 − 1 + ) 2<br />
8<br />
From the first order conditions in the first stage of the game, we can<br />
obtain the reaction function of each platform:<br />
1 ( 2 )= (2−7)+(2+1) 2<br />
; <br />
2−8+1 2 ( 1 )= (− 1)<br />
4+<br />
From the intersection of platforms’ quality reaction functions, we obtain<br />
the levels of advertising, market shares and profits at the SPE of this game:<br />
9<br />
11