A Two-Sided Market Model of Optimal Price Structure for Instant Messenger

Table 2

The optimal price structure of duopolistic IM platforms when advertisers choose multi-homing.

	𝑐^𝐴+𝜏>𝛼+((1/2)𝛽−𝑐^𝑡+𝜃)((3/2)𝛽−𝑐^𝑡+𝜃)4	𝑐^𝐴+𝜏<𝛼+((1/2)𝛽−𝑐^𝑡+𝜃)((3/2)𝛽−𝑐^𝑡+𝜃)4
𝛽+2𝑐^𝑡>2𝜃	𝑝^𝐴=𝑐^𝐴()+𝜏−𝛼−1/2𝛽−𝑐^𝑡+𝜃(3/2)𝛽−𝑐^𝑡+𝜃4,	𝑝^𝐴=0,
	𝑝^𝑡=𝛽+2𝑐^𝑡−2𝜃4,	𝑝^𝑡=𝛽+2𝑐^𝑡−2𝜃4,
	𝜃𝑟=𝛽−2𝑐^𝑡+2𝜃8	𝜃𝑟=𝛽−2𝑐^𝑡+2𝜃8
	𝑐^𝐴+𝜏>𝛼+𝛽𝜃−𝑐^𝑡	𝑐^𝐴+𝜏<𝛼+𝛽𝜃−𝑐^𝑡
𝛽+2𝑐^𝑡<2𝜃	𝑝^𝐴=𝑐^𝐴+𝜏−𝛼−𝛽𝜃−𝑐^𝑡,	𝑝^𝐴=0,
	𝑝^𝑡=0,	𝑝^𝑡=0,
	𝑟=𝛽𝜃4	𝑟=𝛽𝜃4

Note: the first and third rows and the first column of Table 1 list different combination of parameter region. The optimal price structure is summarized in the cells located in the second and fourth rows of Table 2.