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

Table 1

The optimal price structure of monopolistic IM platform.

	𝑐^𝐴≥𝑝^𝑡−𝑐^𝑡+𝑎𝑟𝜀𝑛𝑡^𝑟|𝑛𝑡(1+𝜀𝑡|𝑛)𝑡	𝑐^𝐴≤𝑝^𝑡−𝑐^𝑡+𝑎𝑟𝜀𝑛𝑡^𝑟|𝑛𝑡(1+𝜀𝑡|𝑛)𝑡
𝑐^𝑡≥𝑎𝑟𝜀𝑛𝑡^𝑟|𝑛𝑡	𝑝^𝐴−𝑐^𝐴−𝑝^𝑡−𝑐^𝑡+(𝑎𝑟/𝑛𝑡)𝜀𝑟|𝑛𝑡1+𝜀𝑡|𝑛𝑡𝑝^𝐴=1𝜀𝑝𝐴,	𝑝^𝐴=0,
	𝑝^𝑡−𝑐^𝑡−(𝑎𝑟/𝑛𝑡)𝜀𝑟|𝑛𝑡𝑝^𝑡=1𝜀𝑝𝑡,	𝑝^𝑡−𝑐^𝑡−(𝑎𝑟/𝑛𝑡)𝜀𝑟|𝑛𝑡𝑝^𝑡=1𝜀𝑝𝑡,
	𝑟+𝑝^𝐴−𝑐^𝐴+𝑝^𝑡−𝑐^𝑡+(𝑎𝑟/𝑛𝑡)𝜀𝑟|𝑛𝑡1+𝜀𝑡|𝑛𝑡𝜀𝑛|𝑎(𝑛/𝑎)𝑟 = 1𝜀𝑟	𝑟+𝑝^𝑡−𝑐^𝑡+(𝑎𝑟/𝑛𝑡)𝜀𝑟|𝑛𝑡1+𝜀𝑡|𝑛𝑡−𝑐^𝐴𝜀𝑛|𝑎(𝑛/𝑎)𝑟 = 1𝜀𝑟
𝑐^𝑡≤𝑎𝑟𝜀𝑛𝑡^𝑟|𝑛𝑡	𝑝^𝐴−𝑐^𝐴−(𝑎𝑟/𝑛𝑡)𝜀𝑟|𝑛𝑡−𝑐^𝑡1+𝜀𝑡|𝑛𝑡𝑝^𝐴=1𝜀𝑝𝐴,	𝑝^𝐴=0,
	𝑝^𝑡=0,	𝑝^𝑡=0,
	𝑟+𝑝^𝐴−𝑐^𝐴+(𝑎𝑟/𝑛𝑡)𝜀𝑟|𝑛𝑡−𝑐^𝑡1+𝜀𝑡|𝑛𝑡𝜀𝑛|𝑎(𝑛/𝑎)𝑟 = 1𝜀𝑟	𝑟+(𝑎𝑟/𝑛𝑡)𝜀𝑟|𝑛𝑡−𝑐^𝑡1+𝜀𝑡|𝑛𝑡−𝑐^𝐴𝜀𝑛|𝑎(𝑛/𝑎)𝑟 = 1𝜀𝑟

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