Consider an online support group that tackles opioid addiction patients. This is an example of digital health social network (DHSN).

Suppose that there are 2 potential influencers and 40 potential patients.

• Let n1 be the number of influencers who decide to join the network.
• Let n2 be the number of patients who decide to join the network.

Assume that a patient/influencer will join the network if and only if his/her willingness to pay is higher than or equal to his/her time cost.

The time cost of joining the network is $20 and $5 for influencers and patients, respectively. Assume the willingness-to-pay functions described below are expressed in dollar value.

Influencers (side 1) are content contributors, their willingness-to-pay function (u^I) of joining the network is:

If n2 = 0, u = 0. If n2 > 0, ul = 2*n2 n1 Patients (side 2), who seek help, have the following willingness-to-pay function (u ): If n1 = 0, up = 0. If n1 = 1: u =10, for n210. [Too many participants > congestion! ]3 . If n1 = 2: u =10, for n220. 0.05*n2