The purpose of this study is to model people's behavior on both sides of the kidney market. The healthy person decides to donate a live kidney (for a certain amount) on the supply side. On the demand side, the patient chooses between the two existing kidney queues, the living kidney and the cadaveric kidney, based on the individual's income and belief from the waiting time in each of the two queues. The sick person faces two critical risks in life: risk of death and kidney failure. To model these two risks, it is assumed that each person has a level of health that consists of two deterministic and stochastic parts. In this way, with a deterministic rate, a person's health level will decrease...