Elmira rafie - Master degree, Applied mathematics, Tehran Shahed university
Hamidreza navidi - Associate professor, Applied mathematics, Tehran Shahed university

More than 500 million people around the world suffer renal disease and millions of people lose their life annually due to heart and cerebral attacks resulting from chronic kidney disease (CKD), whose most important treatment method is transplantation. Since renal disease is a quiescent illness, it is often diagnosed late. Most hygiene systems and various types of science in different worldwide have become aware of the disease, including game theory. Given games theory deals with game rules and understanding the impact of the rules on the game results, it is an important tool for the design of the mechanism and processes of matching. One of the main difficulties of the kidney market is matching both sides of the market to solve the problems of kidney patients. In this market, a tool is needed to match the supplied and demanded kidneys together and in order to solve the problem we use the market design and matching without using the conventional mechanism (that is without utilizing buy and sale). In this paper, our purpose is to investigate the works done on the matching. In this regard, the studies conducted by Roth et al., can be mentioned. Studying on the market design and making it applicable, Roth succeeded in winning the Noble Economics Prize in 2012. In this paper, in order to solve the matching, we used the pair replacement method and also owing to large numbers of incompatible pairs, we modeled the game in a cooperative way

Game theory, cooperative game, matching, kidney