According to the 2009 to 2014 data published by the Ministry of Health and Welfare in Taiwan, the number of private and public hospitals slightly decreased in the five years, but the number of expensive healthcare treating machines increased significantly. The two opposite trends show that, to raise healthcare service quality as well as to attract patients, both for-profit and non-profit hospitals kept acquiring new medical equipment. Since medical equipment is always very expensive, it is important for a hospital to negotiate with vendors to reduce the purchasing costs. The contract format thus matters. Two common ways of acquiring medical equipment in practice are purchasing and renting. In this thesis, our main research objective is to figure out whether the management type of a hospital, i.e., non-profit or for-profit, will affect its preference between renting and buying a treating machine. By adopting game-theoretic modeling, we study the information asymmetry between one hospital as the buyer and one vendor who supplies the medical machine with hidden reliability. We analytically examine how a hospital may reduce the cost raised from the agency problem through contract design, how the contract format is dependent on the optimal treatment price, and the impact of the hospital’s management type. Our research finds that if all other conditions are the same, it should be more likely to observe a public hospital renting a machine than a private hospital. We also collect the acquisition records of one machine from 27 hospitals in Taiwan. We conclude that our theoretical finding is indeed supported by the empirical data.