A queuing game theory approach to strategies for supplementing medical alliances with internet hospitals.

With large hospitals actively establishing Internet-based healthcare initiatives to facilitate the downward referral of discharged patients, it is essential to examine the conditions under which such implementations are truly beneficial. This study categorizes medical alliances (MAs) into two types: tightly integrated and loosely integrated. Utilizing queuing-game theory, we constructed a two-stage model to evaluate referral efficiency, measured by the volume of downward referrals from tertiary hospitals and the effort levels exerted by community hospitals. By comparing MAs with and without supplementary internet hospitals, we identify the circumstances in which hospital-established internet hospitals enhance patient referrals. The findings indicate that within tightly integrated MAs, the referral volume increases with the potential patient arrival rate. When the cost coefficient of internet hospitals is low, MAs that incorporate internet hospitals demonstrate both higher referral volumes and increased effort, with profits favored by Internet-based healthcare under low arrival rates. In loosely integrated MAs, effort levels exhibit a similar pattern while referral volume depends heavily on the revenue-sharing ratio of the internet hospital. Specifically, referral volume increases when the ratio is low, arrival rates are high, and cost coefficients remain low. Conversely, at high revenue-sharing ratios, referral volumes rise regardless of the cost coefficient, provided arrival rates are either low or high. For tertiary hospitals, profits are higher with Internet-based healthcare only under low arrival rates when the revenue-sharing ratio is low; this threshold declines as the cost coefficient increases. When the ratio is high, digital healthcare consistently yields higher profits. For community hospitals, a low ratio leads to higher profits only within a moderate range of arrival rates-a range that narrows with rising cost coefficients. Under high ratios, profitability improves only at low arrival rates and increases alongside the cost coefficient.