Measuring the price of anarchy in critical care unit interactions

Hospital throughput is often studied and optimised in isolation, ignoring the interactions between hospitals. In this paper, critical care unit (CCU) interaction is placed within a game theoretic framework. The methodology involves the use of a normal form game underpinned by a two-dimensional continuous Markov chain. A theorem is given that proves that a Nash Equilibrium exists in pure strategies for the games considered. In the United Kingdom, a variety of utilisation targets are often discussed: aiming to ensure that wards/hospitals operate at a given utilisation value. The effect of these target policies is investigated justifying their use to align the interests of individual hospitals and social welfare. In particular, we identify the lowest value of a utilisation target that aligns these.