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Top1. Introduction
Patient’s level of satisfaction with hospital care is to be considered if they were to visit the hospital. Nurses play a vital role in taking care of patients by providing services such as on-time-injection, cleaning, blood pressure check-up and sort out different problems faced by patients. So, sincere nurses are important to the hospital and patients. Since different types of the patient come, so each patient may not require the same number of nurses or the same type of nurses. Different type of nurses may be required for different types of diseases e.g., Cardiac patients require nurses, an expert in dealing with cardiac-related ailments. Again, according to the availability of doctors and patient’s conditions, different types of nurses can be assigned. It is unnecessary to assign nurses with no experience in a specific department and overqualified (Rafii, F., Hajinezhad, M. E., & Haghani, H., 2008). It is also unnecessary to assign nurses with over experience to normal patients. Thus, nurses are assigned to patients according to their educational qualification & experience together with suitability match for patients.
Generally, the main aim of the patient is to get effective care and satisfactory services. The factors for a patient emphasise for visiting the hospital is treatment and proper nursing care (Azizi-Fini, I., Mousavi, M. S., Mazroui-Sabdani, A., & Adib-Hajbaghery, M., 2012). There are various grades of nurses ranging from registered nurses to junior nurses. Because of varied training and specializations, specific types of nurses are to be staffed for a word, requiring specific skills. The salary of the nurses is considered according to their qualification, experience and performance. From a patient’s point of view, the cost of the nurses will be considered according to the type of service they provide and how much time they serve. Time may be hourly or per day or monthly (McGivern, S., 1999).
According to Robert J. Aumann, a Game theory is an optimal decision-making process in the presence of others with different objectives (Hart, S., 2006). Game theory is a mathematical theory of interactive decision-making process based on situations. These situations are characterized by a group of agents where each agent has to make a decision, an outcome that results as a function of the decisions of all agents and each agent has his preferences on the set of possible outcomes. A mathematical decision theory (on the basis to develop game theory) is to be developed for situations in which several decision-makers interact. Decision theory deals with problems and in a decision problem, there is a decision-maker who has to choose one or more alternatives out of a set A (say) (Edwards, W., 1954). The decision-maker has to consider over A, which are usually modelled through a binary relation RÌA×A referred to as “alternative relation” in our context. Here aRb is interpreted as the decision-maker either prefer an over b or is indifferent between a and b. Requirements are imposed on R as follows:
R is symmetric i.e. a R b & b R aR is transitive i.e. a R b, b R c implies a R c
The Nash Equilibrium is a concept of game theory, where the optimal outcome of a game is no player has an incentive to deviate from his chosen strategy after considering an opponent’s choice. Overall an individual can receive no incremental benefit from changing actions assuming other players remain constant in their strategies. A game may have multiple Nash Equilibrium or none at all (Myerson R. B., 1978). In the Nash Equilibrium, we may not reach an equilibrium point. So perfect equilibrium may be used to reach an equilibrium point. Here sub-game is found and of that sub-game, Nash equilibrium is to be found called subgame perfect equilibrium (Fudenberg, D., & Levine, D., 1983).