An application of cooperative bargaining theory to an allocation problem in medicine
6 Results and outlook
In the final section we summarize the results of this work. First, we present the theoretical results of both versions of the model. We explain the property mix fulfilled by two solution concepts in both models and compare the Nash and the Kalai/Smorodinsky solutions. Second, we reflect upon properties and solutions within a medical health system. We discuss two interpretations of the solution concepts and give examples from medicine that support theoretical results. Finally, we conclude with an outlook. We discuss an application in other areas beside medicine and state further research questions. 6.1 Theoretical results of the medical allocation problem In the basic version (chapter 3) of the model we apply bargaining theory to the simple case of two groups with one patient in each group. By assumption these two patients are representatives for patients in their groups. Here, the bargaining concepts of Nash and Kalai/Smorodinsky lead to the same unique solution. Each patient receives treatment with the probability of ½ such that a patient realizes equal (proportional) expected gains in living quality compared to the status quo. This is equivalent to equal (proportional) expected decreases in living quality compared to the ideal point. In this special case the solution concepts of Nash and Kalai/Smorodinsky represent a special egalitarian principle. On the bargaining set of the considered two-person cases in the basic version of the model the solution mechanism of Nash and Kalai/Smorodinsky can be uniquely characterized by the properties of weak Pareto efficiency, symmetry, and invariance under positive affine...
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