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Distributing medical resources

An application of cooperative bargaining theory to an allocation problem in medicine


Antje Köckeritz

Allocating scarce medical resources has become an important topic in public discussion. In the German statutory health system we are facing a situation of lacking adequate funds for all needs. The financial restrictions force us to use resources wisely. This emphasizes the need of general allocation rules and criteria applied in medical allocation situations. The purpose of this work is to implement and interpret properties of cooperative bargaining theory to special allocation situations in medicine. The author shows how the concepts of Nash and Kalai/Smorodinsky can be applied to a medical allocation problem and discusses implications of their properties and solutions for the German health system.


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is greater than ≤ is less than or equal to ≥ is greater than or equal to is not equal to = is equal to for all there exists is an element of is not an element of is a subset of is a subset Is intersected with product of sum of Max maximum of Min minimum of ch convex hull of αi parameter for positive affine transformation βi parameter for positive affine transformation permutation set of all groups V and W number of sequence Μ Kalai/Smorodinsky solution μi Kalai/Smorodinsky solution for i Ŋ group of persons/ patients A2 set of allocation problems for a A allocation problem Bn+, B2+, 2~B BV+, BW+ class of bargaining problems C vector of chances ci chance for i to receive treatment 16 C set of chance vectors ic chance of not receiving the medical good for i D condition of being treated D condition of not being treated D status quo di status quo for i E chance of success F set of feasible deterministic allocations F bargaining solution fi bargaining solution for i G set of feasible deterministic allocations of chances of success H allocation rule I group of patients I person, group J group of patients J person K number of persons L, L~ , L’ set of chances of success LSYM set of all symmetric allocations of chances of success LWPO set of all weakly Pareto optimal allocations of chance of success l, l~ vector of chances of success li, il ~ chances of success for...

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