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Distributing medical resources

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

Series:

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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Table of figures ................................................................................................ 11 Table of abbreviations ...................................................................................... 13 Table of symbols .............................................................................................. 15 1 Motivation ................................................................................................... 19 2 Scarce resources in the German health system – an overview ...................... 23 2.1 Introduction to the German statutory system .............................................. 23 2.2 Examples of medical bargaining situations ................................................. 28 2.3 Interdisciplinary discussion of scarce medical resources ............................ 33 2.3.1 Interconnectedness ....................................................................... 33 2.3.2 Notations and Methods from health economics ............................ 34 2.3.3 Results from FOR 655 „Prioritizing in medicine“......................... 36 2.3.4 A specific medical allocation problem .......................................... 40 2.4 An introduction to cooperative bargaining theory ....................................... 41 2.4.1 The notion of bargaining .............................................................. 41 2.4.2 The Nash concept ......................................................................... 44 2.4.3 The Nash bargaining solution ....................................................... 46 2.4.4 The Kalai/Smorodinsky bargaining solution for two groups of patients (n = 2).............................................................................. 49 2.4.5 The Kalai/Smorodinsky bargaining solution for more than two groups of patients (n > 2) .............................................................. 51 3 A cooperative bargaining model for two groups of patients ......................... 55 3.1 Introduction ................................................................................................ 55 3.2 Definition of an allocation problem ............................................................ 56 3.2.1 An example .................................................................................. 59 3.2.2 A cooperative bargaining problem of chances of success ............. 62 3.3 Axiomatic characterization and solution concepts ...................................... 65 3.4 Results and Conclusion .............................................................................. 70 4 A cooperative bargaining model with two patients groups, their individual needs and different group size ..................................................................... 73 4.1 Introduction ................................................................................................ 73 4.2 The model .................................................................................................. 74 4.3 A cooperative bargaining model ................................................................. 81 4.4 Properties and solution concepts from cooperative bargaining theory ........ 83 10 4.5 Results and conclusion .............................................................................. 92 5 Different types of monotonicity in a cooperative bargaining model of distributing medical resources ..................................................................... 97 5.1 Introduction ................................................................................................ 97 5.2 Monotonicity in patients groups ................................................................. 98 5.3 Monotonicity in number...

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