Resource allocation problems with concave reward functions

Soesja Grundel, Peter Borm and Herbert Hamers ()
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Soesja Grundel: CZ Healthcare, Department Operations
Herbert Hamers: Tilburg University

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2019, vol. 27, issue 1, No 6, 37-54

Abstract: Abstract In a resource allocation problem, there is a common-pool resource, which has to be divided among agents. Each agent is characterized by a claim on this pool and an individual concave reward function on assigned resources, thus generalizing the model of Grundel et al. (Math Methods Oper Res 78(2):149–169, 2013) with linear reward functions. An assignment of resources is optimal if the total joint reward is maximized. We provide a necessary and sufficient condition for optimality of an assignment, based on bilateral transfers of resources only. Analyzing the associated allocation problem of the maximal total joint reward, we consider corresponding resource allocation games. It is shown that the core and the nucleolus of a resource allocation game are equal to the core and the nucleolus of an associated bankruptcy game.

Keywords: Resource allocation games; Concave reward function; Core; Nucleolus; 91A12 (search for similar items in EconPapers)
Date: 2019
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Working Paper: Resource Allocation Problems with Concave Reward Functions (2013)
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DOI: 10.1007/s11750-018-0482-7

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