On the complexity of the Shapley-Scarf economy with several types of goods

Title:

On the complexity of the Shapley-Scarf economy with several types of goods

Creator:

Cechlárová, Katarína

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:64d55fa5-efdf-45ef-9c0f-a0de575c8267
uuid:64d55fa5-efdf-45ef-9c0f-a0de575c8267

Subject:

Shapley-Scarf economy, core, algorithm, and NP-completeness

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In the Shapley-Scarf economy each agent is endowed with one unit of an indivisible good (house) and wants to exchange it for another, possibly the most preferred one among the houses in the market. In this economy, core is always nonempty and a core allocation can be found by the famous Top Trading Cycles algorithm. Recently, a modification of this economy, containing Q >= 2 types of goods (say, houses and cars for Q=2) has been introduced. We show that if the number of agents is 2, a complete description of the core can be found efficiently. However, when the number of agents is not restricted, the problem to decide the nonemptyness of the core becomes NP-hard already in the case of two types of goods. We also show that even the problem to decide whether an allocation exists in which each agent strictly improves compared to his endowment, is NP-complete.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[689]-700

Source:

Kybernetika | 2009 Volume:45 | Number:5

Harvested from:

CDK

Metadata only:

false