scholarly journals Multi-issue bankruptcy problems with crossed claims

2021 ◽  
Author(s):  
Rick K. Acosta ◽  
Encarnación Algaba ◽  
Joaquín Sánchez-Soriano
Keyword(s):  
Allocation Rule ◽  
Real Problem ◽  
Bankruptcy Problem ◽  
Bankruptcy Problems ◽  
Model Study ◽  
Constrained Equal Awards Rule ◽  
Linear Programming Problems ◽  
Divisible Goods ◽  
Constrained Equal Awards ◽  
Novel Model

AbstractIn this paper, we introduce a novel model of multi-issue bankruptcy problem inspired from a real problem of abatement of emissions of different pollutants in which pollutants can have more than one effect on atmosphere. In our model, therefore, several perfectly divisible goods (estates) have to be allocated among certain set of agents (claimants) that have exactly one claim which is used in all estates simultaneously. In other words, unlike of the multi-issue bankruptcy problems already existent in the literature, this model study situations with multi-dimensional states, one for each issue and where each agent claims the same to the different issues in which participates. In this context, we present an allocation rule that generalizes the well-known constrained equal awards rule from a procedure derived from analyzing this rule for classical bankruptcy problems as the solution to a sucession of linear programming problems. Next, we carry out an study of its main properties, and we characterize it using the well-known property of consistency.

The Constrained Equal Awards Rule for Bankruptcy Problems with a Priori Unions

2005 ◽  
Vol 137 (1) ◽  
pp. 211-227 ◽  
Author(s):  
Peter Borm ◽  
Luisa Carpente ◽  
Balbina Casas-Méndez ◽  
Ruud Hendrickx
Keyword(s):  
A Priori ◽  
Bankruptcy Problems ◽  
Constrained Equal Awards Rule ◽  
Constrained Equal Awards

Transboundary water allocation under water scarce and uncertain conditions: a stochastic bankruptcy approach

Water Policy ◽  
2016 ◽  
Vol 19 (3) ◽  
pp. 479-495 ◽  
Author(s):  
Dagmawi Mulugeta Degefu ◽  
Weijun He ◽  
Jian Hua Zhao
Keyword(s):  
Resource Sharing ◽  
Water Allocation ◽  
Stochastic Game ◽  
River Basins ◽  
Allocation Rule ◽  
Transboundary Water ◽  
Constrained Equal Awards Rule ◽  
Game Theoretic ◽  
Water Scarce ◽  
Constrained Equal Awards

Designing a feasible and stable water sharing mechanism for transboundary river basins is a big challenge. The stochastic and uncertain characteristics of water flow in these rivers is among the main reasons which make the formation of cooperative coalitions with feasible water allocations and self-enforceable allocation agreements difficult. When the water in these river basins is scarce the task becomes even more challenging. This article focuses on the application of stochastic game theoretic extension of the bankruptcy concept to transboundary water resource sharing under water scarce and uncertain conditions. Among the water allocation vectors obtained from stochastic bankruptcy rules only the ones from the stochastic constrained equal awards rule were self-enforcing under uncertainty. Furthermore, the authors also proposed an allocation rule that can be used under a stochastic setting. The proposed rule provides water allocations that are self-enforcing in the absence of uncertainty. Generally, the application of the stochastic bankruptcy approach could be a source of important strategic information which can serve for the sustainable sharing and management of these vital sources of fresh water, particularly during water scarcity.

scholarly journals A Simplified Novel Technique for Solving Linear Programming Problems with Triangular Fuzzy Variables via Interval Linear Programming Problems

2021 ◽  
pp. 82-93
Author(s):  
Ladji Kané ◽  
Lassina Diabaté ◽  
Daouda Diawara ◽  
Moussa Konaté ◽  
Souleymane Kané
Keyword(s):  
Linear Programming ◽  
Simplex Method ◽  
Real Problem ◽  
Interval Linear Programming ◽  
Numerical Examples ◽  
Fuzzy Variables ◽  
Novel Technique ◽  
Interval Linear ◽  
Linear Programming Problems

This study proposes a novel technique for solving Linear Programming Problems with triangular fuzzy variables. A modified version of the well-known simplex method and the Existing Method for Solving Interval Linear Programming problems are used for solving linear programming problems with triangular fuzzy variables. Furthermore, for illustration, some numerical examples and one real problem are used to demonstrate the correctness and usefulness of the proposed method. The proposed algorithm is flexible, easy, and reasonable.

scholarly journals Bankruptcy Problem Allocations and the Core of Convex Games

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
William Olvera-Lopez ◽  
Francisco Sanchez-Sanchez ◽  
Iván Tellez-Tellez
Keyword(s):  
Convex Functions ◽  
Tu Game ◽  
Convex Games ◽  
Bankruptcy Problem ◽  
Bankruptcy Problems ◽  
The Core ◽  
Bankruptcy Games ◽  
Bankruptcy Game

A well-known result related to bankruptcy problems establishes that a vector is a bankruptcy allocation if and only if it belongs to the core of the associated O’Neill’s bankruptcy game. In this paper we show that this game is precisely the unique TU-game based on convex functions that satisfies the previous result. In addition, given a bankruptcy problem, we show a way for constructing bankruptcy games such that the set of bankruptcy allocations is a subset of their core or their core is a subset of the set of bankruptcy allocations. Also, we show how these results can be applied for finding new bankruptcy solutions.

scholarly journals Water Allocation Using the Bankruptcy Model: A Case Study of the Missouri River

Water ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 619 ◽  
Author(s):  
Heshani Wickramage ◽  
David Roberts ◽  
Robert Hearne
Keyword(s):  
Water Allocation ◽  
Missouri River ◽  
Water Levels ◽  
Sharing Rule ◽  
Reservoir Water ◽  
Allocation Rules ◽  
Navigation Channel ◽  
Constrained Equal Awards Rule ◽  
Constrained Equal Awards

This research applies cooperative game theory—specifically, the bankruptcy model—to address conflicts arising from the scarcity of water resources shared by multiple agents. This case study addresses potential outcomes of five allocation rules applied to the apportionment of water between two agents in the Missouri River. Currently, there is no interstate compact to apportion Missouri River and frequent disputes between upstream and downstream states occur. Upstream states favor managing reservoir water levels to support reservoir recreation and downstream states want water for the downstream navigation channel. The five allocation rules studied are (1) Proportional Sharing, (2) Constrained Equal Awards, (3) Constrained Equal Losses, (4) Sequential Sharing based on Proportional Sharing, and (5) a proposed Modified Constrained Equal Awards rule. The results of the analysis of apportionment during four dry years in the 2000s show that the best approaches are the proposed Modified Constrained Equal Awards Rule and the Proportional Sharing Rule.

scholarly journals Developing new scenarios for water allocation negotiations: a case study of the Euphrates River Basin

2016 ◽  
Vol 374 ◽  
pp. 9-15 ◽  
Author(s):  
Mohammad Reza Jarkeh ◽  
Ameneh Mianabadi ◽  
Hojjat Mianabadi
Keyword(s):  
Game Theory ◽  
Water Allocation ◽  
Cooperative Game Theory ◽  
Allocation Rule ◽  
Theory Method ◽  
Euphrates River ◽  
Equitable Allocation ◽  
Constrained Equal Awards ◽  
Bankruptcy Theory

Abstract. Mismanagement and uneven distribution of water may lead to or increase conflict among countries. Allocation of water among trans-boundary river neighbours is a key issue in utilization of shared water resources. The bankruptcy theory is a cooperative Game Theory method which is used when the amount of demand of riparian states is larger than total available water. In this study, we survey the application of seven methods of Classical Bankruptcy Rules (CBRs) including Proportional (CBR-PRO), Adjusted Proportional (CBR-AP), Constrained Equal Awards (CBR-CEA), Constrained Equal Losses (CBR-CEL), Piniles (CBR-Piniles), Minimal Overlap (CBR-MO), Talmud (CBR-Talmud) and four Sequential Sharing Rules (SSRs) including Proportional (SSR-PRO), Constrained Equal Awards (SSR-CEA), Constrained Equal Losses (SSR-CEL) and Talmud (SSR-Talmud) methods in allocation of the Euphrates River among three riparian countries: Turkey, Syria and Iraq. However, there is not a certain documented method to find more equitable allocation rule. Therefore, in this paper, a new method is established for choosing the most appropriate allocating rule which seems to be more equitable than other allocation rules to satisfy the stakeholders. The results reveal that, based on the new propose model, the CBR-AP seems to be more equitable to allocate the Euphrates River water among Turkey, Syria and Iraq.

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