Multi-issue bankruptcy problems with crossed claims

In 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.

A Double-Weighted Bankruptcy Method to Allocate CO2 Emissions Permits

Global warming, as a result of greenhouse gases, is exceeding the planet’s temperature stabilization capacities. Thus, greenhouse gas emissions must be reduced. We analyse a bankruptcy situation aimed at allocating emissions permits of CO2, the predominant greenhouse gas emitted by human activities. Inspired by the Constrained Equal Awards (CEA) solution for bankruptcy situations, we introduce a new allocation protocol based on the extension of the CEA solution over double-weighted bankruptcy situations, including two exogenous parameters aimed at providing a balance, in the request of emissions permits, between economic activities and the production of renewable energy. In these bi-criteria allocation problems, we focus on a computational approach to find an allocation protocol that does not prioritize any particular parameter. As an application of our method, we first consider CO2 permit allocation problems in European Union (EU) countries, using real data about the gross domestic product (GDP), the production rate of renewable energies, and countries’ ‘demands’ of CO2 emissions from 2010 to 2014. Then, we compare our approach with the CEA solution and its single-weighted extension to show the impact of using two weights over the distribution of CO2 emissions permits; we analyse the correlation between allocations of CO2 emission permits and the distribution of power within the EU Council to study the acceptability of alternative allocations.

Allocation of allowable pollution load by using the bankruptcy solution rules

Bankruptcy solution methods are widely used and efficient methods for conflict resolution which attract considerable attention in the area of solving conflicts related to water resources. However, most of the related studies have focused on the use of bankruptcy solution methods in solving quantitative water resources conflicts. In this study, four bankruptcy solution rules including proportional (PRO), constrained equal awards (CEA), constrained equal losses (CEL), and Talmud (TAL) rules were used to develop four models to allocate the allowable pollution loads to pollution sources. One of the novel aspects of the current study is to consider the amount of each flow discharge in addition to the pollution concentration of each pollution source. Evaluation of performances of the selected bankruptcy solution rules in a reach of Karun River in Iran showed that the CEA-based model can be considered as the most desirable option for small pollution sources whereas the CEL-based model seems to be the most appropriate option for large pollution sources. The models based on PRO and TAL rules provide results between those of CEA and CEL rules which can be considered as more probable options to reach agreement on between small and large pollution sources.

A Game Theoretic Analysis of the Relative Payouts to Operational Creditors and Financial Creditors from Bankruptcy Resolution in India

This paper analyses the outcomes of the cases resolved under Insolvency and Bankruptcy Code of India to examine the treatment of admitted claims for the two main classes of creditors i.e. operational and financial creditors. It shows that, at an aggregate level, operational creditors and financial creditors realize an equal percentage of their claims. However, at an individual level, there is wide heterogeneity in the treatment of the two classes of creditors. Three benchmark division rules – Proportional division, Constrained Equal Losses and Constrained Equal Awards, are used to characterize the actual divisions in each case. This analysis allows us to hypothesize that when aggregate claims of operational creditors are tiny, the Constrained Equal Awards (that is extremely generous to small creditors), does well. When aggregate claims of operational creditors are large, the Proportional rule does well. But when the claims of operational creditors fall in an intermediate range, the Constrained Equal Losses rule which is most unfavourable to the operational creditor comes to the fore. Hence, some broad guidelines that can be applied on a case by case basis appear to be desirable.

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

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.

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

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.

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

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.