The bankruptcy problem involves the distribution of perfectly divisible goods. Particular attention is paid to the situations, where the amount of goods available is not enough to cover the demand. An example of real life situations that can be solved using various bankruptcy rules may be a division of a heritage or when a company goes bankrupt and its estates are sold to satisfy interested parties' claims. This paper introduces to the problem a linear structure of the participants, meaning that participants are now satisfied one after another in a preset order. It applies the equal awards (CEA) and the equal losses (CEL) solutions on the revised problem. Since their axiomatization is no longer valid, both solutions are extended and new characterizations are given in the thesis. The thesis contains a series of original proofs for both extended solutions and whole problem is examined in the setting of the well-known river sharing problem.

The economic growth and the increase in population has led to an increased demand for water for various purposes such as domestic consumption, irrigation, industrial use, power generation, navigation, recreation, and ecological requirements. With the increase in population, the per-capita water availability is continuously decreasing. Due to increase in demand and accompanying scarcity of water the conflict among the potential users of the resource is on raise. Hence, the allocation of the available water resource is a big challenge as the intersect oral and inter-regional water allocation is often competing and conflicting in nature. In the above context a good model to manage the available water resources would require reliable inputs on the available water resources. In the first part of this thesis we compare different techniques that are typically used for modeling the river water flow. Time series analysis (ARIMA) is compared with machine learning techniques such as support-vector regression (SVR) and neural network models. The performance of these techniques is compared by applying them to a long-term time-series data of the inflows of three tributaries of the river Cauvery into the Krishnaraja Sagar reservoir (KRS). Flow data over a period of 30 years from three different observation points established in upper Cauvery river sub-basin is analyzed. Specifically, a multi-layer feed forward network trained with a back-propagation algorithm and support vector regression with epsilon-insensitive loss function is compared with the ARIMA models. It is found that the performance of support vector regression model is superior to those of the other techniques considered. The second part of our thesis is to develop a model for optimal water allocation to the different sectors with the aim of maximizing the total utility of available water resource in a river basin. A hydro-economic modeling framework is developed that incorporates the economic assessment of the value of water. This inter-sectoral allocation problem is studied in the context of enforcing certain minimum water rights to every person for domestic use and a certain minimum irrigation need set out by the contingency plans of the state agriculture department in Cauvery river basin. A non-linear optimization model is built to obtain an optimal inter-sectoral water allocation policy. The study evaluates the economic impact of different parameters of competing demands such as water availability, population, basic water right (quantity), ground water contribution, and crop benefit. The optimal policies that implements the water allocation priorities as set out by the National Water Policy (2012) are compared. Further, results show that the basic water right can be secured for essential needs with optimal management of available surface and ground water resources. In the third part of thesis, we study the conflict of water sharing that arises between sectors/regions. We consider the river water-sharing problem between two agents along a river. Each agent has a stated claim to the river water. The Absolute Territorial Sovereignty (ATS) and Absolute Territorial Integrity (ATI) principles are promoted by different agents along the river as a means to maximize their individual benefit. However, these principles are invariably considered to be unjust by one or more of the other agents. Hence, it is preferred to have a negotiated water treaty that is perceived to be equitable and just by all. A one way downstream stream bilateral bargaining model can be used to guide the negotiated water treaty between the agents. In this bargaining framework we introduce the issue of negative externalities imposed by the upstream agent on the downstream agent/s in the form of pollution and/or flooding. This imposes a cost on the downstream agent to mitigate losses due to the negative externalities. A bargaining model that incorporates the impact of negative externalities is developed to guide the negotiated treaties. We identify individually rational bargaining strategies for a two agents transferable utility one way downstream river water sharing problem. The results characterize the agreement and disagreement points for bilateral trading