# An Asymmetric Bargaining Model for Natural-Gas Distribution
###### Abstract  
For the sustainable socio-economic growth, the energy supply is one of the foundations for any country. The gas shortage is one of the most significant impediments to any emerging country's economic progress, making it a contested and disputed resource. In the middle of a supply-demand mismatch, distributing limited available gas across administrative units/provinces with competing requirements is a key challenge. In this work, an asymmetric gas allocation bargaining model is proposed under gas shortage to resolve natural gas-related disputes among Pakistan's administrative units/provinces. Each administrative unit/province is characterized by its gas demand. Results show that the Nash bargaining theory, when applied under equal and bargaining weights, can address the supply-demand mismatches of the gas sector in Pakistan. Such an approach could help policymakers to make a fair gas-supply management system during gas shortage periods and would help in resolving the disputes between the provinces. gas demand; gas allocation; bankruptcy problem; Nash bargaining theory +
Footnote †: journal: Applied  
0000-0001-6000-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000  
Pakistan's socio-economic development is heavily dependent on the gas supply. Therefore, the allocation of gas among the provinces must be fair and efficient. The shortage of gas and its allocation among different stakeholders can be addressed from different perspectives. One such technique is the Game-theoretic approach which can be helpful for equitable resource allocation among the stakeholders. This approach can help the decision-makers, stakeholders, and planners make the right decision by analyzing and addressing the supply-demand gap for different sectors. Natural resources shared among the countries, states, or provinces can be a major source of conflict and cooperation [5; 6; 7], and natural gas is one of these resources. Nash bargaining solution and bankruptcy concept are the two approaches that allocate the scarce resource among the various stakeholders. Bankruptcy is described in economics as a scenario in which all resources are insufficient to fulfill the stakeholders' demands. The condition during the gas shortage is similar to the concept of bankruptcy. Therefore, the bankruptcy problem concept can be utilized for gas distribution among various Pakistan provinces. In a typical bankruptcy problem, the scarce resources are distributed among the various gas demanding clients/stakeholders using the classical bankruptcy rules and Nash bargaining solution. The constrained equal award, proportional, and constrained equal loss are the most utilized bankruptcy rules [8; 9; 10]. These rules satisfy several desirable properties, and each rule can be used in different bankruptcy scenarios. Bankruptcy theory and Nash bargaining has been applied to various resource allocation scenarios by various researchers [5; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. The available approaches of resources optimal allocation mainly focus on mathematical programming based on group rationality, nucleolus solution concept, and noncooperative game based on individual rationality and of cooperative game based on both individual rationality and group rationality [27]. Cooperative game is a suitable method for the natural resource allocation which achieves both individual profit optimization and group profit optimization [28]. Cooperative game is a transferable utility game which requires strict conditions and requires all the agents to cooperate. The Nash bargaining approach is able to achieve the cooperation among the agents through a noncooperative way. In Nash bargaining solution, two or more players or agents infinitely offer an allocation scheme of payoff or cost from a joint collaboration until both parties accept or disagree with the scheme.