Cooperative game theory models for allocation problems applied to the distribution of CO₂ emission permits

In this thesis, we approach the problem of CO₂ emissions as a bankruptcy problem. In our study, we consider that the countries of the European Union (EU) are agents that claim the right to emit. However, the sum of all claims is more than the amount of CO₂ emissions decided by the Kyoto protocol. This study concerns the emissions of the countries for 5 years, from 2010 to 2014. First, we used the classical bankruptcy methods to determine the allocations of each country. By looking separately at each method and its evolution over time, we found that the constrained equal awards (CEA) method is the most appropriate method for our problem. Then, we introduced as a weight a first parameter representing the GDP and we noticed the influence of adding parameters in the distribution of allocations. In a second step, we studied the bankruptcy problem with two weights (GDP and renewable energy production) from an algorithmic approach, on the one hand, for the method that does not favor any criteria. This method offers the best allocations to countries that respect a balance threshold between CO₂ emissions, GDP production, and renewable energy production. On the other hand, we have implemented a method giving priority to one of the weights and have tested the two situations where GDP is favorable and then a situation where renewable energy production is prioritized. Throughout our study, we compared the results of the allocations generated by the different methods used and classified the countries into similar groups using the k-means classification method, with the aim of highlighting the impact of the groups' votes during negotiations and decisions making at the European Council. (author)