Contributions in cooperative game theory and applications

Resumo

This thesis is framed within the scope of cooperative game theory and it is structured in three independent parts, each of one devoted to a different topic. The first part is devoted to the analysis of two centralized inventory probles without holding costs. For every model, we determine the optimal inventory policy and the associated cost game is theoretically studied, by defining cost allocation procedures. For the inventory model with two acquisition costs, the structure of efficient coalitions can be determined using mathematical programming results. In the case of assuming general transportation costs, we establish conditions under which cooperation is profitable and we define a core allocation, close to the Shapley value of airport games. The second part focuses on analysing general sequencing problems in a single machine, where processing costs are given by non-linear functions. We study the case of exponential and logarithmic costs. The main goal in this class of problems consists of determining the optimal order of processing the jobs. Once it is obtained, we analyse the cost savings obtained by rearranging the jobs from a game-theoretic approach. In contrast to the linear case, the notion of neighbour switching gain is generally redefined in terms of a time-dependent function. The establishment of general conditions on this function characterize the optimal order in some special cases and ensure the convexity of the associated cost savings game. The last part of this thesis analyses methodologies in the approximation of two coalitional values with prior unions: the Owen value and the Banzhaf-Owen value, respectively. Specifically, several sampling techniques base the proposed procedures for their estimation. After the analysis of the statistical properties of the estimators, results are established to bound the error when estimating the coalitional values under this approach. We complete this study with the evaluation of our proposals on different examples in the literature, in order to calibrate the quality of the provided approximations.