Complaint, compromise and solution concepts for cooperative games

Abstract

This thesis mainly focuses on solution concepts for cooperative games. We investigate the solution concepts concerning the complaints of players. Motivated by the work the procedural values, we study the formation of the grand coalition and define a new kind of complaint for individual players. We then reveal that the solutions for both models coincide with the ENSC value either based on the lexicographic criterion or the least square criterion. We propose the so called alpha-ENSC value by considering the egoism of players. We implement the alpha-ENSC value by means of optimization and also the satisfier of a set of properties. Following the similar idea, we propose two kinds of complaints for coalitions and define the optimal compromise values based on the lexicographic criterion. It turns out that the optimal compromise values coincides with the ENSC value and the CIS value under corresponding complaint. We show an application of the previous mentioned method. We introduce and axiomatize a class of cost sharing methods for polluted river sharing systems that consists of the convex combinations of the known Local Responsibility Sharing (LR) method and the Upstream Equal Sharing (UES) method. We also deals with the solution concepts based on the compromise between the ideal and minimal payoffs for players, which is inspired by the definition of the tau value but in a more general way. We reveal the relations between the general compromise value with several well known solution concepts. Furthermore, we investigate the solution concepts for cooperative games with stochastic payoffs. We focus on a subset of all allocations and introduce the stochastic complaint for players. Under the least square criterion, the most stable solutions and the fairest solutions are proposed. Moreover, the optimal solution stays the same whether the optimization model depends on the coalitions or individual players.