Two approximation algorithms for probabilistic coalition structure generation with quality bound

Abstract

AbstractHow to form effective coalitions is an important issue in multi-agent systems. Coalition Structure Generation ($${{\mathsf {CSG}}}$$CSG) is a fundamental problem whose formalization can encompass various applications related to multi-agent cooperation. $${{\mathsf {CSG}}}$$CSG involves partitioning a set of agents into coalitions such that the social surplus (i.e., the sum of the values of all coalitions) is maximized. In traditional $${\mathsf {CSG}}$$CSG, we are guaranteed that all coalitions will be successfully established, that is, the attendance rate of each agent for joining any coalition is assumed to be 1.0. Having the real world in mind, however, it is natural to consider the uncertainty of agents’ availabilities, e.g., an agent might be available only two or three days a week because of his/her own schedule. Probabilistic Coalition Structure Generation ($${{\mathsf {PCSG}}}$$PCSG) is an extension of $${\mathsf {CSG}}$$CSG where the attendance type of each agent is considered. The aim of this problem is to find the optimal coalition structure which maximizes the sum of the expected values of all coalitions. In $${\mathsf {PCSG}}$$PCSG, since finding the optimal coalition structure easily becomes intractable, it is important to consider approximation algorithms, i.e., to consider a trade-off between the quality of the returned solution and tractability. In this paper, a formal framework for $${\mathsf {PCSG}}$$PCSG is introduced. Approximation algorithms for $${\mathsf {PCSG}}$$PCSG called Bounded Approximation Algorithm based on Attendance Types ($${{\mathsf {BAAAT}}}$$BAAAT) and Involved $${\mathsf {BAAAT}}$$BAAAT ($${{\mathsf {IBAAAT}}}$$IBAAAT) are then presented. We prove a priori bounds on the quality of the solution returned by $${\mathsf {BAAAT}}$$BAAAT and $${\mathsf {IBAAAT}}$$IBAAAT with respect to the optimum and perform experimental evaluations on a number of benchmarks.