Coalition Structure Generation Utilizing Graphical Representation of Partition Function Games

Abstract

Forming effective coalition is a central research challenge in AI and multi-agent systems. The Coalition Structure Generation (CSG) problem is well-known as one of major research topics in coalitional games. The CSG problem is to partition a set of agents into coalitions so that the sum of utilities is maximized. This paper studies a CSG problem for partition function games (PFGs), where the value of a coalition differs depending on the formation of other coalitions generated by non-member agents. Traditionally, in PFGs, the input of a coalitional game is a black-box function called a partition function that maps an embedded coalition (a coalition and the coalition structure) to its value. Recently, a novel concise representation scheme called the Partition Decision Trees (PDTs) has been proposed. The PDTs is a graphical representation based on multiple rules. In this paper, we propose new algorithms that can solve a CSG problem by utilizing PDTs representation. More specifically, we modify PDTs representation to effectively handle negative value rules and apply the depth-first branch and bound algorithm. We experimentally show that our algorithm can solve a CSG problem well.

Dividing the Indivisible : Algorithms, Empirical Advances, and Complexity Results for Value-Maximizing Combinatorial Assignment Problems

“…A final welfare function that we investigate from a computational perspective is cross-bundle dependent welfare, which has applications that have attracted considerable interest in the multi-agent systems and game theory literature, see e.g., [153,36,60,135,193,203,124,225]. We refer to the corresponding optimization problem as cross-bundle combinatorial assignment (XCA).…”