Ayumi Igarashi

Fair Division of a Graph

We consider fair allocation of indivisible items under an additional constraint: there is an undirected graph describing the relationship between the items, and each agents share must form a connected subgraph of this graph. This framework captures, e.g., fair allocation of land plots, where the graph describes the accessibility relation among the plots. We focus on agents that have additive utilities for the items, and consider several common fair division solution concepts, such as proportionality, envy-freeness and maximin share guarantee. While finding good allocations according to these solution concepts is computationally hard in general, we design efficient algorithms for special cases wherethe underlying graph has simple structure, and/or the number of agents---or, less restrictively, the number of agent types---is small. In particular, despite non-existence results in the general case, we prove that for acyclic graphs a maximin share allocation always exists and can be found efficiently.

Multi-criteria Coalition Formation Games

When forming coalitions, agents have different utilities per coalition. Game-theoretic approaches typically assume that the scalar utility for each agent for each coalition is public information. However, we argue that this is not a realistic assumption, as agents may not want to divulge this information or are even incapable of expressing it. To mitigate this, we propose the multi-criteria coalition formation game model, in which there are different publicly available quality metrics (corresponding to different criteria) for which a value is publicly available for each coalition. The agents have private utility functions that determine their preferences with respect to these criteria, and thus also with respect to the different coalitions. Assuming that we can ask agents to compare two coalitions, we propose a heuristic (best response) algorithm for finding stable partitions in MC2FGs: local stability search (LSS). We show that while theoretically individually stable partitions need not exist in MC2FGs in general, empirically stable partitions can be found. Furthermore, we show that we can find individually stable partitions after asking only a small number of comparisons, which is highly important for applying this model in practice.