Arbitration, fairness and stability

• Main Author: Yair Zick
• Other Authors: School of Physical and Mathematical Sciences
• Format: Theses and Dissertations
• Language: English
• Published: 2014
• Subjects: DRNTU::Science::Mathematics::Discrete mathematics::Algorithms
• Online Access: https://hdl.handle.net/10356/60824
• Institution: Nanyang Technological University

We study the problem of dividing revenue among several collaborative entities. In our setting, each player possesses a nite amount of some divisible resource, and may allocate parts of his resource in order to work on various projects. Having completed tasks and generated pro ts, players must agree on some way of dividing pro ts among them. Using the overlapping coalition formation (OCF) model proposed by Chalkiadakis et al. [2010] as the basis of our work, we develop a model for handling deviation in OCF games. Using our framework, which we term arbitration functions, we propose several new solution concepts for OCF games. In the rst part of this thesis, we analyze the arbitrated core of an OCF game; we show some necessary and su cient conditions for the non-emptiness of some arbitrated cores, and explore methods for computing outcomes in the core of an OCF game. Next, we describe and analyze the arbitrated nucleolus, bargaining set and two notions of a value for OCF games. All of the solution concepts we propose draw strong similarities to their non-OCF counterparts, and in fact contain the classic cooperative solution concepts as a special case. We conclude this thesis by proposing a solution concept for OCF (and non-OCF) cooperative settings that is based on a natural revenue allocation dynamic. In our setting, player revenue in time t acts as his available resources at time t + 1. Assuming that players are not myopic and care about their long-term rewards, we show that under certain conditions, players' incentives become aligned with what is socially optimal. In other words, choosing a payo division that maximizes long-term social welfare will be agreeable for all players.