Coalitional Resource Games (crgs) are a form of Non-Transferable Utility (ntu) game, which provide a natural formal framework for modelling scenarios in which agents must pool scarce resources in order to achieve mutually satisfying sets of goals. Although a number of computational questions surrounding crgs have been studied, there has to date been no attempt to develop solution concepts for crgs, or techniques for constructing solutions. In this paper, we rectify this omission. Following a review of the crg framework and a discussion of related work, we formalise notions of coalition structures and the core for crgs, and investigate the complexity of questions such as determining nonemptiness of the core. We show that, while such questions are in general computationally hard, it is possible to check the stability of a coalition structure in time exponential in the number of goals in the system, but polynomial in the number of agents and resources. As a consequence, checking stability is feasible for systems with small or bounded numbers of goals. We then consider constructive approaches to generating coalition structures. We present a negotiation protocol for crgs, give an associated negotiation strategy, and prove that this strategy forms a subgame perfect equilibrium. We then show that coalition structures produced by the protocol satisfy several desirable properties: Pareto optimality, dummy player, and pseudo-symmetry.
Bibliographical noteFunding Information:
We are extremely grateful to the referees for their detailed and encouraging comments. This research was supported by a Royal Society travel grant, by the epsrc under project GR/T10657/01 (“Market Based Control of Complex Computational Systems”), by the U.S. Army Research Laboratory and the U.S. Army Research Office under grant number W911NF-08-1-0144, by NSF grant 0705587 and ISF #1357/07.
- Coalitional games
- NTU games
- Solution concepts
- The core