We address the problem of how a set of agents can decide to share a resource,
represented as a unit-sized pie. The pie can be generated by the entire set but
also by some of its subsets. We investigate a finite horizon non-cooperative bargaining
game, in which the players take it in turns to make proposals on how the resource
should for this purpose be allocated, and the other players vote on whether or not to
accept the allocation. Voting is modelled as a Bayesian weighted voting game with
uncertainty about the players’ weights. The agenda, (i.e., the order in which the players
are called to make offers), is defined exogenously. We focus on impatient players
with heterogeneous discount factors. In the case of a conflict, (i.e., no agreement by
the deadline), no player receives anything. We provide a Bayesian subgame perfect
equilibrium for the bargaining game and conduct an ex-ante analysis of the resulting
outcome. We show that the equilibrium is unique, computable in polynomial time,
results in an instant Pareto optimal outcome, and, under certain conditions provides
a foundation for the core and also the nucleolus of the Bayesian voting game. In
addition, our analysis leads to insights on how an individual’s bargained share is in-
fluenced by his position on the agenda. Finally, we show that, if the conflict point of
the bargaining game changes, then the problem of determining the non-cooperative
equilibrium becomes NP-hard even under the perfect information assumption. Our
research also reveals how this change in conflict point impacts on the above mentioned
results.
Funding
Michael
Wooldridge was supported by the ERC under Advanced Grant 291528 (RACE)
History
School
Science
Department
Computer Science
Published in
Journal of autonomous agents and multiagent systems
Volume
-
Issue
-
Pages
- - - (-)
Citation
FATIMA, S. and WOOLDRIDGE, M., 2016. Majority bargaining for resource division. Autonomous Agents and Multi-Agent Systems, 30(2), pp.331-363.
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/
Publication date
2016
Notes
The final publication is available at Springer via http://dx.doi.org/10.1007/s10458-015-9290-8