Multilateral bargaining for resource division
2015-02-13T09:53:10Z (GMT)
by
We address the problem of how a group of agents can
decide to share a resource, represented as a unit-sized pie. 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 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), all the players get nothing. 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 agreement, and, under certain conditions provides a
foundation for the core of the Bayesian voting game. Our analysis
also 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 a non-cooperative equilibrium becomes NP-hard even
under the perfect information assumption.