Majority bargaining for resource division

S. Shaheen Fatima, Michael J. Wooldridge

Abstract: We are concerned with the problem of how a collection of agents can decide to share a resource, represented as a unit sized pie. We investigate a simple and natural non-cooperative bargaining protocol for this problem, in which 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 weighted voting game: each player is assigned a weight, and a proposal for allocation is implemented if the weight of players in favour of that proposal meets or exceeds a given quota. The agenda, (i.e., the order in which the players are called to make offers), is defined exogenously. Thus, the outcome is an offer that has majority support. We consider two variants of this protocol, provide subgame perfect equilibrium strategies for both, and investigate their properties. Finally, we give those conditions for which the non-cooperative equilibria for the two games is in the core of the weighted voting game and those for which it is not.