Abstract
This note reconsiders the Rubinstein bargaining game under the assumption that a rejected offer is only costly to the proposer who made the rejected offer. It is shown that then, the classic result of Shaked that, in the multilateral version of this game, every division of the good can be sustained in SPE no longer holds. Specifically, there are many SPE, but players’ (expected) payoffs in SPE are unique. The assumption further leads to a responder advantage.
Highlights
We departed from the classic alternating offers bargaining game of Rubinstein (1982) [1] by assuming that rejection is only costly to the proposer who made the rejected offer, and not to the responders who chose to reject
The implication of this modeling choice is that the payoffs in subgame perfect equilibrium (SPE) are unique, even when the game features three or more players. This is in stark contrast with the classic version of the game, where every partition of the pie can be sustained in SPE
A further implication of our modeling choice is that we have a proposer disadvantage: the further a player is from being the proposer, the higher his/her expected payoff in the game
Summary
Game with Proposers in the Hot Seat. Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Is that at each stage, with some non-zero probability 1 − δ, a rejected proposal leads to termination of the game, and all players receive a zero payoff. We assume that with probability 1 − δ, rejection terminates the game for the proposer, but not for the responders. Should party A’s offer be found unreasonable and rejected, it is not uncommon for another party to take the initiative and to build a successful coalition from which party A is excluded This is precisely what happened in the Belgian formation of 2019–2020. The Flemish nationalist party NVA received the highest share of the vote (16%), and was given the initiative to form a government.
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