Demand Commitment Bargaining: - The Case Of Apex Games -

Abstract

An apex game is a bargaining situation in which there is one major (apex) player and n “minor” players. The only profitable coalitions contain either the apex player and any one of the minor players or else all of the minor players. The demand commitment model is a bargaining procedure, i.e. an extensive form game. This paper investigates the payoffs that result (as subgame perfect outcomes) for apex games when players use the demand commitment bargaining procedure. We show that whenever the apex player has the first move he forms a coalition with a minor player and obtains the fraction (n − 1)/n of the coalition’s value while his (minor-player) partner obtains the remaining 1/n. When a minor player has the first move he either forms a coalition with the apex player (and obtains 1/n) or else forms a coalition with all of the remaining minor players. When this minor-player coalition forms there are many subgame perfect payoff distributions. A refinement of subgame perfection is proposed and is shown to select a unique payoff distribution (1/n for each minor player) for the minor-player coalition.