Kalai-Smorodinsky and Maschler-Perles Solutions under Pre-donation

Abstract

This paper examines Kalai-Smorodinsky and Maschler-Perles solutions under pre-donation for a two-person bargaining problem with a linear utility possibility frontier and an arbitrary threat point. At the pre-donation stage “Lucky Bargainer”, i.e., the bargainer with the higher ideal payoff, donates a portion of her would-be payoff to her opponent before they bargain. Results show that, under both solutions, there is always an incentive for pre-donation except in one special case where Unlucky Bargainer’s threat payoff is zero and the ideal payoff of Lucky Bargainer is sufficiently low. Efficient division requires sufficiently high threat payoff for Unlucky Bargainer. Collusion in an asymmetric duopoly is presented as an example, where the threat outcomes are assumed to be those of Cournot, Bertrand or Stackelberg equilibria. For these specific bargaining problems, there is always an incentive for pre-donation.