Noncooperative foundations for the Kalai-Smorodinsky and equal sacrifice solutions via prominence structures

In bargaining, players may adopt different prominence structures when making demands: (i) each player might use (1/N)th of his maximum monetary payoff as the prominence level or (ii) players might use a common prominence level. This paper considers a scheme in which players alternate making demands. It turns out that if the prominence levels described by (i) are used and if players have utilities linear in money, the outcome of this scheme converges to that of the Kalai-Smorodinsky solution as players' prominence levels get smaller. If the common prominence level of (ii) is used and if players have identical constant marginal utilities of money, the outcome of this scheme converges to that of the equal sacrifice solution as that prominence level gets smaller.