This chapter examines the Kalai–Smorodinsky bargaining solution, which was proposed as an alternative to the Nash bargaining solution, also known as proportional fairness. Whereas the Nash solution can reduce an individual stakeholder’s utility allotment when the feasible set is enlarged, the Kalai–Smorodinsky fairness criterion is designed to avoid this outcome. The chapter states the socially optimal solution, subject to a budget constraint and upper bounds on utility, in closed form. When there are no upper bounds, the solution is the same as the maximin solution. The chapter also proves a sufficient and easily checkable condition under which the problem is regionally decomposable.

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Kalai–Smorodinsky Bargaining

  • Özgün Elçi,
  • John Hooker,
  • Peter Zhang

摘要

This chapter examines the Kalai–Smorodinsky bargaining solution, which was proposed as an alternative to the Nash bargaining solution, also known as proportional fairness. Whereas the Nash solution can reduce an individual stakeholder’s utility allotment when the feasible set is enlarged, the Kalai–Smorodinsky fairness criterion is designed to avoid this outcome. The chapter states the socially optimal solution, subject to a budget constraint and upper bounds on utility, in closed form. When there are no upper bounds, the solution is the same as the maximin solution. The chapter also proves a sufficient and easily checkable condition under which the problem is regionally decomposable.