“Nash-in-Nash” Bargaining: A Microfoundation for Applied Work
为双边寡头分析中常用的“纳什中的纳什”谈判模型提供了非合作博弈基础，扩展了鲁宾斯坦交替出价模型至多上游和下游企业，并给出了均衡存在性和价格唯一性的条件。
A "Nash equilibrium in Nash bargains" has become a workhorse bargaining model in applied analyses of bilateral oligopoly. This paper proposes a noncooperative foundation for "Nash-in-Nash" bargaining that extends Rubinstein's alternating offers model to multiple upstream and downstream firms. We provide conditions on firms' marginal contributions under which there exists, for sufficiently short time between offers, an equilibrium with agreement among all firms at prices arbitrarily close to Nash-in-Nash prices, that is, each pair's Nash bargaining solution given agreement by all other pairs. Conditioning on equilibria without delayed agreement, limiting prices are unique. Unconditionally, they are unique under stronger assumptions.