We study Kantian equilibria of an $n$-player bargaining game, which is a modified version of the well-known divide-the-dollar game. We first show that the Kantian equilibrium exists under fairly minimal assumptions. Second, if the bankruptcy rule used satisfies equal treatment of equals, and is almost nowhere proportional, then only equal division can prevail in any Kantian equilibrium. On the other hand, we show that an “anything goes” type result emerges only under the proportional rule. Finally, using hybrid bankruptcy rules that we construct in a novel fashion, we can characterize the whole equilibrium set. Our results highlight the interactions between institutions (axiomatic properties of division rules) and agents' equilibrium behavior.

中文翻译：

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一类纳什讨价还价博弈的康德均衡

我们研究康德均衡$n$-玩家讨价还价游戏，这是著名的分钱游戏的修改版。我们首先证明康德均衡在相当小的假设下存在。其次，如果所使用的破产规则满足平等对待，并且几乎不成比例，那么在任何康德均衡中只有平等分配才能占上风。另一方面，我们表明“一切皆有可能”类型的结果仅在比例规则下出现。最后，使用我们以新颖方式构建的混合破产规则，我们可以表征整个均衡集。我们的结果强调了制度（划分规则的公理性质）和代理人的均衡行为之间的相互作用。