Kantian equilibria of a class of Nash bargaining games

We study Kantian equilibria of an n $n$-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.