We study Kantian equilibria (Roemer, 2010) of an n-player bargaining game, which is a modified version of the well-known divide the dollar game (Nash, 1953). We first show that the Kantian equilibrium (multiplicative version) 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 under the proportional rule. Finally, using hybrid bankruptcy rules that we construct in a novel fashion, we can characterize the whole equilibrium set. These results are extended to the additive definition of the Kantian equilibrium. Our results highlight the interactions between institutions (axiomatic properties of division rules), optimization protocol (Kantian or Nashian), and agents' equilibrium behavior.