In two-sided assignment markets with transferable utility, we first introduce two weak monotonicity properties that are compatible with stability. We show that for a fixed population, the sellers-optimal (respectively the buyers-optimal) stable rules are the only stable rules that satisfy object-valuation antimonotonicity (respectively buyer-valuation monotonicity). Essential in these properties is that, after a change in valuations, monotonicity is required only for buyers that stay matched with the same seller. Using Owen's derived consistency, the two optimal rules are characterized among all allocation rules for two-sided assignment markets with a variable population, without explicitly requiring stability.

Whereas these two monotonicity properties suggest an asymmetric treatment of the two sides of the market, valuation fairness axioms require a more balanced effect on the payoffs of buyers and sellers when the valuation of buyers for the objects owned by the sellers change. For assignment markets with a variable population, we introduce grand valuation fairness requiring that, if all valuations decrease by the same amount, as long as all optimal matchings still remain optimal, this leads to equal changes in the payoff of all agents. We show that the fair division rules are the only rules that satisfy this grand valuation fairness and a weak derived consistency property.

在具有可转移效用的双边分配市场中，我们首先引入两个与稳定性兼容的弱单调性。我们表明，对于固定的总体，卖方最优（分别是买方最优）稳定规则是唯一满足对象估值反单调性（分别是买方估值单调性）的稳定规则。这些属性的本质是，在估值发生变化后，只有与同一卖家保持匹配的买家才需要单调性。使用 Owen 的派生一致性，这两个最优规则在具有可变人口的双边分配市场的所有分配规则中都有特征，而没有明确要求稳定性。

尽管这两个单调性表明对市场两侧的不对称处理，但估值公平公理要求当买方对卖方拥有的对象的估值发生变化时，对买方和卖方的收益产生更平衡的影响。对于具有可变人口的分配市场，我们引入了大估值公平性，要求如果所有估值下降相同的数量，只要所有最优匹配仍然保持最优，这将导致所有代理的收益变化相等。我们表明，公平划分规则是唯一满足这种大估值公平性和弱派生一致性属性的规则。