Strategy-Proof and Fair Wages

A fair division problem with indivisible objects, e.g. jobs, and one divisible good (money) is considered. The individuals consume one object and money. The class of strategy-proof and fair allocation rules is characterized. The allocation rules in the class are like a Vickrey auction bossy and like the Clark-Groves mechanisms in general not "budget balanced". The efficiency loss due to fairness and strategy-proofness becomes measurable in monetary terms. Two interpretations of the formal model is discussed. First, it is a situation where a given sum of money has to be distributed as wages and fair wages are to be implemented. Second, it is as an auction model where a number of objects are simultaneously traded.