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Competitive Market Mechanisms For Fair Division of Indivisible Goods

Student: Iuliia Ibragimova

Supervisor: Fedor Sandomirskiy

Faculty: St.Petersburg School of Economics and Management

Educational Programme: Economics (Bachelor)

Year of Graduation: 2016

We consider a problem of fair division of a family of divisible goods between agents with additive utilities. CEEI or Competitive Equilibrium with Equal Incomes is a popular solution to this problem that meets the two most desired properties: envy-freeness (every agent thinks that his own share is weakly better that any other's one) and efficiency (we cannot make an agent happier by redistributing goods without making another agent less happy). It is known that there always exists a CEEI allocation such that the number of goods that do not entirely belong to one agent does not exceed n-1, where n is a number of agents. Hence, if the number of goods is large, then CEEI allocation is “close” to an integral allocation, where no goods are cut. Our goal is to investigate how often CEEI rule produces integral allocations. For this purpose we consider agents with random utilities. Our simulations show that the probability of integral CEEI allocation tends to a limit bounded away from 0, as number of goods m tends to infinity. Moreover, the corresponding conditional probability given that “tastes of agents are different enough” tends to 1.

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