In the real world many social and economic decisions have to be made with imperfect information and uncertainty. In the past two decades, economists and mathematicians have devoted a great deal of time and effort into the study of ambiguity and much progress has been made in modeling ambiguity....

We study the problem of how to allocate a set of indivisible objects like jobs or houses and an amount of money among a group of people as fairly and as efficiently as possible. A particular constraint for such an allocation is that every person should be assigned with the same number of objects...

In this paper we show how theorems of Borsuk-Ulam and Tucker can be used to construct a consensus-halving: a division of an object into two portions so that each of n people believe the portions are equally split. Moreover, the division takes at most n cuts, which is best possible. This extends...

In this work, we solve a real-world facility location problem by means of a mixed integer linear programming model. The problem is faced by an Italian multi-utility company operating in the sector of waste management. The company works in several Italian regions to collect and treat the urban...

We study the problem of determining memberships to the groups in a Boolean algebra. The Boolean algebra is composed of basic groups (e.g., “J” and “K”) and the other groups that are derived from basic groups through the conjunction, disjunction, or negation operations (e.g., “J and...

In ordinal (probabilistic) assignment problems, each agent reports his preference rankings over objects and receives a lottery defined over those objects. A common efficiency notion, sd-efficiency, is obtained by extending the preference rankings to preferences over lotteries by means of...

This study investigates efficient and strategy‐proof mechanisms for allocating indivisible goods under constraints. First, we examine a setting without endowments. In this setting, we introduce a class of constraints-ordered accessibility-for which the serial dictatorship (SD) mechanism is...

In the current FIFA penalty shootout mechanism, a coin toss decides which team will kick first. Empirical evidence suggests that the team taking the first kick has a higher probability to win a shootout. We design sequentially fair shootout mechanisms such that in all symmetric Markov-perfect...

This paper contains two results. The first result says that given any efficient non-monetary allocation there is a balanced vector of transfers so that the resulting allocation is fair. The second result says that given any efficient non-monetary allocation there is a pricing function defined on...

We solve the problem of a social planner who seeks to minimize inequality via transfers with a fixed public budget in a distribution of exogenously given incomes. The appropriate solution method depends on the objective function: If it is convex, as in the case of the absolute mean deviation, it...