Results 1 
6 of
6
Fair Assignment Of Indivisible Objects Under Ordinal Preferences
"... We consider the discrete assignment problem in which agents express ordinal preferences over objects and these objects are allocated to the agents in a fair manner. We use the stochastic dominance relation between fractional or randomized allocations to systematically define varying notions of prop ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
We consider the discrete assignment problem in which agents express ordinal preferences over objects and these objects are allocated to the agents in a fair manner. We use the stochastic dominance relation between fractional or randomized allocations to systematically define varying notions of proportionality and envyfreeness for discrete assignments. The computational complexity of checking whether a fair assignment exists is studied systematically for the fairness notions. We characterize the conditions under which a fair assignment is guaranteed to exist. For a number of fairness concepts, polynomialtime algorithms are presented to check whether a fair assignment exists or not. Our algorithmic results also extend to the case of variable entitlements of agents. Our NPhardness result, which holds for several variants of envyfreeness, answers an open problem posed by
Manipulating the Probabilistic Serial Rule
"... The probabilistic serial (PS) rule is one of the most prominent randomized rules for the assignment problem. It is wellknown for its desirable fairness and welfare properties. However, PS is not immune to manipulative behaviour by the agents. We initiate the study of the computational complexity ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
The probabilistic serial (PS) rule is one of the most prominent randomized rules for the assignment problem. It is wellknown for its desirable fairness and welfare properties. However, PS is not immune to manipulative behaviour by the agents. We initiate the study of the computational complexity of an agent manipulating the PS rule. We show that computing an expected utility better response is NPhard. On the other hand, we present a polynomialtime algorithm to compute a lexicographic best response. For the case of two agents, we show that even an expected utility best response can be computed in polynomial time. Our result for the case of two agents relies on an interesting connection with sequential allocation of discrete objects.
Welfare Maximization Entices Participation
"... We consider randomized mechanisms with optional participation. Preferences over lotteries are modeled using skewsymmetric bilinear (SSB) utility functions, a generalization of classic von NeumannMorgenstern utility functions. We show that every welfaremaximizing mechanism entices participation ..."
Abstract
 Add to MetaCart
We consider randomized mechanisms with optional participation. Preferences over lotteries are modeled using skewsymmetric bilinear (SSB) utility functions, a generalization of classic von NeumannMorgenstern utility functions. We show that every welfaremaximizing mechanism entices participation and that the converse holds under additional assumptions. Two important corollaries of our results are characterizations of an attractive randomized voting rule that satisfies Condorcetconsistency and entices participation. This stands in contrast to a wellknown result by Moulin (1988), who proves that no deterministic voting rule can satisfy both properties simultaneously. 1
Strategic aspects of the probabilistic serial rule for the allocation of goods
"... The probabilistic serial (PS) rule is one of the most prominent randomized rules for the assignment problem. It is wellknown for its superior fairness and welfare properties. However, PS is not immune to manipulative behaviour by the agents. We examine computational and noncomputational aspects of ..."
Abstract
 Add to MetaCart
The probabilistic serial (PS) rule is one of the most prominent randomized rules for the assignment problem. It is wellknown for its superior fairness and welfare properties. However, PS is not immune to manipulative behaviour by the agents. We examine computational and noncomputational aspects of strategising under the PS rule. Firstly, we study the computational complexity of an agent manipulating the PS rule. We present polynomialtime algorithms for optimal manipulation. Secondly, we show that expected utility best responses can cycle. Thirdly, we examine the existence and computation of Nash equilibrium profiles under the PS rule. We show that a pure Nash equilibrium is guaranteed to exist under the PS rule. For two agents, we identify two different types of preference profiles that are not only in Nash equilibrium but can also be computed in linear time. Finally, we conduct experiments to check the frequency of manipulability of the