5,946 research outputs found
Allocation by coercion
The problem of allocating indivisible goods is considered when groups of individuals can make use of their power to plunder other groups. A monarch in a group of individuals is an individual who always obtains one of his most preferred goods. A Paretian condition together with a requirement of robust stability lead to the existence of monarchs in all subsets of individuals, except possibly one.Allocation rule; dictator; indivisible good; power; coalition formation.
Approximate Maximin Shares for Groups of Agents
We investigate the problem of fairly allocating indivisible goods among
interested agents using the concept of maximin share. Procaccia and Wang showed
that while an allocation that gives every agent at least her maximin share does
not necessarily exist, one that gives every agent at least of her share
always does. In this paper, we consider the more general setting where we
allocate the goods to groups of agents. The agents in each group share the same
set of goods even though they may have conflicting preferences. For two groups,
we characterize the cardinality of the groups for which a constant factor
approximation of the maximin share is possible regardless of the number of
goods. We also show settings where an approximation is possible or impossible
when there are several groups.Comment: To appear in the 10th International Symposium on Algorithmic Game
Theory (SAGT), 201
Incentive Ratios for Fairly Allocating Indivisible Goods: Simple Mechanisms Prevail
We study the problem of fairly allocating indivisible goods among strategic
agents. Amanatidis et al. show that truthfulness is incompatible with any
meaningful fairness notions. Thus we adopt the notion of incentive ratio, which
is defined as the ratio between the largest possible utility that an agent can
gain by manipulation and his utility in honest behavior under a given
mechanism. We select four of the most fundamental mechanisms in the literature
on discrete fair division, which are Round-Robin, a cut-and-choose mechanism of
Plaut and Roughgarden, Maximum-Nash-Welfare and Envy-Graph Procedure, and
obtain extensive results regarding the incentive ratios of them and their
variants.
For Round-Robin, we establish the incentive ratio of for additive and
subadditive cancelable valuations, the unbounded incentive ratio for cancelable
valuations, and the incentive ratios of and for
submodular and XOS valuations, respectively. Moreover, the incentive ratio is
unbounded for a variant that provides the -approximate maximum social
welfare guarantee. For the algorithm of Plaut and Roughgarden, the incentive
ratio is either unbounded or with lexicographic tie-breaking and is
with welfare maximizing tie-breaking. This separation exhibits the essential
role of tie-breaking rules in the design of mechanisms with low incentive
ratios. For Maximum-Nash-Welfare, the incentive ratio is unbounded.
Furthermore, the unboundedness can be bypassed by restricting agents to have a
strictly positive value for each good. For Envy-Graph Procedure, both of the
two possible ways of implementation lead to an unbounded incentive ratio.
Finally, we complement our results with a proof that the incentive ratio of
every mechanism satisfying envy-freeness up to one good is at least ,
and thus is larger than by a constant
Egalitarian-equivalent Groves Mechanisms in the Allocation of Heterogeneous Objects
We study the problem of allocating objects when monetary transfers are possible. We are interested in mechanisms that allocate the objects in an efficient way and induce the agents to report their true preferences. Within the class of such mechanisms, first we characterize egalitarian-equivalent mechanisms. Then, we add a bounded-deficit condition and characterize the corresponding class. Finally, we investigate the relations between egalitarian-equivalence and other fairness notions such as no-envy.fairness, allocation of indivisible goods and money, task assignments, strategy-proofness, the Vickrey-Clarke-Groves mechanisms, egalitarian-equivalence, no-envy, order preservation
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