Weakly Fair Allocations and Strategy-Proofness
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This paper investigates the problem of allocating two types of indivisible objects among a group of agents when a priority-order must be respected and when only restricted monetary transfers are allowed. Since the existence of a fair allocation not generally is guaranteed due the the restrictions on the money transfers, the concept of fairness is weakened, and a new concept of fairness is introduced. This concept is called weak fairness. We define an allocation rule that implements weakly fair allocations and demonstrate that it is coalitionally strategy-proof. In fact, it is the only coalitionally strategy-proof allocation rule that implements a weakly fair allocation.Keywords:
Max-min fairness
Fair share
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Sequence (biology)
Optimal allocation
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This paper considers a fair division problem with indivisible objects, like jobs, houses, positions, etc., and one divisible good (money). The individuals consume money and one object each. The class of fair allocation rules that are strategy-proof in the strong sense that no coalition of individuals can improve the allocation for all of its members, by misrepresenting their preferences, is characterized. It turns out that given a regularity condition, the outcome of a fair and coalition strategy-proof allocation rule must maximize the use of money subject to upper quantity bounds determined by the allocation rule. Due to these restrictions the outcomes of the allocation rule are Pareto efficient only for some preference profiles. In a multi-object auction interpretation of the model, the result is a complete characterization of coalition strategy-proof auction rules.
Fair division
Pareto efficiency
Pareto optimal
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Pareto efficiency
Incentive compatibility
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A common real-life problem is to fairly allocate a number of indivisible objects and a fixed amount of money among a group of agents.Fairness requires that each agent weakly prefers his consumption bundle to any other agent's bundle.In this context, fairness is incompatible with budget balance and nonmanipulability (Green and Laffont 1979).Our approach here is to weaken or abandon nonmanipulability.We search for the rules that are minimally manipulable among all fair and budget-balanced rules.First, we show for a given preference profile, all fair and budget-balanced rules are either (all) manipulable or (all) nonmanipulable.Hence, measures based on counting profiles where a rule is manipulable or considering a possible inclusion of profiles where rules are manipulable do not distinguish fair and budget-balanced rules.Thus, a "finer" measure is needed.Our new concept compares two rules with respect to their degree of manipulability by counting for each profile the number of agents who can manipulate the rule.Second, we show that maximally preferred fair allocation rules are the minimally (individually and coalitionally) manipulable fair and budget-balanced allocation rules according to our new concept.Such rules choose allocations with the maximal number of agents for whom the utility is maximized among all fair and budget-balanced allocations.
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We consider the problem of probabilistically allocating a single indivisible good among agents when monetary transfers are allowed. We construct a new strategy-proof rule, called the second price trading rule, and show that it is second best efficient. Furthermore, we give the second price trading rule three characterizations with (1) strategy-proofness, budget-balance, treatment of equals, weak decision-efficiency, and simple generatability, (2) strategy-proofness, equal rights lower bound, treatment of equals, weak decision-efficiency, and simple generatability, (3) strategy-proofness, envy-freeness, no-trade-no-transfer, treatment of equals, weak decision-efficiency, and simple generatability.
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We consider the standard indivisible object allocation problem without monetary transfer and allow each object to have a weak priority over agents. It is well known that generally in such a problem stability (or no justified-envy) is not compatible with efficiency. We characterize the priority structures for which a stable and efficient assignment always exists, as well as the priority structures which admit a stable, efficient and (group) strategy-proof rule. While house allocation and housing market are two classical allocation problems that admit a stable, efficient and group strategy-proof rule, any priority-augmented allocation problem with more than three objects admits such a rule if and only if it is decomposable into a sequence of subproblems, each of which has the house allocation or the housing market structure.
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We investigate the efficiency of fair allocations of indivisible goods using the well-studied price of fairness concept. Previous work has focused on classical fairness notions such as envy-freeness, proportionality, and equitability. However, these notions cannot always be satisfied for indivisible goods, leading to certain instances being ignored in the analysis. In this paper, we focus instead on notions with guaranteed existence, including envy-freeness up to one good (EF1), balancedness, maximum Nash welfare (MNW), and leximin. We mostly provide tight or asymptotically tight bounds on the worst-case efficiency loss for allocations satisfying these notions.
Proportionality
Fairness measure
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I analyze an economy with uncertainty in which a set of indivisible objects and a certain amount of money is to be distributed among agents. The set of intertemporally fair social choice functions based on envy-freeness and Pareto efficiency is characterized. I give a necessary and sufficient condition for its non-emptiness and propose a mechanism that implements the set of intertemporally fair allocations in Bayes-Nash equilibrium. Implementation at the ex ante stage is considered, too. I also generalize the existence result obtained with envy-freeness using a broader fairness concept, introducing the aspiration function.
Ex-ante
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