Strategy-Proof Rule in Probabilistic Allocation Problem of an Indivisible Good and Money
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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.Cite
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This note studies the design of a strategy-proof resource allocation rule in an environment with perfectly divisible commodities and single-peaked preferences. In this environment, the uniform rule has played a central role in the literature. Sprumont(1991) and Ching(1994) show that the uniform rule is the only rule which satisfies strategy-proofness, Pareto efficiency and some equity conditions when there is only one commodity. However, in the environment with multiple commodities the uniform rule does not satisfy Pareto efficiency. We adopt a concept of second best efficiency instead of Pareto efficiency. In the main theorem, we give a full characterization of the uniform rule with the second best e fficiency in a two person economy. Journal of Economic LiteratureClassification Numbers : D63, D71.
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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.
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We consider the multi-object allocation problem with monetary transfers where each agent obtains at most one object (unit-demand). We focus on allocation rules satisfying individual rationality, no subsidy, efficiency, and strategy-proofness. Extending the result of Morimoto and Serizawa (2015), we show that for an arbitrary number of agents and objects, the minimum price Walrasian is characterized by the four properties on the classical domain.
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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.
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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 problem of allocating objects to a group of agents and how much agents should pay. Each agent receives at most one object and has non-quasi-linear preferences. Non-quasi-linear preferences describe environments where payments influence agents' abilities to utilize objects or derive benefits from them. The minimum price Walrasian (MPW) rule is the rule that assigns a minimum price Walrasian equilibrium allocation to each preference profile. We establish that the MPW rule is the unique rule satisfying strategy-proofness, efficiency, individual rationality, and no subsidy for losers. Since the outcome of the MPW rule coincides with that of the simultaneous ascending (SA) auction, our result supports SA auctions adopted by many governments.
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