Strategy-proofness and identical preferences lower bound in allocation problem of indivisible objects

2017 ◽  
Vol 65 (4) ◽  
pp. 1045-1078
Author(s):  
Kazuhiko Hashimoto
Keyword(s):  
Lower Bound ◽  
Allocation Problem ◽  
Indivisible Objects ◽  
Identical Preferences Lower Bound ◽  
Strategy Proofness

Vote budgets and Dodgson’s method of marks

2019 ◽  
Vol 72 (1) ◽  
pp. 235-246 ◽  
Author(s):  
Walter Bossert ◽  
Kotaro Suzumura
Keyword(s):  
Lower Bound ◽  
Preference Ordering ◽  
Voting Rules ◽  
Feasible Allocation ◽  
Richness Condition ◽  
Strategy Proofness

AbstractWe examine voting rules that are inspired by Dodgson’s method of marks (to be distinguished from the procedure that is commonly referred to as Dodgson’s rule) by means of two criteria. Each voter decides how to allocate a vote budget (which is common to all voters, and need not be exhausted) to the candidates. Our first criterion is a richness condition: we demand that, for any possible preference ordering a voter may have, there is a feasible allocation of votes that reflects these preferences. A (tight) lower bound on the vote budget is established. Adding a strategy-proofness condition as a second criterion, we recommend that the vote budget be given by the lower bound determined in our first result.

scholarly journals Serial dictatorship mechanisms with reservation prices: heterogeneous objects

2021 ◽  
Author(s):  
Bettina Klaus ◽  
Alexandru Nichifor
Keyword(s):  
Econ Theory ◽  
Reservation Price ◽  
Price Vector ◽  
Heterogeneous Objects ◽  
Indivisible Objects ◽  
Reservation Prices ◽  
Priority Ordering ◽  
Serial Dictatorship ◽  
Strategy Proofness

AbstractWe adapt a set of mechanisms introduced by Klaus and Nichifor (Econ Theory 70:665–684, 2020), serial dictatorship mechanisms with (individual) reservation prices, to the allocation of heterogeneous indivisible objects, e.g., specialist clinic appointments. We show how the characterization of serial dictatorship mechanisms with reservation prices for homogeneous indivisible objects (Klaus and Nichifor 2020, Theorem 1) can be adapted to the allocation of heterogeneous indivisible objects by adding neutrality: mechanism $$\varphi $$ φ satisfies minimal tradability, individual rationality, strategy-proofness, consistency, independence of unallocated objects, neutrality, and non wasteful tie-breaking if and only if there exists a reservation price vector r and a priority ordering $$\succ $$ ≻ such that $$\varphi $$ φ is a serial dictatorship mechanism with reservation prices based on r and $$\succ $$ ≻ .

scholarly journals Dominant Resource Fairness with Meta-Types

2021 ◽  
Author(s):  
Steven Yin ◽  
Shatian Wang ◽  
Lingyi Zhang ◽  
Christian Kroer
Keyword(s):  
Resource Allocation ◽  
Pareto Optimality ◽  
Real Life ◽  
Substitution Effect ◽  
Problem Formulation ◽  
Allocation Problem ◽  
Linear Programs ◽  
Resource Allocation Problem ◽  
Alternative Approaches ◽  
Strategy Proofness

Inspired by the recent COVID-19 pandemic, we study a generalization of the multi-resource allocation problem with heterogeneous demands and Leontief utilities. Unlike existing settings, we allow each agent to specify requirements to only accept allocations from a subset of the total supply for each resource. These requirements can take form in location constraints (e.g. A hospital can only accept volunteers who live nearby due to commute limitations). This can also model a type of substitution effect where some agents need 1 unit of resource A \emph{or} B, both belonging to the same meta-type. But some agents specifically want A, and others specifically want B. We propose a new mechanism called Dominant Resource Fairness with Meta Types which determines the allocations by solving a small number of linear programs. The proposed method satisfies Pareto optimality, envy-freeness, strategy-proofness, and a notion of sharing incentive for our setting. To the best of our knowledge, we are the first to study this problem formulation, which improved upon existing work by capturing more constraints that often arise in real life situations. Finally, we show numerically that our method scales better to large problems than alternative approaches.

scholarly journals Robust group strategy‐proofness

2021 ◽  
Vol 16 (4) ◽  
pp. 1351-1389
Author(s):  
Steven Kivinen ◽  
Norovsambuu Tumennasan
Keyword(s):  
Private Information ◽  
Truth Telling ◽  
Private Goods ◽  
Group Strategy ◽  
Free Disposal ◽  
Ex Post ◽  
Indivisible Objects ◽  
Social Choice Functions ◽  
Deferred Acceptance ◽  
Strategy Proofness

Strategy‐proofness (SP) is a sought‐after property in social choice functions because it ensures that agents have no incentive to misrepresent their private information at both the interim and ex post stages. Group strategy‐proofness (GSP), however, is a notion that is applied to the ex post stage but not to the interim stage. Thus, we propose a new notion of GSP, coined robust group strategy‐proofness (RGSP), which ensures that no group benefits by deviating from truth telling at the interim stage. We show for the provision of a public good that the Minimum Demand rule (Serizawa (1999)) satisfies RGSP when the production possibilities set satisfies a particular topological property. In the problem of allocating indivisible objects, an acyclicity condition on the priorities is both necessary and sufficient for the Deferred Acceptance rule to satisfy RGSP, but is only necessary for the Top Trading Cycles rule. For the allocation of divisible private goods among agents with single‐peaked preferences (Sprumont (1991)), only free disposal, group replacement monotonic rules within the class of sequential allotment rules satisfy RGSP.

scholarly journals A Pseudo-Market Approach to Allocation with Priorities

2018 ◽  
Vol 10 (3) ◽  
pp. 272-314 ◽  
Author(s):  
Yinghua He ◽  
Antonio Miralles ◽  
Marek Pycia ◽  
Jianye Yan
Keyword(s):  
School Choice ◽  
Market Mechanism ◽  
Allocation Problem ◽  
Incentive Compatible ◽  
Indivisible Objects ◽  
Classical Setting ◽  
Monetary Transfer ◽  
Pareto Efficient ◽  
Market Approach ◽  
Special Case

We propose a pseudo-market mechanism for no-monetary-transfer allocation of indivisible objects based on priorities such as those in school choice. Agents are given token money, face priority-specific prices, and buy utility-maximizing random assignments. The mechanism is asymptotically incentive compatible, and the resulting assignments are fair and constrained Pareto efficient. Hylland and Zeckhauser’s (1979) position-allocation problem is a special case of our framework, and our results on incentives and fairness are also new in their classical setting. (JEL D63, D82, H75, I21, I28)

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