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Efficient Combinatorial Allocations: Individual Rationality versus Stability

  • Hitoshi Matsushima EMAIL logo
Veröffentlicht/Copyright: 4. Januar 2018
The B.E. Journal of Theoretical Economics
Aus der Zeitschrift The B.E. Journal of Theoretical Economics Band 19 Heft 1

Abstract

We investigate combinatorial allocations with opt-out types and clarify the possibility of achieving efficiency under incomplete information. We introduce two distinct collective decision procedures. The first procedure assumes that the central planner designs a mechanism and players have the option to exit. The mechanism requires interim individual rationality. The second procedure assumes that players design a mechanism by committing themselves to participate. The mechanism requires marginal stability against blocking behavior by the largest proper coalitions. We show that the central planner can earn non-negative revenue in the first procedure, if and only if he cannot do so in the second.

Keywords: efficient combinatorial allocations; bayesian incentive compatibility; opt-out types; interim individual rationality; marginal stability
JEL Classification: D44; D61; D82

Notes

This study was supported by a grant-in-aid for scientific research (KAKENHI 25285059) from the Japan Society for the Promotion of Science (JSPS) and the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of the Japanese government.

Appendix

Proof of Lemma 1

From payoff equivalence, without loss of generality, we can assume x~∈X^. According to Arrow (1979) and D’Aspremont and Gérard-Varet (1979), it is evident that there exists x′∈X such that (g,x′) satisfies BIC and the balanced budgets in the sense that

∑i∈N⁡xi′(ω)=0 for all ω∈Ω.

From payoff equivalence, it is evident that there exists (bi)i∈N∈Rn such that

E[x~i(ω)|ωi]=E[xi′(ω)|ωi]+bi for all i∈N and all ωi∈Ωi,

where note that

∑i∈Nbi=E[∑i∈Nx~i(ω)].

We specify x∈X by

xi(ω)=xi′(ω)+bi for all i∈N and all ω∈Ω.

From this specification, it is clear that (g,x) satisfies BIC,

E[xi(ω)|ωi]=E[x′i(ω)|ωi]+bi

=E[x~i(ω)|ωi] for all i∈N and ωi∈Ωi,

and

∑i∈Nxi(ω)=∑i∈Nx′i(ω)+∑i∈Nbi=E[∑i∈Nx~i(ω)] for all ω∈Ω.

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Published Online: 2018-01-04

© 2019 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Articles
  2. Privatizing Multi-subsidiary Public Firm in Location Model
  3. Efficient Combinatorial Allocations: Individual Rationality versus Stability
  4. On Decay Centrality
  5. Sequential Auctions with Decreasing Reserve Prices
  6. The core of a strategic game
  7. Targeted Advertising on Competing Platforms
  8. Representation in Multi-Issue Delegated Bargaining
  9. Endogenous Mergers in Markets with Vertically Differentiated Products
  10. Standards of Proof and Civil Litigation: A Game-Theoretic Analysis
  11. Retained Earnings, Interest Rates and Lending Relationship
  12. Uniform Price Auctions with Asymmetric Bidders
  13. Conformity and Influence
  14. Sellouts, Beliefs, and Bandwagon Behavior
  15. Notes
  16. Eco-Firms and the Sequential Adoption of Environmental Corporate Social Responsibility in the Managerial Delegation
  17. Vertical Contract and Competition Intensity in Hotelling’s Model
  18. Constrained Allocation of Projects to Heterogeneous Workers with Preferences over Peers
  19. Irrelevance of the Strategic Variable in the Case of Relative Performance Maximization
  20. Critical Efficiencies as Upward Pricing Pressure with Feedback Effects
  21. On the Openness of Unique Pure-Strategy Nash Equilibrium
  22. Forecast Dispersion in Finite-Player Forecasting Games
https://doi.org/10.1515/bejte-2017-0072
Schlagwörter für diesen Artikel
efficient combinatorial allocations; bayesian incentive compatibility; opt-out types; interim individual rationality; marginal stability

Artikel in diesem Heft

  1. Articles
  2. Privatizing Multi-subsidiary Public Firm in Location Model
  3. Efficient Combinatorial Allocations: Individual Rationality versus Stability
  4. On Decay Centrality
  5. Sequential Auctions with Decreasing Reserve Prices
  6. The core of a strategic game
  7. Targeted Advertising on Competing Platforms
  8. Representation in Multi-Issue Delegated Bargaining
  9. Endogenous Mergers in Markets with Vertically Differentiated Products
  10. Standards of Proof and Civil Litigation: A Game-Theoretic Analysis
  11. Retained Earnings, Interest Rates and Lending Relationship
  12. Uniform Price Auctions with Asymmetric Bidders
  13. Conformity and Influence
  14. Sellouts, Beliefs, and Bandwagon Behavior
  15. Notes
  16. Eco-Firms and the Sequential Adoption of Environmental Corporate Social Responsibility in the Managerial Delegation
  17. Vertical Contract and Competition Intensity in Hotelling’s Model
  18. Constrained Allocation of Projects to Heterogeneous Workers with Preferences over Peers
  19. Irrelevance of the Strategic Variable in the Case of Relative Performance Maximization
  20. Critical Efficiencies as Upward Pricing Pressure with Feedback Effects
  21. On the Openness of Unique Pure-Strategy Nash Equilibrium
  22. Forecast Dispersion in Finite-Player Forecasting Games
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