Abstract
This paper studies secure implementability (T. Saijo, T. Sjostrom and T. Yamato, “Secure Implementation,” Theoretical Economics, Vol. 2, No. 3, 2007, pp. 203-229) in queueing problems. Our main result shows that the social choice function satisfies strategy-proofness and strong non-bossiness (Z. Ritz, “Restricted Domains, Arrow-Social Welfare Functions and Noncorruptible and Non-Manipulable Social Choice Correspondences: The Case of Private Alternatives,” Mathematical Social Science, Vol. 4, No. 2, 1983, pp. 155-179), both of which are necessary for secure imple- mentation, if and only if it is constant on the domains that satisfy weak indifference introduced in this paper. Weak in- difference is weaker than minimal richness (Y. Fujinaka and T. Wakayama, “Secure Implementation in Economies with Indivisible Objects and Money,” Economics Letters, Vol. 100, No. 1, 2008, pp. 91-95). Our main result illustrates that secure implementation is too difficult in queueing problems since many reasonable domains satisfy weak indifference, for example, convex domains.
Highlights
In this paper, we consider queueing problems of allocating positions in a queue to agents, each of whom has a constant unit waiting cost, with monetary transfers
The strategyproof mechanism might have a Nash equilibrium which induces a non-optimal outcome. This problem is solved by secure implementation (Saijo, et al [2]), that is, double implementation in dominant strategy equilibria and Nash equilibria2
On the basis of this fact, we study the possibility of secure implementation in queueing problems
Summary
We consider queueing problems of allocating positions in a queue to agents, each of whom has a constant unit waiting cost, with monetary transfers. The strategyproof mechanism might have a Nash equilibrium which induces a non-optimal outcome This problem is solved by secure implementation (Saijo, et al [2]), that is, double implementation in dominant strategy equilibria and Nash equilibria. This paper is most closely related to the one written by Fujinaka and Wakayama [9] They show a constancy result on secure implementation when the domain satisfies minimal richness (Fujinaka and Wakayama [9]). Our main result shows that only constant social choice functions satisfy strategy-proofness and strong non-bossiness (Ritz [12]), both of which are necessary for secure implementation, on the domains satisfy weak indifference, which is weaker than minimal richness, introduced in this paper.
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