Abstract
We consider a mechanism design problem for the provision of a binary excludable public good. We characterize the augmented serial rules (Ohseto, Econ Theory 26:589–606 2005) by strategy-proofness, envy-freeness, and access independence. This result is the positive answer to the first open question posed by Ohseto (Econ Theory 26:589–606, 2005). We also show that, in addition to the augmented serial rules, there exists a rule satisfying strategy-proofness, symmetry, access independence, and non-bossiness. This result is the negative answer to the second open question posed by Ohseto (Econ Theory 26:589–606, 2005).
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Notes
Although Moulin (1994) has considered the divisible case, the serial rule applies to the binary case.
Yu (2007) has characterized the rule in the multiple units case.
Massó et al. (2015) have also shown that there exists a rule that satisfies strategy-proofness and individual rationality, and that achieves strictly lower maximal welfare loss than the serial rule in more than two agents case.
Thomson (2014) has discussed this condition extensively.
This condition is sometimes called as consumer sovereignty. For example, in Moulin (1999), Juarez (2008), and Juarez (2013a).
Moulin and Shenker (2001) have used the same term, consumer sovereignty, as a weaker notion, which requires that each agent has the option to obtain the good, regardless of other agents’ valuations. That is, it does not require the option not to obtain the good. With this weaker form, however, our characterization is not valid. Consider the rule that always assigns \((1,\frac{1}{n})\) to all agents.
This condition is sometimes called as voluntary participation.
When \(n=2\), Ohseto (2003) has shown that there does not exist another rule satisfying them.
This rule does not also satisfy a weaker form of non-bossiness, called non-bossiness in welfare on the conclusion side (Thomson 2014). It requires that if a change in an agent’s valuations is not accompanied by a change in his assignment, then the welfare of none of the other agents should be affected. Consider the assignments of agents 1 and 2 at the valuation profiles \((0,\frac{1}{n-2}, \frac{1}{n-1},\ldots , \frac{1}{n-1})\) and \((\frac{1}{n+1},\frac{1}{n-2}, \frac{1}{n-1},\ldots , \frac{1}{n-1})\).
Notice that \(p^1(S)\) (\(p^0(S)\)) does not express the payment of each agent in S (\(N\setminus S\)) when S are consumers.
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Hashimoto, K., Saitoh, H. Strategy-proof rules for an excludable public good. Soc Choice Welf 46, 749–766 (2016). https://doi.org/10.1007/s00355-015-0933-0
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DOI: https://doi.org/10.1007/s00355-015-0933-0