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On Axioms Underlying Use of Reserve Price

Mukherjee, Conan LU (2015) In Working Paper / Department of Economics, School of Economics and Management, Lund University
Abstract
This paper establishes reserve price as an ethical necessity contrary to its popular interpretation as an instrument of revenue maximization. It provides an axiomatic justification to reserve pricing at Vickrey auction in single as well as multiple objects settings. In particular, it provides a topological interpretation of a reserve price as the infimum of the set of non-negative real numbers satisfying the following property: if all agents bid the same number from this set, then at least one object is allocated. Further, it shows how existence of this reserve price as well as the associated efficiency properties, are implications of ethical and strategic axioms. In particular, for the single object case, it is shown that any anonymous... (More)
This paper establishes reserve price as an ethical necessity contrary to its popular interpretation as an instrument of revenue maximization. It provides an axiomatic justification to reserve pricing at Vickrey auction in single as well as multiple objects settings. In particular, it provides a topological interpretation of a reserve price as the infimum of the set of non-negative real numbers satisfying the following property: if all agents bid the same number from this set, then at least one object is allocated. Further, it shows how existence of this reserve price as well as the associated efficiency properties, are implications of ethical and strategic axioms. In particular, for the single object case, it is shown that any anonymous strategy-proof mechanism that satisfies non-bossiness (in decision) must have an allocation rule same as that of a Vickrey auction with reserve price (VARP). Further, two axiomatizations are provided for the class of VARP mechanisms in the single object context. In the multiple objects context, two new complications arise. One, any one agent getting the object no longer implies that all other agents do not get the object and two, at each profile of reports, all objects need not be allocated. To account for these complications, we introduce an ethical axiom called minimal impartiality (which requires that either all objects or no object be allocated at any profile where all agents report the same value) and a technical regularity condition. Under these restrictions, the single object results are shown to hold in the multiple objects case, too. Finally, we generalize the maxmed mechanisms of Sprumont [JET, 2013] to the multiple objects setting and provide an axiomatization. (Less)
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author
organization
publishing date
type
Working Paper
publication status
published
subject
keywords
Anonymous, non-bossy, strategy-proof mechanism, maxmed mechanisms
in
Working Paper / Department of Economics, School of Economics and Management, Lund University
issue
7
pages
21 pages
publisher
Department of Economics, Lund Universtiy
language
English
LU publication?
yes
id
750be96a-b838-4af9-b6db-b240da25e07a (old id 5159473)
alternative location
http://swopec.hhs.se/lunewp/abs/lunewp2015_007.htm
date added to LUP
2015-03-23 13:18:05
date last changed
2016-04-16 08:51:50
@misc{750be96a-b838-4af9-b6db-b240da25e07a,
  abstract     = {This paper establishes reserve price as an ethical necessity contrary to its popular interpretation as an instrument of revenue maximization. It provides an axiomatic justification to reserve pricing at Vickrey auction in single as well as multiple objects settings. In particular, it provides a topological interpretation of a reserve price as the infimum of the set of non-negative real numbers satisfying the following property: if all agents bid the same number from this set, then at least one object is allocated. Further, it shows how existence of this reserve price as well as the associated efficiency properties, are implications of ethical and strategic axioms. In particular, for the single object case, it is shown that any anonymous strategy-proof mechanism that satisfies non-bossiness (in decision) must have an allocation rule same as that of a Vickrey auction with reserve price (VARP). Further, two axiomatizations are provided for the class of VARP mechanisms in the single object context. In the multiple objects context, two new complications arise. One, any one agent getting the object no longer implies that all other agents do not get the object and two, at each profile of reports, all objects need not be allocated. To account for these complications, we introduce an ethical axiom called minimal impartiality (which requires that either all objects or no object be allocated at any profile where all agents report the same value) and a technical regularity condition. Under these restrictions, the single object results are shown to hold in the multiple objects case, too. Finally, we generalize the maxmed mechanisms of Sprumont [JET, 2013] to the multiple objects setting and provide an axiomatization.},
  author       = {Mukherjee, Conan},
  keyword      = {Anonymous,non-bossy,strategy-proof mechanism,maxmed mechanisms},
  language     = {eng},
  number       = {7},
  pages        = {21},
  publisher    = {ARRAY(0x7ae3370)},
  series       = {Working Paper / Department of Economics, School of Economics and Management, Lund University},
  title        = {On Axioms Underlying Use of Reserve Price},
  year         = {2015},
}