Implementable and ex-post IR rules in bilateral trading with discrete values

Janos Flesch, Marc Schröder, Dries Vermeulen

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We study bargaining problems between one buyer and one seller for a single object when each set of valuations is finite. We derive a necessary and sufficient condition for interim-implementable trading rules, analogous to the result in Myerson and Satterthwaite (1983), and a necessary condition for mechanisms that are free from ex post regret on and off equilibrium path. Based on these two theorems, our contribution is three-fold. First, we illustrate the results by means of three examples. Second, in contrast to the continuous model, there always exist strictly positive probability mass functions such that ex post efficiency and interim-implementability is feasible. Third, we show the difference between interim- and ex post-implementation. In the class of threshold trading rules, interim-implementation only precludes inefficient trade, while ex post-implementation is equivalent to posted price implementation. (C) 2016 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)68-75
Number of pages8
JournalMathematical Social Sciences
Volume84
DOIs
Publication statusPublished - Nov 2016

Keywords

  • EFFICIENT MECHANISMS
  • AUCTIONS
  • DESIGN

Cite this

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title = "Implementable and ex-post IR rules in bilateral trading with discrete values",
abstract = "We study bargaining problems between one buyer and one seller for a single object when each set of valuations is finite. We derive a necessary and sufficient condition for interim-implementable trading rules, analogous to the result in Myerson and Satterthwaite (1983), and a necessary condition for mechanisms that are free from ex post regret on and off equilibrium path. Based on these two theorems, our contribution is three-fold. First, we illustrate the results by means of three examples. Second, in contrast to the continuous model, there always exist strictly positive probability mass functions such that ex post efficiency and interim-implementability is feasible. Third, we show the difference between interim- and ex post-implementation. In the class of threshold trading rules, interim-implementation only precludes inefficient trade, while ex post-implementation is equivalent to posted price implementation. (C) 2016 Elsevier B.V. All rights reserved.",
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Implementable and ex-post IR rules in bilateral trading with discrete values. / Flesch, Janos; Schröder, Marc ; Vermeulen, Dries.

In: Mathematical Social Sciences, Vol. 84, 11.2016, p. 68-75.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Implementable and ex-post IR rules in bilateral trading with discrete values

AU - Flesch, Janos

AU - Schröder, Marc

AU - Vermeulen, Dries

N1 - No data used

PY - 2016/11

Y1 - 2016/11

N2 - We study bargaining problems between one buyer and one seller for a single object when each set of valuations is finite. We derive a necessary and sufficient condition for interim-implementable trading rules, analogous to the result in Myerson and Satterthwaite (1983), and a necessary condition for mechanisms that are free from ex post regret on and off equilibrium path. Based on these two theorems, our contribution is three-fold. First, we illustrate the results by means of three examples. Second, in contrast to the continuous model, there always exist strictly positive probability mass functions such that ex post efficiency and interim-implementability is feasible. Third, we show the difference between interim- and ex post-implementation. In the class of threshold trading rules, interim-implementation only precludes inefficient trade, while ex post-implementation is equivalent to posted price implementation. (C) 2016 Elsevier B.V. All rights reserved.

AB - We study bargaining problems between one buyer and one seller for a single object when each set of valuations is finite. We derive a necessary and sufficient condition for interim-implementable trading rules, analogous to the result in Myerson and Satterthwaite (1983), and a necessary condition for mechanisms that are free from ex post regret on and off equilibrium path. Based on these two theorems, our contribution is three-fold. First, we illustrate the results by means of three examples. Second, in contrast to the continuous model, there always exist strictly positive probability mass functions such that ex post efficiency and interim-implementability is feasible. Third, we show the difference between interim- and ex post-implementation. In the class of threshold trading rules, interim-implementation only precludes inefficient trade, while ex post-implementation is equivalent to posted price implementation. (C) 2016 Elsevier B.V. All rights reserved.

KW - EFFICIENT MECHANISMS

KW - AUCTIONS

KW - DESIGN

U2 - 10.1016/j.mathsocsci.2016.08.003

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JF - Mathematical Social Sciences

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